A Robust Test for Additive Gene-Environment Interaction Under the Trend Effect of Genotype Using an Empirical Bayes-Type Shrinkage Estimator

Evaluating gene by environment (G × E) interaction under an additive risk model (i.e., additive interaction) has gained wider attention. Recently, statistical tests have been proposed for detecting additive interaction, utilizing an assumption on gene-environment (G-E) independence to boost power, that do not rely on restrictive genetic models such as dominant or recessive models. However, a major limitation of these methods is a sharp increase in type I error when this assumption is violated. Our goal was to develop a robust test for additive G × E interaction under the trend effect of genotype, applying an empirical Bayes-type shrinkage estimator of the relative excess risk due to interaction. The proposed method uses a set of constraints to impose the trend effect of genotype and builds an estimator that data-adaptively shrinks an estimator of relative excess risk due to interaction obtained under a general model for G-E dependence using a retrospective likelihood framework. Numerical study under varying levels of departures from G-E independence shows that the proposed method is robust against the violation of the independence assumption while providing an adequate balance between bias and efficiency compared with existing methods. We applied the proposed method to the genetic data of Alzheimer disease and lung cancer.