Genome Analysis Wiki - User contributions [en]

File:Raremetal.4.13.6.tar.gz

2017-07-13T17:03:04Z

Saichen:

RAREMETAL DOWNLOAD & BUILD

2017-07-13T17:01:39Z

Saichen: /* OLD VERSIONS */

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from GitHub:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you prefer to build from scratch, then do the following in your Raremetal directory:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.

==OLD VERSIONS==
(All linux versions)
* [[Media:Raremetal.4.13.8.tar.gz ‎|'''v4.13.8''']]
* [[Media:Raremetal.4.13.6.tar.gz ‎|'''v4.13.6''']]

RAREMETAL DOWNLOAD & BUILD

2017-07-13T17:01:31Z

Saichen: /* OLD VERSIONS */

File:Raremetal.4.13.8.tar.gz

2017-07-13T17:00:58Z

Saichen:

RAREMETAL DOWNLOAD & BUILD

2017-07-13T17:00:36Z

Saichen: /* OLD VERSIONS */

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from GitHub:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you prefer to build from scratch, then do the following in your Raremetal directory:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.

==OLD VERSIONS==
(All linux versions)
* [[Media:raremetal.4.13.8.tar.gz ‎|'''v4.13.8''']]
* [[Media:raremetal.4.13.6.tar.gz ‎|'''v4.13.6''']]

RAREMETAL DOWNLOAD & BUILD

2017-07-13T15:12:43Z

Saichen:

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from GitHub:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you prefer to build from scratch, then do the following in your Raremetal directory:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.

==OLD VERSIONS==
(All linux versions)
* [[Media:raremetal.4.13.8.tgz ‎|'''v4.13.8''']]
* [[Media:raremetal.4.13.6.tgz ‎|'''v4.13.6''']]

RAREMETAL Change Log

2016-11-27T20:11:02Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** '''Optimized method for unbalanced studies with no family structure (--useExact)'''. Check [[RAREMETAL METHOD]]
** bug fixes in conditional analysis
** fixed headers
** more methods in burden test

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Command Reference

2016-11-27T20:09:20Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact optimized method for unbalanced studies with unrelated samples,
described [[RAREMETAL METHOD#SINGLE_VARIANT_SCORE_TEST]].
--burden burden test with equal weight
--MAB burden test with MAF as weight
--MB burden test with sqrt(maf(1-maf)) as weight
--BBeta beta distribution as weight
--VT variant threshold test
--SKAT standard SKAT test
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL Command Reference

2016-11-27T20:08:56Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact optimized method for unbalanced studies with unrelated samples,
described [[RAREMETAL METHOD#SINGLE_VARIANT_SCORE_TEST]].
--burden burden test with equal weight
--MAB burden test with MAF as weight
--MB burden test with sqrt(maf(1-maf)) as weight
--VT variant threshold test
--SKAT standard SKAT test
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL Command Reference

2016-11-27T20:08:44Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact optimized method for unbalanced studies with unrelated samples,
described [[RAREMETAL METHOD#SINGLE_VARIANT_SCORE_TEST]].
--burden burden test with equal weight
--MAB burden test with MAF as weight
--MB burden test with sqrt(maf(1-maf)) as weight
--VT variant threshold test
--SKAT standard SKAT test
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL Command Reference

2016-11-27T20:08:32Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact optimized method for unbalanced studies with unrelated samples,
described [[RAREMETAL METHOD#SINGLE_VARIANT_SCORE_TEST]].
--burden burden test with equal weight
--MAB burden test with MAF as weight
--MB burden test with sqrt(maf(1-maf)) as weight
--VT variant threshold test
--SKAT standard SKAT test
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL Command Reference

2016-11-27T20:08:10Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact optimized method for unbalanced studies with unrelated samples, described [[RAREMETAL METHOD#SINGLE_VARIANT_SCORE_TEST]].
--burden burden test with equal weight
--MAB burden test with MAF as weight
--MB burden test with sqrt(maf(1-maf)) as weight
--VT variant threshold test
--SKAT standard SKAT test
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL METHOD

2016-11-27T19:42:52Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}^{2}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}^{2}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:42:34Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}^{2}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:41:33Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}^{2}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}_{2}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:41:20Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}^{2}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:40:44Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:39:50Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

<math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}})}/(n-1)</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:37:28Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:35:45Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}-4n_{k}(ff'-f_{k}f_{k}'))}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:35:06Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

<math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{V_{ii,k}-4n_{k}(ff'-f_{k}f_{k}')}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:32:35Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

'''Optimized method for unbalanced studies (--useExact)''':

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:32:09Z

Saichen: /* NOTATIONS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}</math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}</math> variant in <math>k^{th}</math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}</math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:31:26Z

Saichen: /* NOTATIONS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of <math>i^{th}<\math> variant

<math> f_{i,k} </math> is the allele frequency of <math>i^{th}<\math> variant in <math>k^{th}<\math> study

<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th}<\math> study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:30:36Z

Saichen: /* NOTATIONS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of i^{th} variant

<math> f_{i,k} </math> is the allele frequency of i^{th} variant in k^{th} study

<math> {\delta_{k}} </math> is the deviation of trait value of k^{th} study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:30:18Z

Saichen: /* NOTATIONS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of i^{th} variant

<math> f_{i,k} </math> is the allele frequency of i^{th} variant in k^{th} study

<math> {\delta_{k}} </math> is the deviation of trait value of study k

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:29:16Z

Saichen: /* NOTATIONS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> f_{i} </math> is the pooled allele frequency of i^{th} variant

<math> f_{i,k} </math> is the allele frequency of i^{th} variant in k^{th} study

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:27:17Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f_{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:27:04Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f_{i}-f{i,k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:26:20Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f-f{k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:25:59Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\boldsymbol{\Omega_{k}}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f-f{k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:23:50Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}-\sum_{k=1}^S{2n_{k}{\delta_{k}(f-f{k})}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:23:01Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}-\sum_{k=1}^S{2n_{k}{\delta_{k}}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:22:18Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}-sum_{k=1}^S{2n_{k}{\delta}}</math>

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL METHOD

2016-11-27T19:14:11Z

Saichen: /* SINGLE VARIANT META ANALYSIS */

==INTRODUCTION==
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.ncbi.nlm.nih.gov/pubmed/24336170 '''Liu et. al''']. The main formulae are tabulated in the following:

==KEY FORMULAE==

===NOTATIONS===
We denote the following to describe our methods:

<math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study

<math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study

<math>U_{i,k} </math> and <math>V_{ij,k} </math> are described in detail in [[RAREMETALWORKER_method#SINGLE_VARIANT_SCORE_TEST|'''RAREMETALWORKER method''']].

<math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study.

<math>\mathbf{V_k}</math> is the variance-covariance matrix of score statistics of rare variants in a gene from the <math> k^{th} </math> study, or <math>\mathbf{V_k} = cov(\mathbf{U_k})</math>

<math> S </math> is the number of studies

<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.

===SINGLE VARIANT META ANALYSIS===
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generated by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as

<math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}}</math>

and its variance

<math>V_{meta_i}=\sum_{k=1}^S{V_{ii,k}}</math>.

Then the score test statistics for the <math>i^{th}</math> variant <math>T_{meta_i}</math> asymptotically follows standard normal distribution

<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.

Optimized method for unbalanced studies:

===BURDEN META ANALYSIS===

Burden test has been shown to be powerful detecting a group of rare variants that are unidirectional in effects. Once single variant meta analysis statistics are constructed, burden test score statistic for a gene can be easily reconstructed as

<math>T_{meta_{burden}}=\mathbf{w^TU_{meta}}\bigg/\sqrt{\mathbf{w^TV_{meta}w}} \sim\mathbf{N}(0,1)</math>,

where <math>\mathbf{U_{meta}} = (U_{meta_1},U_{meta_2},...,U_{meta_m})^T</math> and <math> \mathbf{V_{meta}}=cov(\mathbf{U_{meta}})</math>, representing a vector of single variant meta-analysis scores of <math>m</math> variants in a gene and the covariance matrix of the scores across <math>m</math> variants.

===VT META ANALYSIS===

Including variants that are not associated to phenotype can hurt power. Variable threshold test is designed to choose the optimal allele frequency threshold amongst rare variants in a gene, to gain power. The test statistic is defined as the maximum burden score statistic calculated using every possible frequency threshold

<math>T_{meta_{VT}}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)})</math>,

where <math>T_{b\left(f_i\right)}</math> is the burden test statistic under allele frequency threshold <math>f_i</math>, and can be constructed from single variant meta-analysis statistics using

<math>T_{b\left(f_j\right)}=\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{U_{meta}}\bigg/\sqrt{\boldsymbol{\phi}_{f_j}^\mathbf{T}\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}} </math>,

where <math>j</math> represents any allele frequency in a group of rare variants, <math>\boldsymbol{\phi}_{f_j}</math> is a vector of 0 and 1, indicating if a variant is included in the analysis using frequency threshold <math>f_i</math>.

As described by [http://www.ncbi.nlm.nih.gov/pubmed/21885029 '''Lin et. al'''], the p-value of this test can be calculated analytically using the fact that the burden test statistics together follow a multivariate normal distribution with mean <math>\mathbf{0}</math> and covariance <math>\boldsymbol{\Omega}</math>, written as

<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Omega}\right) </math>,

where <math>\boldsymbol{\Omega_{ij}}=\frac{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}{\sqrt{\boldsymbol{\phi}_{f_i}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_i}}\sqrt{\boldsymbol{\phi}_{f_j}^T\mathbf{V_{meta}}\boldsymbol{\phi}_{f_j}}}</math>.

===SKAT META ANALYSIS===

SKAT is most powerful when detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

RAREMETAL Documentation

2016-11-27T19:13:29Z

Saichen: /* Useful Wiki Pages */

== Useful Wiki Pages ==

* Git hub page: https://github.com/traxexx/Raremetal

* The [[RAREMETAL_Change_Log | Change Log]]

* The [[RAREMETAL_DOWNLOAD_%26_BUILD | DOWNLOAD page]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Quick Start Tutorial]]
* The [[RAREMETAL METHOD]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETAL Command Reference]]

* The [[RAREMETALWORKER|RAREMETALWORKER documentation]]

The [http://genome.sph.umich.edu/wiki/Rvtests '''rvtests'''] tool for rare-variant association analysis can also generate output compatible with RAREMETAL.

== Brief Description ==

'''RAREMETAL''' is a computationally efficient tool for meta-analysis of rare variants using sequencing or genotyping array data. It takes summary statistics and LD matrices generated by [[Rare-Metal-Worker|'''RAREMETALWORKER''']] or [http://genome.sph.umich.edu/wiki/Rvtests '''rvtests'''], handles related and unrelated individuals, and supports both single variant and burden meta-analysis. It generates high quality plots by default and has options that allow users to build reports at different levels.

'''RAREMETAL''' is developed by Shuang Feng, Dajiang Liu and Gonçalo Abecasis. A R-package written by Dajiang Liu using the same methodology is [[RareMetals|'''available''']].

== Key Features ==
'''RAREMETAL''' has the following features:
* Performs gene-based or region-based meta analysis using Burden tests with the following methods: CMC_counts, Madsen-Browning, SKAT, and Variable Threshold.
* Performs single variant metal-analysis by default.
* Allows customized groups of variants to be tested.
* Allows conditional analysis to be performed in both gene-level meta-analysis and single variants meta-analysis.
* Generate QQ plots and manhattan plots by default.

== Approach ==

The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. Our method has been published in [http://www.nature.com/ng/journal/v46/n2/abs/ng.2852.html '''Liu et. al'''] in Nature Genetics. Please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_method '''method'''] for details.

== Download and Installation ==
* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/bin/

=== Where to Download ===

We have tested compilation using our source code on several platforms including Linux, MAC OS X, and Windows.

For source code and executables together with instructions of building from source, please go to [[RAREMETAL_DOWNLOAD_%26_BUILD |'''DOWNLOAD source and executables''']].

For questions about compilation, please go to [[RAREMETAL_FAQ | '''FAQ''']].

== Basic Usage Instructions ==

'''RAREMETAL''' is a command line tool. It is typically run from a Linux or Unix prompt by invoking the command <code>raremetal</code>. In the following are descriptions of basic usage for meta analysis. A detailed [[Tutorial:_RareMETAL|'''TUTORIAL''']] with toy data are also available.

==== Prepare Input Files====
'''RAREMETAL''' requires the following basic input files: summary statistics and covariance matrices of score statistics generated by '''RAREMETALWORKER''' or [http://genome.sph.umich.edu/wiki/Rvtests '''rvtests'''], a file with list of studies to be included and a group file if gene-level meta-analysis is expected.

=====Summary Statistics=====
Files containing summary statistics and LD matrices generated by '''RAREMETALWORKER''' should be compressed and [http://samtools.sourceforge.net/tabix.shtml '''tabix'''] indexed using the following commands (Note in RAREMETALWORKER, if --zip is specified, these .gz and .tbi files will be automatically generated):

bgzip study1.singlevar.score.txt
tabix -s 1 -b 2 -e 2 -c "#" study1.singlevar.score.txt.gz
bgzip study1.singlevar.cov.txt
tabix -s 1 -b 2 -e 2 -c "#" study1.singlevar.cov.txt.gz

Files containing summary statistics and LD matrices generated by '''rvtests''' should be compressed and [http://samtools.sourceforge.net/tabix.shtml '''tabix'''] indexed using the following commands:

bgzip study1.MetaScore.assoc
tabix -s 1 -b 2 -e 2 -S 1 study1.MetaScore.assoc.gz
tabix -s 1 -b 2 -e 2 -S 1 study1.MetaCov.assoc.gz

=====List of Studies=====
* --summaryFiles option is crucial for '''RAREMETAL''' to work. Ignoring this option would lead to FATAL ERROR and '''RAREMETAL''' would stop.
* The file should contain the path and prefix of the studies you want to include.
* If there is one or more studies that you want to excluded from your list, but want to save some effort of generating a new file, you can put a "#" in front of the line of record. '''RAREMETAL''' would automatically exclude that study from meta analysis. An example list of summary file is in the following:

/net/fantasia/home/sfengsph/prj/raremetal/raremetal/bin/META/TwinsUK/TwinsUK.TG.singlevar.score.txt.gz
#/net/fantasia/home/sfengsph/prj/raremetal/raremetal/bin/META/HUNT/RareMetalWorker/HUNT_MI_case.TG.singlevar.score.txt.gz

* When gene-level analysis is requested, --covFiles option should be used to specify the covariance files. An example file is:

/net/fantasia/home/sfengsph/prj/raremetal/raremetal/bin/META/TwinsUK/TwinsUK.TG.singlevar.cov.txt.gz
#/net/fantasia/home/sfengsph/prj/raremetal/raremetal/bin/META/HUNT/RareMetalWorker/HUNT_MI_case.TG.singlevar.cov.txt.gz

* The above example study name file guides '''RAREMETAL''' to look for summary statistics from TwinsUK study only, because "HUNT" study is commented out. The following two files are needed for '''RAREMETAL''' to perform further analysis together with their tabix index file are needed.

* Please sepcify --dosage option if input files were generated from dosage instead of genotype.

=====Group Rare Variants=====

====== From a Group File ======
* Grouping methods are only necessary when doing gene-based or group-based burden tests in meta-analysis.
* If none of the grouping method is specified, then only single variant meta-analysis will be performed.
* With --groupFile option, you can specify particular set of variants to be grouped for burden tests.
* The group file must be a tab or space delimited file in the following format:
GROUP_ID MARKER1_ID MARKER2_ID MARKER3_ID ...
* MARKER_ID must be in the following format:
CHR:POS:REF:ALT
* An example group file is:
PLEKHN1 1:901922:G:A 1:901923:C:A 1:902088:G:A 1:902128:C:T 1:902133:C:G 1:902176:C:T 1:905669:C:G
HES4 1:934735:A:C 1:934770:G:A 1:934801:C:T 1:935085:G:A 1:935089:C:G
ISG15 1:949422:G:A 1:949491:G:A 1:949502:C:T 1:949608:G:A 1:949802:G:A 1:949832:G:A
AGRN 1:970687:C:T 1:976963:A:G 1:977028:G:T 1:977356:C:T 1:977396:G:A 1:978628:C:T 1:978645:G:A
C1orf159 1:1021285:G:T 1:1021302:T:C 1:1021315:A:C 1:1021386:G:A 1:1022534:C:T 1:1025751:C:T 1:1026913:C:T

====== From an Annotated VCF File ======
If --groupFile option is '''NOT''' specified, '''RAREMETAL''' will look for an annotated vcf file as blue print for variants to group. Users are also allowed to generate a vcf file based on the superset of variants from pooled samples, and annotate outside RAREMETAL. Then, annotated vcf file can be used as input for RAREMETAL for gene-level meta-analysis, or group files can be generated based on the annotated vcf file. Detailed description of these options are [[Rare-Metal#Group_Rare_Variants_from_Annotated_VCF|'''available''']]. There are also [[Rare-Metal#Example_Command_lines|'''examples''']] of this usage at the bottom of this page.

==== QC Options ====
* '''RAREMETAL''' allows filtering of variants from individual studies by their HWE pvalue and call rate, which are generated as part of the output from '''RAREMETALWORKER''' or [http://genome.sph.umich.edu/wiki/Rvtests '''rvtests'''].
* To filter by HWE p-values, --hwe option should be used. The default is 0.0, which means not filtering any of the variants.
* To filter by call rate, --callRate option can be specified. The default is 0.0, which allows no filtering utilized.

==== Association Options====
* Currently, CMC type burden test, Madsen-Browning burden test, Variable Threshold burden test and SKAT are provided in '''RAREMETAL''', by specifying --burden, --MB, --VT and --SKAT.
* --maf specifies the minor allele frequency cutoff when doing gene-based or group-based burden tests. Variants with maf '''above''' this threshold will be ignored. The default is maf<0.05.
* In '''a single study''' of sample size N, if a site is monomorphic or not reported in vcf/ped, it is considered that the sample size of this study is not large enough to sample the rare allele. Thus, this study contributes 2*N reference alleles and 0 alternative allele towards meta-analysis. To let such studies contribute no alleles towards pooled allele frequency, specify --altMAF.

==== Conditional Analysis====
* To decide whether a signal is caused by shadowing a significant common variant nearby, '''RAREMETAL''' also enables conditional analysis with a list of variants to be conditioned upon provided in a file as input for --condition option. An example input file should be space or tab delimited as in the following. When alleles do not match the ref and alt alleles from samples, the variant will be skipped from conditional analysis.

1:861349:C:T 1:905901:G:A 20:986998:G:C 22:3670691:A:G

== Additional Analysis Options ==

=== Generate a VCF File to Annotate Outside RAREMETAL ===
* --writeVCF allows user to write a VCF file including pooled single variants from all studies. Then users can use their favorite annotation tool to annotate the VCF file. After annotating the VCF file, users can use that file as input for '''RAREMETAL''' for further gene-based or region-based meta analysis.
* The output vcf file will be name as: yourPrefix.pooled.variants.vcf. An example output vcf file is in the following:
#CHROM POS ID REF ALT QUAL FILTER INFO
1 115658497 115658497 G A . . ALT_AF=0.380906;
2 74688884 74688884 G A . . ALT_AF=8.33611e-05;
3 121414217 121414217 C A . . ALT_AF=0.0747833;
===Annotation===
* RAREMETAL automatically recognizes the annotation format generated by [[TabAnno | '''ANNO''']] or [[EPACTS#Annotating_VCF_file_using_EPACTS | '''EPACTS''']].
* To annotate a the VCF generated in previous step, you can use the following command:
./anno --in your.in.vcf.gz --out your.out.vcf.gz

=== Group Rare Variants from Annotated VCF ===
* If --groupFile option is '''NOT''' specified, '''RAREMETAL''' will look for an annotated vcf file as blue print for variants to group.
* The annotated VCF file should be specified using --annotatedVcf option.
* --annotation should be used with --annotatedVcf together when specific category of functional variants are of interest to be grouped. For example, if grouping nonsynonymous and splicing variants are of interests, the following should be included in command line:
* (! only available after v4.13.8) when --annotation is not specified, raremetal groups all non-intergenic variants.

--annotatedVcf your.annotated.vcf --annotation nonsyn/splicing
Note: this allows you to group variants that are annotated starting with nonsyn or splicing (not case-sensitive).

* Special format for the annotated VCF file is required: all annotation information should be coded in INFO field in VCF file, starting with the key "ANNO=". An example annotated VCF file is in the following:

#CHROM POS ID REF ALT QUAL FILTER INFO
1 19208194 . G A 100 PASS
AC=3;'''ANNO='''nonsynonymous:ALDH4A1:NM_170726:exon8:c.C866T:p.P289L,ALDH4A1:NM_001161504:exon8:c.C686T:p.P229L,ALDH4A1:NM_003748:exon8:c.C866T:p.P289L,;
'''ANNO='''splicing:ALDH4A1
1 19208293 . G C 100 PASS AC=7;STUDIES=5;MAC=7;MAF=0.001;DESIGN=TBD_ASSAY;DSCORE=1.00;
'''ANNO='''nonsynonymous:ALDH4A1:NM_170726:exon8:c.C767G:p.P256R,ALDH4A1:NM_001161504:exon8:c.C587G:p.P196R,ALDH4A1:NM_003748:exon8:c.C767G:p.P256R,

* Notice that each variant is allowed to have more than one annotations; but each annotation should start with a new key "ANNO=" followed by annotation:genename:other transcript information.
* Generated group file will be named test.groupfile under your running directory.

===Options for Report Generation===
* --correctGC generates QQ plots and manhattan plots with pvalues corrected using genomic control.
* --prefix allows customized prefix for output files.
* --longOutput allows users to output not only burden test results but also the single variant results (allele frequencies, effect sizes, and p-values) for the variants being grouped together. Please refer to the output files section for detailed explanation and examples.
* --tabulateHits works with --hitsCutoff together to generate reports for genes that have p-value less than specified cutoff from burden tests or SKAT. The default cutoff of p-value for genes to be reported is 1.0e-06, which can be specified by --hitsCutoff option. For more explanations and examples, please go to [[Rare-Metal#TABULATED_HITS| Tabulated Hits]].

===Miscellaneous Options===
* --tabix allows rapid analysis when number of groups/genes of interests are small. Currently, when number of groups is less than 100, --tabix option is automatically turned on.

== Reports Generated by RAREMETAL ==
=== Single Variant Meta Analysis Output ===

==== TABLES ====

* Single variant meta analysis output has the following components: header, results and footnote.
* Header lines start with "##" shows summary of the meta analysis including method used, number of studies, and total sample size.
* Header line starts with "#" are column headers for results table.
* Footnote also starts with "#", where genomic controls from each study and the overall sample are reported.
* An example single variant meta analysis output is shown below:

##Method=SinglevarScore
##STUDY_NUM=2
##TotalSampleSize=14308
#CHROM POS REF ALT POOLED_ALT_AF EFFECT_SIZE DIRECTION_BY_STUDY PVALUE
1 115658497 G A 0.380906 0.00954332 ++ 0.45828
2 74688884 G A 8.33611e-05 -0.196387 -! 0.845372
3 121414217 C A 0.0747833 0.0216982 -+ 0.34453
6 137245814 G C 0.000803746 0.105693 ++ 0.601805
* A detailed explanation of each column is in the following:

CHROM: Chromosome Name
POS: Variant Position
REF: Reference Allele Label
ALT: Alternative Allele Label
POOLED_ALT_AF: Pooled Alternative Allele Frequency
EFFECT_SIZE: Alternative Allele Effect Size
DIRECTION_BY_STUDY: Effect size direction of alternative allele from each study.
The order of study is consistent with the order of studies listed in the input file for option --summaryFiles.
"?" means the variant is not observed or monomorphic from the study.
"!" means the variant observed from this study has different alleles from those in the first study.

==== PLOTS====

'''RAREMETAL''' generates QQ plots and manhattan plots from single variant meta-analysis by default. Three QQ plots are generated, one with all variants included, one of variants with maf<0.05 and one of variants with maf<0.01. All plots are saved in a pdf file named yourPrefix.meta.plots.pdf. Genomic controls are also reported in the title of plots. When --correctGC option is specified, GC corrected plots are also generated.
{| border="1" cellpadding="5" cellspacing="0" align="center"
|-
| align="center" width="100" | [[File:QQ.png]]
|-
| align="center" width="200" | [[File:Single_var_manhattan.png]]
|}

=== Gene-level Tests Meta-Analysis Output ===

==== LONG TABLES ====
When --longOutput is used, output includes both burden test results of genes and single variant results of the variants included in burden tests. Here is an example of output file from SKAT when --longOutput is specified.
##Method=Burden
##STUDY_NUM=2
##TotalSampleSize=14308
#GROUPNAME NUM_VAR VARs MAFs SINGLEVAR_EFFECTs SINGLEVAR_PVALUEs AVG_AF MIN_AF MAX_AF EFFECT_SIZE PVALUE
NOC2L 7 1:880502:C:T;1:881918:G:A;1:887799:C:T;1:888659:T:C;1:889238:G:A;1:891591:C:T;1:892380:G:A 0.000166722,0.0242172,0.0109203,0.0355845,0.0333729,0.00700233,0.00200067 -0.183575,-0.00228307,-0.0598337,0.0220595,0.0229464,-0.0302768,-0.0200417 0.790161,0.953446,0.515806,0.503548,0.499251,0.791773,0.926625 0.0161807 0.000166722 0.0355845 0.00667875 0.662531
KLHL17 2 1:897285:A:G;1:898869:C:T 0.0148408,0.00108369 -0.0502034,-0.0256403 0.528269,0.934606 0.00796222 0.00108369 0.0148408 -0.0484494 0.528878

==== SHORT TABLES ====
Otherwise, single variant results of variants included in burden tests will not be included in the output. Here is an example of output file from SKAT when --longOutput is not specified.

##Method=Burden
##STUDY_NUM=2
##TotalSampleSize=14308
#GROUPNAME NUM_VAR VARs AVG_AF MIN_AF MAX_AF EFFECT_SIZE PVALUE
NOC2L 7 1:880502:C:T;1:881918:G:A;1:887799:C:T;1:888659:T:C;1:889238:G:A;1:891591:C:T;1:892380:G:A 0.0161807 0.000166722 0.0355845 0.00667875 0.662531
KLHL17 2 1:897285:A:G;1:898869:C:T 0.00796222 0.00108369 0.0148408 -0.0484494 0.528878

==== TABULATED HITS ====
* When --tabulateHits is specified, top hits from Burden tests will be generated. Each method will have an individual tabulated file generated. The purpose of this tabulated file is to list burden test results of top hits together with single variant results from variants being grouped in burden tests. The difference between this file and the standard long-format output file from burden test is that each row of the file represents a single variant that is included in the gene for burden test. This format allows each sorting on users end.

* Tabulated top hits are saved in the file:
yourPrefix.meta.tophits.youMethod.tbl (example files names: TG.meta.tophits.burden.tbl, LDL.meta.tophits.SKAT.tbl)

* The following items are tabulated in the output:
GENE: Gene name.
METHOD: Burden test used.
GENE_PVALUE: P-value from gene-based burden tests.
MAF_CUTOFF: MAF cutoff used when doing gene-based tests.
ACTUAL_CUTOFF: Actual MAF cutoff used. (This will be different from MAF_CUTOFF only for Variable Threshold method.
Otherwise, it will be the same as MAF_CUTOFF.)
VAR: Variant name in CHR:POS:REF:ALT format.
MAF: Single variant pooled MAF from all samples.
EFFSIZE: Effect size from single variant meta analysis.
PVALUE: Pvalue from single variant meta analysis.

* An example of tabulated hits from a standard burden test with maf<0.05 as criterion is shown in the following:

GENE METHOD GENE_PVALUE MAF_CUTOFF ACTUAL_CUTOFF VARS MAFS EFFSIZES PVALUES
PCSK9 BURDEN_0.050 7.54587e-11 0.05 0.05 1:55505647:G:T 0.0396631 -0.442192 2.10159e-46
PCSK9 BURDEN_0.050 7.54587e-11 0.05 0.05 1:55518371:G:A 0.0237138 0.0548733 0.430246
PCSK9 BURDEN_0.050 7.54587e-11 0.05 0.05 1:55529187:G:A 0.0433324 0.0946321 0.00129942
APOE BURDEN_0.050 2.83457e-72 0.05 0.05 19:45412079:C:T 0.0413056 -0.554561 2.83457e-72

* According to the example above, PCSK9 had a p-value of 7.54587e-11 from the gene-based burden test, where three variants from this gene were included. Another hit from this meta analysis is APOE, where only one variant was included in the burden test.

==== PLOTS ====
'''RAREMETAL''' generates QQ plots and manhattan plots from single variant and gene-level meta-analysis by default. Example QQ plots and manhattan plots are:
{| border="1" cellpadding="5" cellspacing="0" align="center"
|-
| align="center" width="200" | [[File:manhattan.png]]
|}

==== LOG ====

* A log file is automatically generated by '''RAREMETAL''' to save the parameters in effect. An example is in the following:

The following parameters are in effect:

List of Studies:
============================
--studyName [studyName.SardiNia]

Grouping Methods:
============================
--groupFile [genes.file]
--annotatedVcf []
--annotation []
--writeVcf [OFF]

QC Options:
============================
--hwe [0]
--callRate [0]

Association Methods:
============================
--burden [true]
--MB [false]
--SKAT [false]
--VT [false]
--condition [condition.file]

Other Options:
============================
--tabix [OFF]
--correctGC [ON]
--prefix [test]
--maf [0.05]
--longOutput [false]
--tabulateHits [false]
--hitsCutoff [1e-06]
--dosage [false]
--altMAF [false]

==Example Command lines==

* Here is an example command line to do single variant meta analysis only:
./raremetal --summaryFiles your.list.of.summary.files --prefix yourPrefix

* When you want to do all burden tests using a group file to specify which variants to group:
./raremetal --summaryFiles your.list.of.summary.files --covFiles your.list.of.cov.files --groupFile your.groupfile --burden --MB --SKAT --VT --maf 0.01 --prefix yourPrefix
(NOTE: this will generate single variant meta analysis result and the short format output for burden test results.)

* Here is how to do all SKAT meta analysis using a group file and request a long format output together with tabulated hits:
./raremetal --summaryFiles your.list.of.summary.files --covFiles your.list.of.cov.files --groupFile your.groupfile --SKAT --longOutput --tabulateHits --hitsCutoff 1.0e-07 --prefix yourPrefix

* Here is an example of adding QC filters to variants when doing meta analysis.
./raremetal --summaryFiles your.list.of.summary.files --covFiles your.list.of.cov.files --groupFile your.groupfile --SKAT --longOutput --tabulateHits --hitsCutoff 1.0e-07 --hwe 1e-06 --callRate 0.98 --prefix yourPrefix

* Here is how to do the same thing but reading grouping information from an annotated VCF file:
./raremetal --summaryFiles your.list.of.summary.files --covFiles your.list.of.cov.files --annotatedVcf your.annotated.vcf --annotation nonsyn/stop/splicing --SKAT --longOutput --tabulateHits --hitsCutoff 1.0e-07 --hwe 1e-06 --callRate 0.98 --prefix yourPrefix

* If you want to write a VCF file of pooled variants from all studies, annotate them using your favorite annotation program, and then come back to '''RAREMETAL''' with the annotate VCF file to do burden tests:
First, use the following command to write the VCF file:
./raremetal --summaryFiles your.list.of.summary.files --writeVcf --prefix yourPrefix
Second, annotate the VCF file using your favorite annotation program. (Annotated VCF file has to follow the format described here: [[Rare-Metal#Group_Rare_Variants_from_Annotated_VCF|annotated VCF format]])
Third, use the following command to do meta analysis:
./raremetal --summaryFiles your.list.of.summary.files --covFiles your.list.of.cov.files --annotatedVcf your.annotated.vcf --annotation nonsyn/splicing/stop --burden --MB --SKAT --VT --maf 0.01 --prefix yourPrefix

==Other Useful Info==

* Summary specs can be found [[Summary Files Specification for RAREMETAL]]

==TUTORIAL==
* For a comprehensive tutorial of RAREMETALWORKER and RAREMETAL using example data sets, please go to the following:

[http://genome.sph.umich.edu/wiki/Tutorial:_RareMETAL '''RAREMETAL Tutorial''']

* For a brief tutorial of rvtests, please go to:

[http://genome.sph.umich.edu/wiki/Rvtests '''rvtests''']

==CONTACT==

Please email Sai Chen (saichen at umich dot edu) for questions.

Also check [[Raremetal Incoming updates | '''Known issues and incoming update in next version''']] to see if your problem has been reported before

RAREMETAL Command Reference

2016-11-27T19:12:20Z

Saichen: /* Association Methods for Meta-analysis */

==Useful Pages==
* The [[RAREMETAL| Home Page]]

* The [[RAREMETAL_Documentation|RAREMETAL Documentation]]

* The [[Tutorial:_RAREMETAL|RAREMETAL Tutorial]]

* The [[RAREMETAL FAQ]]

* The [[RAREMETALWORKER | RAREMETALWORKER documentation]]

==Command References==
=== Overview of Options ===
Options:
List of Studies : --studyName []
Grouping Methods : --groupFile [], --annotatedVcf [], --annotation [],
--writeVcf
QC Options : --hwe [1.0e-05], --callRate [0.95]
Association Methods : --burden, --MB, --SKAT, --VT, --condition []
Other Options : --labelHits, --correctGC, --prefix [],
--mapFile [../src/refFlat_hg19.txt], --maf [0.05],
--longOutput, --tabulateHits, --hitsCutoff [1.0e-06]
--altMAF

=== Describing Studies ===
--studyName [your.list.of.studies.file]

Additional details on this option is [[Rare-Metal#List_of_Studies_2|available]].

=== Methods to Group Rare Variants ===

--groupFile [your.groups.file]
--annotatedVcf [your.annotated.vcf]
--annotation [nonsyn/stop/splice]
--writeVcf [ON|OFF]

Additional details on [[Rare-Metal#Grouping_from_a_Group_File|groupFile]], [[Rare-Metal#Grouping_from_an_Annotated_VCF_File|annotatedVcf, annotation]] and [[Rare-Metal#Generate_a_VCF_File_to_Annotate_Outside_of_Rare_Metal|writeVcf]] options are available.

=== QC Options ===
--hwe [hwe.pvalue.cutoff] (default = 1e-05)
--callRate [variant.call.rate.cutoff] (default = 0.95)

Additional details on these options are [[Rare-Metal#QC_Options|available]].

=== Association Methods for Meta-analysis ===
--useExact [ON|OFF]
--burden [ON|OFF]
--MB [ON|OFF]
--VT [ON|OFF]
--SKAT [ON|OFF]
--condition [your.list.of variants.to.be.conditioned.upon]
Additional details for these options are [[Rare-Metal#Association_Methods|available]].

=== Other Options for Performance and Amenities ===
--labelHits [ON|OFF]
--correctGC [ON|OFF]
--prefix [your.prefix]
--maf [your.maf.threshold.for.gene-level.tests] (default = 0.05)
--longOutput [ON|OFF]
--tabulateHits [ON|OFF]
--hitsCutoff [your.cutoff.for.hits] (default = 1e-06)
--altMAF [if specified, studies that do not contain the variant will be excluded.]

Additional details for these options are [[Rare-Metal#Other_Options|available]].

RAREMETAL Change Log

2016-11-27T19:09:17Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** '''Optimized method for unbalanced studies with no family structure (--useExact)'''
** bug fixes in conditional analysis
** fixed headers
** more methods in burden test

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Change Log

2016-11-27T19:09:12Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** '''Optimized method for unbalanced studies with no family structure (--useExact)'''
** bug fixes in conditional analysis
** fixed headers
** more method in burden test

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Change Log

2016-11-27T19:08:50Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** '''Optimized method for unbalanced studies with no family structure (--useExact)'''
** bug fixes in conditional analysis
** fixed headers

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Change Log

2016-11-27T19:08:16Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** '''Optimized method for unbalanced studies with no family structure (--useExact)'''
** bug fixes in conditional analysis
** fix some headers

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Change Log

2016-11-27T19:07:52Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** Released an exact method for unbalanced studies with no family structure (--useExact)
** bug fixes in conditional analysis
** fix some headers

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

Raremetal Incoming updates

2016-11-27T19:07:39Z

Saichen: /* Incoming update */

==Main Wiki Page==

* [[RAREMETAL_Change_Log | RAREMETAL Change log]]

==Incoming update==
* Add an option to store group file from vcf
* Take snpeff as annotation input
* When no conditional variant is available, warning is generated but not written to log file.
* enable reading from .gz annotated vcf
* add SKAT-O
* solve the numeric issue of lambda = 0 in SKAT
* In conditional analysis, when cov matrix between the test variant and its conditioned variants is not invertible, MathSVD still tries to invert that matrix and that leads to weird conditional p values.
* '''Optimization for binary traits'''
* '''Memory optimization for gene-based test in large panel'''

Raremetal Incoming updates

2016-11-27T19:07:19Z

Saichen: /* Finished in test version */

==Main Wiki Page==

* [[RAREMETAL_Change_Log | RAREMETAL Change log]]

==Incoming update==
* Add an option to store group file from vcf
* Take snpeff as annotation input
* When no conditional variant is available, warning is generated but not written to log file.
* SKAT conditional analysis misses the last 3 column names. They should be cond_statistics, cond_pvalue_davis, cond_p_value_liu.
* enable reading from .gz annotated vcf
* add SKAT-O
* solve the numeric issue of lambda = 0 in SKAT
* In conditional analysis, when cov matrix between the test variant and its conditioned variants is not invertible, MathSVD still tries to invert that matrix and that leads to weird conditional p values.
* '''Optimization for binary traits'''
* '''Memory optimization for gene-based test in large panel'''

RAREMETAL Change Log

2016-11-27T19:07:05Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released (11/27/2016)
** Released an exact method for unbalanced studies with no family structure (--useExact)
** bug fixes in conditional analysis

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL Change Log

2016-11-27T19:05:39Z

Saichen: /* Change Log */

==Main Wiki Page==
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]

== Change Log ==

* [[Raremetal Incoming updates | Known issues and incoming update in next version]]

* Version 4.14.0 released ()11/27/2016)

* Version 4.13.9 released (07/14/2016)
** The source code has been optimized to prepare for incoming new meta-analysis method in next version.
** Reduced running time when reading >10,000s individuals from vcf
** '''Fixed seg fault in raremetalworker for calculating SNP HWE p value when sample size > 40k'''
** A seg fault: sometimes you only have very few variants but raremetal still tries to calculate GC.

* Version 4.13.8 released (12/13/2015)
** when grouping from vcf, raremetal now obtains information only from "ANNOFULL" field.
** fixed seg fault in matching --annotation option to vcf annotation.
** with empty --annotation option, raremetal now groups all non-intergenic variants.
** '''fixed a bug in conditional analysis when there are multiple variants to condition on'''.
** fixed a seg fault in calculating genomic control.
** add --variantList option in RaremetalWorker to only calculate variance-covariance matrix between certain markers.
** add --range option in both Raremetal and RaremetalWorker to focus on given region only.

* Version 4.13.7 released. (9/18/2015).
** group file generated from annotated vcf is now stored in "test.groupfile" under current running directory.
** use -O0 option in compiling. In very rare situations, gcc optimization will affect the results.
** tabix RMW output with --zip toggled.
** In SKAT meta analysis, skip the variant when all its lambdas are zero.
** bug fixes in conditional analysis: in very rare situation raremetal takes rvtest input as raremetalworker input.
** add --altMAF option to exclude studies in which a variant is not present.

* Version 4.13.6 released. (3/8/2015)
** add a new option --mergedVCFID to recognize VCF files with sample IDs in "FAMID_PID" format
** add a new option --flagDosage to flag the field name to label dosage in VCF file.

* Version 4.13.5 released. (9/29/2014)
** a bug fixed in conditional analysis in raremetal.

* Version 4.13.4 released.
** store beta estimates of intercept and fixed effects in rarmetalworker *.singlevar.score.txt header.

* Version 4.13.3 released.
** read rvtest output format correctly in raremetal.

* Version 4.13.2.
** fixed sqrt_V output when analyzing unrelated individuals without kinship and --inverseNormal is not used and trait variance is not one.

* Version 4.13.1.
** fixed a bug affecting output format when ped/dat files are used together with --dominant --recessive options.

* version 4.13
** fixed bug when using --vcX option.
** Fixed bug estimating kinshipX with female samples.
** Added --kinOnly option for generating kinship only without association analysis.
** Added --geneMap option to allow user input for gene-mapping file.

* version 4.12.1
** fixed command interface display issue in raremetalworker.

* version 4.12
** improved make file for better compilation.

* version 4.11
** fixed a bug for inverse-normalizing traits (a bug only in version 4.9 and later).

* version 4.10
** fixed a bug when analyzing multiple traits is requested in raremetalworker (bug only in version 4.9 and later, and doesn't affect results).

===Version 4.8 and before===
* Released version 0.4.7 (4/24/2014).
** optimized code to increase analysis efficiency and reduce memory use.
** added --separateX option to provide another choice of analyzing chromosome X.
** added --kinxFile option to allow kinship X matrix file with different prefix from the autosomal kinship.
** merged raremetal and raremetalworker in one package following version number of raremetalworker.
** completed testing compiling on various platforms.
* Released version 0.4.6 binary. Fixed a bug in recessive and dominant results. (4/1/2014)
* Released version 0.4.5. Fixed a bug when generating plots for recessive results. (3/18/2014)
* Released version 0.4.4. (3/17/2014)
** bug fixed when alleles are flipped in group file.
** fixed hwe=0.0 issue for monomorphic sites.
* Released version 0.4.3. Fixed a few typo in messages. Added --noeof option for VCF files that does not have a BGZF EOF marker.
* Released version 0.4.2. (3/10/2014)
** fixed a bug that could possibly cause compiling error in some Linux system. male heterozygous
** male genotypes on chromosome X are considered missing.
** bug fixed for SKAT when there are two variants in a group
** bug fixed in Makefile for easy compiling.
* Released version 0.4.1. Fixed a bug handling variants in nonPAR region on chromosome X when all samples are male.
* Released version 0.4.0.
** added phone home function. Saved Recessive and dominant results in separate files.
** a few bugs fixed to properly handling missing genotypes.
** Major change in command options.
** allow user to specify list of summary statistics files and covariance files separately using --summaryFiles and --covFiles options.
* Released version 0.3.7. Added dominant and recessive models as options. The default model is additive. (1/7/2014)
* Released version 0.3.6 and fixed a minor bug that caused by code upgrades from version 0.3.5. (12/4/2013)
* Fixed a few bugs handling chromosome X. Generated warning messages when male genotypes are coded wrong in VCF file. (11/25/2013)
* Version 0.3.1 released to fix a bug when one of the alleles coded as missing.
* Version 0.2.9 released after fixing a bug in SKAT and writing PDF when all variants are monomorphic. (10/7/2013)
* Fixed the bug which causes crash when writing PDF when all variants are monomorphic. (10/6/2013)
* Added support for analyzing dosages from VCF in version 2.9. (8/27/2013)
* Version 0.1.2 released after fixing a few bugs, adding conditional analysis and automatic graphing to the tool. (8/5/2013)
* Fixed bug in handling chromosome X. Added sanity checking steps before analysis. Added graphic support by generating QQ and manhattan plots automatically. Upgraded tool to version 2.8. (till 8/12/2013)
* Updated code to report allele frequencies calculated only from selected samples. (3/3/2013)
* Optimized code to speed up the process of calculating empirical kinship. (3/3/2013)
* Fixed a bug when handling chromosome X. Added sex labels option. (3/2/2013)
* Version 0.0.1 released. (2/24/2013)
* Version 0.0.1 released to U of M CSG group. (2/13/2013)
* Fixed a bug when there is missing genotype from VCF file. (2/2013)
* Fixed a bug when reading vcf file with ref or alt allele is missing. (2/5/2013)
* Changed executable name into bin/raremetalworker. Version 0.0.7 released. (12/10/2012)
* Updated output format for monomorphic sites. (12/7/2012)
* Version 0.0.6 released. (12/6/2012)
* Bug fixed for empirical kinship calculation when genotypes are read from VCF file. Version 0.0.5 released. (12/6/2012)
* Version 0.0.4 released. (12/5/2012)
* More messages coded into log file. (12/4/2012)
* Updated output format. Version 0.0.3 released. (12/3/2012)
* Bugs fixed to solve compiling errors on some machines (Thank you Mary Kate!). Version 0.0.2 released. (11/30/2012)
* Added HWE pvalue and call rate in summary statistics output. (11/27/2012)
* Forced sample IDs to be matched when reading in kinship from a file. Perform a sanity check before reading in kinship file. If a sample of interest is not included in kinship file, then fatal error will occur. (11/19/2012)
* Enabled writing log file by defalut. (11/18/2012)
* Uploaded to public wiki. (11/16/2012)
* Modified Rare-Metal-Worker to let it output LD matrix by a sliding window. (11/14/2012)
* Version 0.0.1 was released on 11/13/2012.

RAREMETAL DOWNLOAD & BUILD

2016-11-27T19:05:06Z

Saichen: /* How to Compile */

RAREMETAL DOWNLOAD & BUILD

2016-11-27T19:04:24Z

Saichen: /* Where to Download */

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from GitHub:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you choose to build from the source files, you could start from decompress the package using the following command:
prompt> tar xvf Raremetal_linux.tgz
prompt> cd Raremetal

* If you prefer to build from scratch, then do the following:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.

RAREMETAL DOWNLOAD & BUILD

2016-11-27T19:00:13Z

Saichen: /* GIT HUB */

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from GitHub:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you choose to build from the source files, you could start from decompress the package using the following command:
prompt> tar xvf Raremetal_linux.tgz
prompt> cd Raremetal

* If you prefer to build from scratch, then do the following:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.

RAREMETAL DOWNLOAD & BUILD

2016-11-27T18:59:53Z

Saichen: /* GIT HUB */

== Useful Wiki Pages ==

* The [[RAREMETALWORKER | '''RAREMETALWORKER documentation''']]
* The [[RAREMETAL_Documentation | '''RAREMETAL documentation''']]
* The [[RAREMETAL FAQ | '''FAQ''']]
* The [[RAREMETAL_Change_Log | '''Change Log''']]

== Where to Download ==

From version 4.13.6, RAREMETALWORKER and RAREMETAL are distributed within the same package.

* University of Michigan CSG users can go to the following:
/net/wonderland/home/saichen/Raremetal/

===GIT HUB===

Please clone or download from Raremetal git hub page:

https://github.com/traxexx/Raremetal

Since v4.13.6, MAC and WINDOWS version are no longer updated. Please download old versions from here:

* [[Media:MAC_raremetal.4.13.6.tgz ‎|'''for MAC OS X''']]

* [[Media:CYGWIN64_raremetal.4.13.6.tgz ‎|'''for Windows/CygWin64''']]

* [[Media:MINGW_raremetal.4.13.6.tgz ‎|'''for Windows/MinGW''']]

===SCRIPTS===

====Calculating Odds Ratio from RAREMETALWORKER output====
*If you want to estimate '''Odds Ratios''' of variants analyzed by RAREMETALWORKER, the script [[Media:CalculateOddsRatio.tgz|'''calculateOddsRatio.pl''']] can help you augment RAREMETALWORKER output with estimated odds ratio to the last column.
*The script can also be found in the RAREMETAL package 4.13.6 and later, under directory '''raremetal/script/calculateOddsRatio.pl'''.

== How to Compile ==

* gfortran is necessary to build RAREMETAL. If your system does not have it yet, please go to [http://gcc.gnu.org/wiki/GFortranBinaries '''GNU gfortran'''] for download.

* If you choose to build from the source files, you could start from decompress the package using the following command:
prompt> tar xvf Raremetal_linux.tgz
prompt> cd Raremetal

* If you prefer to build from scratch, then do the following:
prompt> make clean
prompt> make
#This builds RAREMETAL and RAREMETALWORKER under bin/ directory.

* If you prefer to build individual tool:
prompt> cd Raremetal/raremetalworker/
prompt> make
#This will build RAREMETALWORKER under raremetal/bin/ directory.

prompt> cd Raremetal/raremetal/
prompt> make
#This will build RAREMETAL under raremetal/bin/ directory.

* If your compiler is adaptable to openmp (parallel computing), then use the following to build RAREMETALWORKER that allows parallel computing. For more about openmp, please refer to [http://openmp.org/wp/openmp-compilers/ openMP].
prompt> cd raremetalworker/src
prompt> make openmp
#This will build RAREMETALWORKER under raremetal/bin/ directory.

* If you prefer to use the binary file downloaded above, then no compiling is needed, but it is not guaranteed to work due to system and library requirements.

==FAQ==

For compiling questions, please go to [http://genome.sph.umich.edu/wiki/RAREMETAL_FAQ ''' FAQ'''] for more information.