Abstract
Investigations of gene (G)-environment (E) interactions have led to limited findings to date, possibly due to weak effects of individual genetic variants. Polygenic risk scores (PRS), which capture the genetic susceptibility associated with a set of variants, can be a powerful tool for detecting global patterns of interaction. Motivated by the case-only method for evaluating interactions with a single variant, we propose a case-only method for the analysis of interactions with a PRS in case-control studies. Assuming the PRS and E are independent, we show how a linear regression of the PRS on E in a sample of cases can be used to efficiently estimate the interaction parameter. Furthermore, if an estimate of the mean of the PRS in the underlying population is available, the proposed method can estimate the PRS main effect. Extensions allow for PRS-E dependence due to associations between variants in the PRS and E. Simulation studies indicate the proposed method offers appreciable gains in efficiency over logistic regression and can recover much of the efficiency of a cohort study. We applied the proposed method to investigate interactions between a PRS and epidemiologic factors on breast cancer risk in the UK Biobank (United Kingdom, recruited 2006-2010).