A re-formulation of generalized linear mixed models to fit family data in genetic association studies.

Tao Wang,Kwang Woo Ahn,Peng He,Xujing Wang,Purushottam Laud,Soumitra Ghosh

doi:10.3389/fgene.2015.00120

Abstract

The generalized linear mixed model (GLMM) is a useful tool for modeling genetic correlation among family data in genetic association studies. However, when dealing with families of varied sizes and diverse genetic relatedness, the GLMM has a special correlation structure which often makes it difficult to be specified using standard statistical software. In this study, we propose a Cholesky decomposition based re-formulation of the GLMM so that the re-formulated GLMM can be specified conveniently via “proc nlmixed” and “proc glimmix” in SAS, or OpenBUGS via R package BRugs. Performances of these procedures in fitting the re-formulated GLMM are examined through simulation studies. We also apply this re-formulated GLMM to analyze a real data set from Type 1 Diabetes Genetics Consortium (T1DGC).

Highlights

Generalized linear mixed model (GLMM) provides a rich class of statistical models to model correlated data with responses from the exponential family of distributions including Gaussian, Binomial, Poisson, etc
We propose a Cholesky decomposition based reformulation of the generalized linear mixed model (GLMM) to fit family data with varied sizes and diverse genetic relatedness
It should be pointed out that applying separate Cholesky decompositions on each family does not provide computational or storage benefits comparing with the regular Cholesky decomposition on the whole covariance matrix of the random genetic effects because the non-diagonal blocks in the sparse matrix decomposition are not saved

Summary

Introduction

Generalized linear mixed model (GLMM) provides a rich class of statistical models to model correlated data with responses from the exponential family of distributions including Gaussian, Binomial, Poisson, etc. (see McCulloch and Searle, 2001). A re-formulation of GLMM to fit family data the GLMM by using SAS (Feng et al, 2009; Wang et al, 2011) It appears that these studies have only considered the cases where all the families had the same genetic correlation structure. For the special type of GLMM that models family data with varied family sizes or diverse genetic relatedness, we propose a Cholesky decomposition based re-formulation of the GLMM so that the re-formulated GLMM can be specified conveniently when using some standard statistical software packages. We provide detailed codes on fitting this re-formulated GLMM by using either “proc nlmixed” or “proc glimmix” in SAS, and OpenBUGS with R (via R package BRugs) The performances of these procedures on fitting the re-formulated GLMM are examined through some simulation studies. We apply this re-formulated GLMM to a real data set from Type 1 Diabetes Genetics Consortium (T1DGC)

Methods

In Fitting the GLMM

Simulation Study

Analysis of T1DGC data for Type I Diabetes

Findings

Discussion