An Efficient Test for Gene-Environment Interaction in Generalized Linear Mixed Models with Family Data.

Mauricio Mazo Lopera,Brandon Coombes,Mariza De Andrade

doi:10.3390/ijerph14101134

Abstract

Gene-environment (GE) interaction has important implications in the etiology of complex diseases that are caused by a combination of genetic factors and environment variables. Several authors have developed GE analysis in the context of independent subjects or longitudinal data using a gene-set. In this paper, we propose to analyze GE interaction for discrete and continuous phenotypes in family studies by incorporating the relatedness among the relatives for each family into a generalized linear mixed model (GLMM) and by using a gene-based variance component test. In addition, we deal with collinearity problems arising from linkage disequilibrium among single nucleotide polymorphisms (SNPs) by considering their coefficients as random effects under the null model estimation. We show that the best linear unbiased predictor (BLUP) of such random effects in the GLMM is equivalent to the ridge regression estimator. This equivalence provides a simple method to estimate the ridge penalty parameter in comparison to other computationally-demanding estimation approaches based on cross-validation schemes. We evaluated the proposed test using simulation studies and applied it to real data from the Baependi Heart Study consisting of 76 families. Using our approach, we identified an interaction between BMI and the Peroxisome Proliferator Activated Receptor Gamma (PPARG) gene associated with diabetes.

Highlights

Linear mixed models (LMM) have been used to find associations between continuous phenotypes and genetic variants, genes, and gene-environment (GE) interactions in unrelated and related subjects in genome-wide association (GWA) analysis
Generalized linear mixed models (GLMM) proposed by Breslow and Clayton [1] is an ideal statistical approach to detect such an interaction with non-continuous phenotypes, because it can treat the familiar effect on the phenotype as a random effect
We propose a GLMM GE interaction framework for discrete and continuous phenotypes that treats the coefficients of genetic markers as random effects

Summary

Introduction

Linear mixed models (LMM) have been used to find associations between continuous phenotypes and genetic variants, genes, and gene-environment (GE) interactions in unrelated and related subjects in genome-wide association (GWA) analysis. The analysis can be performed within the generalized linear model framework, for related subjects as in the case of family data, one has to include the kinship matrix to take into account the correlation among the relatives for each family. Generalized linear mixed models (GLMM) proposed by Breslow and Clayton [1] is an ideal statistical approach to detect such an interaction with non-continuous phenotypes, because it can treat the familiar effect on the phenotype as a random effect. Gene-based GE interaction tests have previously been proposed for independent subjects [2,3,4].

Objectives

Methods

Findings

Conclusion