Two-step hypothesis testing to detect gene-environment interactions in a genome-wide scan with a survival endpoint

Abstract

Defined by their genetic profile, individuals may exhibit differential clinical outcomes due to an environmental exposure. Identifying subgroups based on specific exposure-modifying genes can lead to targeted interventions and focused studies. Genome-wide interaction scans (GWIS) can be performed to identify such genes, but these scans typically suffer from low power due to the large multiple testing burden. We provide a novel framework for powerful two-step hypothesis tests for GWIS with a time-to-event endpoint under the Cox proportional hazards model. In the Cox regression setting, we develop an approach that prioritizes genes for Step-2 $G\times E$ testing based on a carefully constructed Step-1 screening procedure. Simulation results demonstrate this two-step approach can lead to substantially higher power for identifying gene-environment ( $G\times E$ ) interactions compared to the standard GWIS while preserving the family wise error rate over a range of scenarios. In a taxane-anthracycline chemotherapy study for breast cancer patients, the two-step approach identifies several gene expression by treatment interactions that would not be detected using the standard GWIS.

Keywords: Cox proportional hazards model; censoring; personalized medicine; survival analysis.

FIGURE 1

Kaplan-Meier curves for G × E combinations on a simulated data set of N = 10,000. Data were generated using an exponential model with binary G and E values under the model: $h(t\mid G,E)=0.01\ast \exp ({\gamma }_{G}G+{\gamma }_{E}E+{\gamma }_{G\times E}(G\times E)$. Independent censoring times were generated using an exponential model with rate 0.005. The exposure (E) is assumed to have a null main effect (HR_E = 1) but affects survival through its interaction (G×E) with G. Panel 1a: Synergistic interaction effect (HR_G×E = 0.5). Panel 1b: Antagonistic interaction effect (HR_G×E = 1.5).

FIGURE 2

Power comparison between the standard GWIS approach and the cG|G×E two-step GWIS across different values of HR_G×E = exp(γ_G×E). Panel A) γ = (0,0,γ_G×E); Panel B) γ = (0,log(0.6), γ_G×E); Panel C) γ = (log(1.2),log(0.6), γ_G×E); Panel D) γ = (log(0.8),log(0.6), γ_G×E). See Section 3.2 for details of the simulation setup (Standard GWIS - Solid Red Line; cG|G × E with weighted screening - Dashed Green Line; mG|G × E with weighted screening - Dashed Blue Line).

FIGURE 3

Manhattan Plot of G × E p-values (on the -log10 scale) from the taxane-anthracycline chemotherapy study in Section 4 using subset testing. Loci marked by a black dot or triangle represent G × E p-values that passed the subset-adjusted significance threshold (red dotted line). As a comparison, the standard GWIS significance threshold is also included (blue dotted line) with the black dot indicating a significant finding.

FIGURE 4

Manhattan Plot of G × E p-values (on the -log10 scale) from the taxane-anthracycline chemotherapy study in Section 4 using weighted Bonferroni testing. G × E p-values for each loci are arranged left to right in ascending order of their respective conditional p-values. Loci marked by a black dot or triangle represent G×E p-values that passed the subset-adjusted significance threshold (red dotted line). As a comparison, the standard GWIS significance threshold is also included (blue dotted line) with the black dot indicating a significant finding.

FIGURE 5

Kaplan-Meier curves comparing AKAP9-treatment effects on distant relapse-free survival.AKAP9 gene expression levels were divided into tertiles; A) Low AKAP9 levels ≤ −0.516); B) Medium AKAP9 levels (−0.516,0.268); C) High AKAP9 levels ≥ 0.268. P-values are calculated using an unweighted log-rank test.