Test for interactions between a genetic marker set and environment in generalized linear models

We consider in this paper testing for interactions between a genetic marker set and an environmental variable. A common practice in studying gene-environment (GE) interactions is to analyze one single-nucleotide polymorphism (SNP) at a time. It is of significant interest to analyze SNPs in a biologically defined set simultaneously, e. g. gene or pathway. In this paper, we first show that if the main effects of multiple SNPs in a set are associated with a disease/trait, the classical single SNP-GE interaction analysis can be biased. We derive the asymptotic bias and study the conditions under which the classical single SNP-GE interaction analysis is unbiased. We further show that, the simple minimum p-value-based SNP-set GE analysis, can be biased and have an inflated Type 1 error rate. To overcome these difficulties, we propose a computationally efficient and powerful gene-environment set association test (GESAT) in generalized linear models. Our method tests for SNP-set by environment interactions using a variance component test, and estimates the main SNP effects under the null hypothesis using ridge regression. We evaluate the performance of GESAT using simulation studies, and apply GESAT to data from the Harvard lung cancer genetic study to investigate GE interactions between the SNPs in the 15q24-25.1 region and smoking on lung cancer risk.