## 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 vector of score statistics of rare variants in a gene 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 |