# Changes

## RAREMETAL Documentation

, 20:11, 7 August 2013
no edit summary
* '''rareMETAL''' allows conditional analysis to be performed in both gene-level meta-analysis and single variants meta-analysis.
* '''rareMETAL''' generated QQ plots and manhattan plots by default.

== Useful Wiki Pages ==

There are a few pages in this Wiki that may be useful to rareMETAL users. Here are links to key pages:

* The [[Tutorial:_RareMETAL|rareMETAL Quick Start Tutorial]]

* The [[rareMETAL FAQ]]

* The [[rareMETAL Command Reference]]

== Brief Description ==

rareMETAL is a tool for meta-analysis rare variants from genotype arrays and sequencing. rareMETAL can combine summary statistics of individual studies generated by [[Rare-Metal-Worker|rareMetalWorker]]. It provides a convenient approach for both single variant and gene-level meta-analysis of rare variants from various studies, when joint-analysis of raw data from these studies are restricted.

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

|+'''Formulae for rareMETAL'''
! scope="col" width="120pt" | Test
! scope="col" width="50pt" | Statistics
! scope="col" width="225pt" | Null Distribution
|-
| Single Variant || $T=\sum_{i=1}^n {U_i}\bigg/\sqrt{\sum_{i=1}^n{V_i}}$ || $T\sim\mathbf{N}(0,1)$
|-
| un-weighted Burden || $T_b=\sum_{i=1}^n{\mathbf{U_i}}\Big/\sqrt{\sum_{i=1}^n{\mathbf{V_i}}}$ || $T_b\sim\mathbf{N}(0,1)$
|-
| Weighted Burden || $T_{wb}=\mathbf{w^T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\mathbf{w^T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\mathbf{w}}$ || $T_{wb}\sim\mathbf{N}(0,1)$
|-style="height: 100pt;"
| VT || $T_{VT}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}),\text{ where}$$T_{b\left(f_i\right)}=\boldsymbol{\nu}_{f_i}^\mathbf{T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\boldsymbol{\nu}_{f_i}^\mathbf{T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\nu}_{f_i}}\text{, where}$ $\boldsymbol{\nu}_{f_i}\text{ is a indicator vector.}$ ||$\left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)$$\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Phi}^\mathbf{T}\sum_{i=1}^n{\mathbf{V_i}}\boldsymbol{\Phi}\right)$
|-
| SKAT || $\mathbf{Q}=\left(\sum_{i=1}^n{\mathbf{U_i^T}}\right) \mathbf{W}\left(\sum_{i=1}^n{\mathbf{U_i}}\right)$ ||$\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2},\text{ where}$ $\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)\text{ are eigen values of}$$\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}\mathbf{W}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)^\frac{1}{2}$
|}

== Basic Usage Instructions ==

raeMETAL is a command line tool. It is typically run from a Linux or Unix prompt by invoking the command <code>raremetal</code>. An example is included at the bottom of this page.

A detailed [[Tutorial:_RareMETAL|'''TUTORIAL''']] with toy data are also available.

=== Input File Columns ===