RAREMETALWORKER METHOD - Revision history

Abought at 21:49, 16 March 2018

2018-03-16T21:49:25Z

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			[[Category:RAREMETALWORKER]]
	==Useful Links==		==Useful Links==

Shuang Feng: /* Useful Links */

2014-04-14T17:33:20Z

Useful Links

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	* The [[RAREMETALWORKER_SPECIAL_TOPICS \| '''RAREMETALWORKER special topics''']]		* The [[RAREMETALWORKER_SPECIAL_TOPICS \| '''RAREMETALWORKER special topics''']]
	* The [[Tutorial:_RAREMETAL \| '''RAREMETALWORKER quick start tutorial''']]		* The [[Tutorial:_RAREMETAL \| '''RAREMETALWORKER quick start tutorial''']]
			* The [[RAREMETAL_method \| '''RAREMETAL method''']]
	* The [[RAREMETAL_FAQ \| '''FAQ''']]		* The [[RAREMETAL_FAQ \| '''FAQ''']]

Shuang Feng at 17:32, 14 April 2014

2014-04-14T17:32:39Z

← Older revision		Revision as of 13:32, 14 April 2014
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			==Useful Links==

			Here are some useful links to key pages:
			* The [[RAREMETALWORKER \| '''RAREMETALWORKER documentation''']]
			* The [[RAREMETALWORKER_command_reference \| '''RAREMETALWORKER command reference''']]
			* The [[RAREMETALWORKER_SPECIAL_TOPICS \| '''RAREMETALWORKER special topics''']]
			* The [[Tutorial:_RAREMETAL \| '''RAREMETALWORKER quick start tutorial''']]
			* The [[RAREMETAL_FAQ \| '''FAQ''']]

	== Brief Introduction==		== Brief Introduction==

Shuang Feng: /* SINGLE VARIANT SCORE TEST */

2014-04-02T04:02:28Z

SINGLE VARIANT SCORE TEST

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	<math> \mathbf{y}=\mathbf{X}\boldsymbol{\beta_c}+\beta_i(\mathbf{G_i}-\bar{\mathbf{G_i}})+\mathbf{g}+\boldsymbol{\varepsilon} </math>.		<math> \mathbf{y}=\mathbf{X}\boldsymbol{\beta_c}+\beta_i(\mathbf{G_i}-\bar{\mathbf{G_i}})+\mathbf{g}+\boldsymbol{\varepsilon} </math>.

	Here, the quantitive trait for an individual is ~~decided by~~ covariate effects, additive genetic effect from the <math> i^{th} </math> variant and the polygenic background effects together with non-shared environmental effect.		Here, the quantitive trait for an individual is a sum of covariate effects, additive genetic effect from the <math> i^{th} </math> variant and the polygenic background effects together with non-shared environmental effect.

	In this model, <math>\beta_i</math> is to measure the additive genetic effect of the <math>i^{th}</math> variant. As usual, the score statistic for testing <math>H_0:\beta_i=0</math> is:		In this model, <math>\beta_i</math> is to measure the additive genetic effect of the <math>i^{th}</math> variant. As usual, the score statistic for testing <math>H_0:\beta_i=0</math> is:

Shuang Feng: /* SINGLE VARIANT SCORE TEST */

2014-04-01T17:58:13Z

SINGLE VARIANT SCORE TEST

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	<math> \mathbf{y}=\mathbf{X}\boldsymbol{\beta_c}+\beta_i(\mathbf{G_i}-\bar{\mathbf{G_i}})+\mathbf{g}+\boldsymbol{\varepsilon} </math>.		<math> \mathbf{y}=\mathbf{X}\boldsymbol{\beta_c}+\beta_i(\mathbf{G_i}-\bar{\mathbf{G_i}})+\mathbf{g}+\boldsymbol{\varepsilon} </math>.

	Here, ~~[explain~~ the ~~formula]~~.		Here, the quantitive trait for an individual is decided by covariate effects, additive genetic effect from the <math> i^{th} </math> variant and the polygenic background effects together with non-shared environmental effect.

	In this model, <math>\beta_i</math> is to measure the additive genetic effect of the <math>i^{th}</math> variant. As usual, the score statistic for testing <math>H_0:\beta_i=0</math> is:		In this model, <math>\beta_i</math> is to measure the additive genetic effect of the <math>i^{th}</math> variant. As usual, the score statistic for testing <math>H_0:\beta_i=0</math> is:

Shuang Feng: /* ANALYZING MARKERS ON CHROMOSOME X */

2014-04-01T17:53:32Z

ANALYZING MARKERS ON CHROMOSOME X

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	where <math>l</math> is the count of variants, <math>G_i</math> and <math>f_i</math> are the genotype vector and estimated allele frequency for the <math>i^{th}</math> variant, respectively. Each element in <math>G_i</math> encodes the minor allele count for one individual. Model parameters <math>\hat{\boldsymbol{\beta}}</math>, <math>\hat{\sigma_g^2}</math> and <math>\hat{\sigma_e^2}</math>, are estimated using maximum likelihood and the efficient algorithm described in [http://www.nature.com/nmeth/journal/v8/n10/full/nmeth.1681.html Lippert et. al]. For convenience, let the estimated covariance matrix of <math>\mathbf{y}</math> be <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{\sigma_e^2}\mathbf{I}</math>.		where <math>l</math> is the count of variants, <math>G_i</math> and <math>f_i</math> are the genotype vector and estimated allele frequency for the <math>i^{th}</math> variant, respectively. Each element in <math>G_i</math> encodes the minor allele count for one individual. Model parameters <math>\hat{\boldsymbol{\beta}}</math>, <math>\hat{\sigma_g^2}</math> and <math>\hat{\sigma_e^2}</math>, are estimated using maximum likelihood and the efficient algorithm described in [http://www.nature.com/nmeth/journal/v8/n10/full/nmeth.1681.html Lippert et. al]. For convenience, let the estimated covariance matrix of <math>\mathbf{y}</math> be <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{\sigma_e^2}\mathbf{I}</math>.

	==ANALYZING MARKERS ON CHROMOSOME X==		===ANALYZING MARKERS ON CHROMOSOME X===

	To analyze markers on chromosome X, we fit an extra variance components <math> {{\sigma_g}_X}^2 </math>, to model the variance explained by chromosome X. A kinship for chromosome X, <math> \boldsymbol{K_X} </math>, can be estimated either from a pedigree, or from genotypes of marker from chromosome X. Then the estimated covariance matrix can be written as <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{{\sigma_g}_X^2}\mathbf{K_X}+\hat{\sigma_e^2}\mathbf{I}</math>.		To analyze markers on chromosome X, we fit an extra variance components <math> {{\sigma_g}_X}^2 </math>, to model the variance explained by chromosome X. A kinship for chromosome X, <math> \boldsymbol{K_X} </math>, can be estimated either from a pedigree, or from genotypes of marker from chromosome X. Then the estimated covariance matrix can be written as <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{{\sigma_g}_X^2}\mathbf{K_X}+\hat{\sigma_e^2}\mathbf{I}</math>.

Shuang Feng: /* Chromosome X */

2014-04-01T17:53:24Z

Chromosome X

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	where <math>l</math> is the count of variants, <math>G_i</math> and <math>f_i</math> are the genotype vector and estimated allele frequency for the <math>i^{th}</math> variant, respectively. Each element in <math>G_i</math> encodes the minor allele count for one individual. Model parameters <math>\hat{\boldsymbol{\beta}}</math>, <math>\hat{\sigma_g^2}</math> and <math>\hat{\sigma_e^2}</math>, are estimated using maximum likelihood and the efficient algorithm described in [http://www.nature.com/nmeth/journal/v8/n10/full/nmeth.1681.html Lippert et. al]. For convenience, let the estimated covariance matrix of <math>\mathbf{y}</math> be <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{\sigma_e^2}\mathbf{I}</math>.		where <math>l</math> is the count of variants, <math>G_i</math> and <math>f_i</math> are the genotype vector and estimated allele frequency for the <math>i^{th}</math> variant, respectively. Each element in <math>G_i</math> encodes the minor allele count for one individual. Model parameters <math>\hat{\boldsymbol{\beta}}</math>, <math>\hat{\sigma_g^2}</math> and <math>\hat{\sigma_e^2}</math>, are estimated using maximum likelihood and the efficient algorithm described in [http://www.nature.com/nmeth/journal/v8/n10/full/nmeth.1681.html Lippert et. al]. For convenience, let the estimated covariance matrix of <math>\mathbf{y}</math> be <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{\sigma_e^2}\mathbf{I}</math>.

	==~~Chromosome~~ X==		==ANALYZING MARKERS ON CHROMOSOME X==

	To analyze markers on chromosome X, we fit an extra variance components <math> {{\sigma_g}_X}^2 </math>, to model the variance explained by chromosome X. A kinship for chromosome X, <math> \boldsymbol{K_X} </math>, can be estimated either from a pedigree, or from genotypes of marker from chromosome X. Then the estimated covariance matrix can be written as <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{{\sigma_g}_X^2}\mathbf{K_X}+\hat{\sigma_e^2}\mathbf{I}</math>.		To analyze markers on chromosome X, we fit an extra variance components <math> {{\sigma_g}_X}^2 </math>, to model the variance explained by chromosome X. A kinship for chromosome X, <math> \boldsymbol{K_X} </math>, can be estimated either from a pedigree, or from genotypes of marker from chromosome X. Then the estimated covariance matrix can be written as <math>\hat{\boldsymbol{\Omega}}=\hat{\sigma_g^2}\mathbf{K}+\hat{{\sigma_g}_X^2}\mathbf{K_X}+\hat{\sigma_e^2}\mathbf{I}</math>.

Shuang Feng: /* NOTATIONS */

2014-04-01T17:52:53Z

NOTATIONS

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	<math>\mathbf{K}</math> is the kinship matrix		<math>\mathbf{K}</math> is the kinship matrix

			<math>\mathbf{K_X}</math> is the kinship matrix of Chromosome X

	<math> \sigma_g^2 </math> is the genetic component		<math> \sigma_g^2 </math> is the genetic component

Shuang Feng: /* NOTATIONS */

2014-04-01T17:51:36Z

NOTATIONS

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	<math>\mathbf{y}</math> is the vector of observed quantitative trait		<math>\mathbf{y}</math> is the vector of observed quantitative trait

	~~<math> \hat{\boldsymbol{\Omega}} </math> is the estimated covariance matrix of <math>\mathbf{y}</math>~~

	~~<math>\mathbf{K}</math> is the kinship matrix~~

	<math>\mathbf{X}</math> is the design matrix		<math>\mathbf{X}</math> is the design matrix
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	<math>\boldsymbol{\varepsilon}</math> is the non-shared environmental effects		<math>\boldsymbol{\varepsilon}</math> is the non-shared environmental effects

			<math> \hat{\boldsymbol{\Omega}} </math> is the estimated covariance matrix of <math>\mathbf{y}</math>

			<math>\mathbf{K}</math> is the kinship matrix

	<math> \sigma_g^2 </math> is the genetic component		<math> \sigma_g^2 </math> is the genetic component

Shuang Feng: /* NOTATIONS */

2014-04-01T17:51:09Z

NOTATIONS

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	<math> {{\sigma_g}_X}^2 </math> is the genetic component for markers on chromosome X		<math> {{\sigma_g}_X}^2 </math> is the genetic component for markers on chromosome X

	<math>\sigma_e^2 </math> is the non-shared ~~environmental~~ component.		<math>\sigma_e^2 </math> is the non-shared-environment component.

	===SINGLE VARIANT SCORE TEST===		===SINGLE VARIANT SCORE TEST===

← Older revision		Revision as of 13:33, 14 April 2014
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	* The [[RAREMETALWORKER_SPECIAL_TOPICS \| '''RAREMETALWORKER special topics''']]		* The [[RAREMETALWORKER_SPECIAL_TOPICS \| '''RAREMETALWORKER special topics''']]
	* The [[Tutorial:_RAREMETAL \| '''RAREMETALWORKER quick start tutorial''']]		* The [[Tutorial:_RAREMETAL \| '''RAREMETALWORKER quick start tutorial''']]
			* The [[RAREMETAL_method \| '''RAREMETAL method''']]
	* The [[RAREMETAL_FAQ \| '''FAQ''']]		* The [[RAREMETAL_FAQ \| '''FAQ''']]