A doubly robust test for gene-environment interaction in family-based studies of affected offspring

We develop a locally efficient test for (multiplicative) gene-environment interaction in family studies that collect genotypic information and environmental exposures for affected offspring along with genotypic information for their parents or relatives. The proposed test does not require modeling the effects of environmental exposures and is doubly robust in the sense of being valid if either a model for the main genetic effect holds or a model for the expected environmental exposure (given the offspring affection status and parental mating types) but not necessarily both. It extends the FBAT-I to allow for missing parental mating types and families of arbitrary size. Simulation studies and the analysis of an Alzheimer's disease study confirm the adequate performance of the proposed test.