# Difference between revisions of "RAREMETAL METHOD"

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===SKAT META ANALYSIS=== | ===SKAT META ANALYSIS=== | ||

− | <math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math> | + | SKAT has been powerful 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 |

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+ | <math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>. | ||

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+ | As shown in Wu et. al, the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as | ||

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## Revision as of 22:12, 8 April 2014

## Contents

## 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. The main formulae are tabulated in the following:

## KEY FORMULAE

### NOTATIONS

We denote the following to describe our methods:

is the score statistic for the variant from the study

is the covariance of the score statistics between the and the variant from the study

and are described in detail in **RAREMETALWORKER method**.

is the vector of score statistics of rare variants in a gene from the study.

is the variance-covariance matrix of score statistics of rare variants in a gene from the study, or

is the number of studies

is the vector of weights for rare variants in a gene.

### SINGLE VARIANT META ANALYSIS

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

and its variance

Then the score test statistics for the variant asymptotically follows standard normal distribution

### BURDEN META ANALYSIS

Once single variant meta analysis statistics are constructed, burden test score statistic can be easily reconstructed as

.

### VT META ANALYSIS

### SKAT META ANALYSIS

SKAT has been powerful 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

.

As shown in Wu et. al, the null distribution of the statistic follows a mixture chi-sqaured distribution described as

Test | Statistics | Null Distribution | Notation |
---|---|---|---|

Single Variant | |||

un-weighted Burden | |||

Weighted Burden | |||

VT | |||

SKAT |