A Screening-Testing Approach for Detecting Gene-Environment Interactions Using Sequential Penalized and Unpenalized Multiple Logistic Regression

Abstract

Gene-environment (G×E) interactions are biologically important for a wide range of environmental exposures and clinical outcomes. Because of the large number of potential interactions in genomewide association data, the standard approach fits one model per G×E interaction with multiple hypothesis correction (MHC) used to control the type I error rate. Although sometimes effective, using one model per candidate G×E interaction test has two important limitations: low power due to MHC and omitted variable bias. To avoid the coefficient estimation bias associated with independent models, researchers have used penalized regression methods to jointly test all main effects and interactions in a single regression model. Although penalized regression supports joint analysis of all interactions, can be used with hierarchical constraints, and offers excellent predictive performance, it cannot assess the statistical significance of G×E interactions or compute meaningful estimates of effect size. To address the challenge of low power, researchers have separately explored screening-testing, or two-stage, methods in which the set of potential G×E interactions is first filtered and then tested for interactions with MHC only applied to the tests actually performed in the second stage. Although two-stage methods are statistically valid and effective at improving power, they still test multiple separate models and so are impacted by MHC and biased coefficient estimation. To remedy the challenges of both poor power and omitted variable bias encountered with traditional G×E interaction detection methods, we propose a novel approach that combines elements of screening-testing and hierarchical penalized regression. Specifically, our proposed method uses, in the first stage, an elastic net-penalized multiple logistic regression model to jointly estimate either the marginal association filter statistic or the gene-environment correlation filter statistic for all candidate genetic markers. In the second stage, a single multiple logistic regression model is used to jointly assess marginal terms and G×E interactions for all genetic markers that pass the first stage filter. A single likelihood-ratio test is used to determine whether any of the interactions are statistically significant. We demonstrate the efficacy of our method relative to alternative G×E detection methods on a bladder cancer data set.

Identifying significant gene‐environment interactions using a combination of screening testing and hierarchical false discovery rate control

“…For the bladder cancer example presented in Frost et al. (), (for the omnibus tests associated with the test stage models populated using the marginal association filter and gene‐environment correlation filter) and for the four SNP‐smoking interactions that had significant Wald tests at a level‐specific FDR of . Therefore, if hierarchical FDR been employed in this case with , approximate FDR control for the interaction‐specific Wald test results would have been achieved at a level of .…”

“…To support comparative evaluation of the extended SPUR method, the same alternative methods used in Frost et al. () were also employed to identify G× E interactions for the simulated and real data sets. For each evaluated data set, G× E interaction detection was performed using three benchmark methods: …”

“…Evaluation of SPUR in Frost et al. () was also based on only a single, small bladder cancer data set with measurements for approximately 1,500 single nucleotide polymorphisms (SNPs) after quality control (QC).…”

“…In Frost et al. (), α was set to 0.999 to provide estimation stability via a small L2 penalty (Friedman, Hastie, & Tibshirani, ) and λ was set so that the number of nonzero coefficients would give a ratio of observations to predictors in the test stage model of 7, per the recommendation of Vittinghoff and McCulloch () for multiple logistic regression.…”

Unsupervised gene set testing based on random matrix theory

“…Although widely applied for gene-environment interaction detection [20–23], p -value weighting can have a significant impact on gene set testing power given the significant growth in the size of common gene set collections, e.g., even the very selective Molecular Signatures Database (MSigDB) [8] now includes over 10,000 sets. For such large gene set collections, MHC can lower statistical power so substantially that it becomes impossible to identify true associations for many genomic data sets [24].…”