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. 2021 Jan 4;190(1):129-141.
doi: 10.1093/aje/kwaa132.

A Likelihood Ratio Test for Gene-Environment Interaction Based on the Trend Effect of Genotype Under an Additive Risk Model Using the Gene-Environment Independence Assumption

Matthieu de Rochemonteix, Valerio Napolioni, Nilotpal Sanyal, Michaël E Belloy, Neil E Caporaso, Maria T Landi, Michael D Greicius, Nilanjan Chatterjee, Summer S Han

A Likelihood Ratio Test for Gene-Environment Interaction Based on the Trend Effect of Genotype Under an Additive Risk Model Using the Gene-Environment Independence Assumption

Matthieu de Rochemonteix et al. Am J Epidemiol. .

Abstract

Several statistical methods have been proposed for testing gene-environment (G-E) interactions under additive risk models using data from genome-wide association studies. However, these approaches have strong assumptions from underlying genetic models, such as dominant or recessive effects that are known to be less robust when the true genetic model is unknown. We aimed to develop a robust trend test employing a likelihood ratio test for detecting G-E interaction under an additive risk model, while incorporating the G-E independence assumption to increase power. We used a constrained likelihood to impose 2 sets of constraints for: 1) the linear trend effect of genotype and 2) the additive joint effects of gene and environment. To incorporate the G-E independence assumption, a retrospective likelihood was used versus a standard prospective likelihood. Numerical investigation suggests that the proposed tests are more powerful than tests assuming dominant, recessive, or general models under various parameter settings and under both likelihoods. Incorporation of the independence assumption enhances efficiency by 2.5-fold. We applied the proposed methods to examine the gene-smoking interaction for lung cancer and gene-apolipoprotein E $\varepsilon$4 interaction for Alzheimer disease, which identified 2 interactions between apolipoprotein E $\varepsilon$4 and loci membrane-spanning 4-domains subfamily A (MS4A) and bridging integrator 1 (BIN1) genes at genome-wide significance that were replicated using independent data.

Keywords: Alzheimer disease; GWAS; additive risk model; case-control design; gene-environment independence; gene-environment interaction; gene-smoking interaction; gene–APOE ɛ4 interaction.

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Figures

Figure 1
Figure 1
The results for power simulation of additive interaction tests based on a prospective likelihood for data generated under trend model and marginal odds ratio (MOR)(E) = 2.5 (A), dominant model and MOR(E) = 2.5 (B), general model and MOR(E) = 2.5 (C), trend model and MOR(E) = 3 (D), dominant model and MOR(E) = 3 (E), general model and MOR(E) = 3 (F). Significance level of formula image = 1 × 10−7 was used. 1,000 replicated data sets were simulated for 5,000 cases and 5,000 controls. For each set of simulation, we applied the following 4 additive interaction tests based on a prospective likelihood: the likelihood ratio test (LRT) under the trend effect of genotype (prospective LRT, LRT-P-trend), a general model (LRT-P-general), a dominant model (LRT-P-dominant), and a recessive model (LRT-P-recessive). RERI, relative excess risk due to interaction.
Figure 2
Figure 2
Comparison of the power of the trend effect–based additive interaction tests for the retrospective likelihood ratio test (LRT-R) versus prospective likelihood ratio test (LRT-P) for data generated with marginal odds ratio (E) (MOR(E)) = 2.5 (A) and MOR(E) = 3 (D). The noncentrality parameter (NCP) for each LRT, for MOR(E) = 2.5 (B) and MOR(E) = 3 (E), was estimated to compare the performances of the tests regardless of significance levels. The relative efficiency of LRT-R with regard to LRT-P, for MOR(E) = 2.5 (C) and MOR(E) = 3 (F), was estimated by taking the ratio of the NCP of LRT-R to the NCP of LRT-P. RERI, relative excess risk due to interaction.
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