Cauchy combination methods for the detection of gene-environment interactions for rare variants related to quantitative phenotypes.

The characterization of gene-environment interactions (GEIs) can provide detailed insights into the biological mechanisms underlying complex diseases. Despite recent interest in GEIs for rare variants, published GEI tests are underpowered for an extremely small proportion of causal rare variants in a gene or a region. By extending the aggregated Cauchy association test (ACAT), we propose three GEI tests to address this issue: a Cauchy combination GEI test with fixed main effects (CCGEI-F), a Cauchy combination GEI test with random main effects (CCGEI-R), and an omnibus Cauchy combination GEI test (CCGEI-O). ACAT was applied to combine p values of single-variant GEI analyses to obtain CCGEI-F and CCGEI-R and p values of multiple GEI tests were combined in CCGEI-O. Through numerical simulations, for small numbers of causal variants, CCGEI-F, CCGEI-R and CCGEI-O provided approximately 5% higher power than the existing GEI tests INT-FIX and INT-RAN; however, they had slightly higher power than the existing GEI test TOW-GE. For large numbers of causal variants, although CCGEI-F and CCGEI-R exhibited comparable or slightly lower power values than the competing tests, the results were still satisfactory. Among all simulation conditions evaluated, CCGEI-O provided significantly higher power than that of competing GEI tests. We further applied our GEI tests in genome-wide analyses of systolic blood pressure or diastolic blood pressure to detect gene-body mass index (BMI) interactions, using whole-exome sequencing data from UK Biobank. At a suggestive significance level of 1.0 × 10, KCNC4, GAR1, FAM120AOS and NT5C3B showed interactions with BMI by our GEI tests.