# Difference between revisions of "RAREMETAL METHOD"

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<math>V_{meta,i}=\sum_{k=1}^S{V_{ii,k}}</math> | <math>V_{meta,i}=\sum_{k=1}^S{V_{ii,k}}</math> | ||

− | Then the score test statistics for the <math>i^{th}</math> variant | + | 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> | <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> |

## Revision as of 20:29, 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

is the number of studies

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

### 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

### VT META ANALYSIS

### SKAT META ANALYSIS

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

Single Variant | |||

un-weighted Burden | |||

Weighted Burden | |||

VT | |||

SKAT |