Detecting rare and common haplotype–environment interaction under uncertainty of gene–environment independence assumption

Summary Finding rare variants and gene–environment interactions (GXE) is critical in dissecting complex diseases. We consider the problem of detecting GXE where G is a rare haplotype and E is a nongenetic factor. Such methods typically assume G‐E independence, which may not hold in many applications. A pertinent example is lung cancer—there is evidence that variants on Chromosome 15q25.1 interact with smoking to affect the risk. However, these variants are associated with smoking behavior rendering the assumption of G‐E independence inappropriate. With the motivation of detecting GXE under G‐E dependence, we extend an existing approach, logistic Bayesian LASSO, which assumes G‐E independence (LBL‐GXE‐I) by modeling G‐E dependence through a multinomial logistic regression (referred to as LBL‐GXE‐D). Unlike LBL‐GXE‐I, LBL‐GXE‐D controls type I error rates in all situations; however, it has reduced power when G‐E independence holds. To control type I error without sacrificing power, we further propose a unified approach, LBL‐GXE, to incorporate uncertainty in the G‐E independence assumption by employing a reversible jump Markov chain Monte Carlo method. Our simulations show that LBL‐GXE has power similar to that of LBL‐GXE‐I when G‐E independence holds, yet has well‐controlled type I errors in all situations. To illustrate the utility of LBL‐GXE, we analyzed a lung cancer dataset and found several significant interactions in the 15q25.1 region, including one between a specific rare haplotype and smoking.