Simple methods for assessing haplotype-environment interactions in case-only and case-control studies

For investigating haplotype-environment interactions in case-control studies, one can implement statistical methods based either on a retrospective likelihood (modeling the probability of haplotype and environment conditional on disease status) or a prospective likelihood (modeling the probability of disease status conditional on haplotype and environment). Retrospective approaches are generally more powerful than prospective approaches, but require an explicit model of the joint distribution of haplotype and environmental factors in the sample with the latter being particularly unattractive to specify. To resolve this issue, we propose a number of simple retrospective procedures for haplotype-environment interaction analysis that do not require explicit modeling of environmental covariates in the sample. We first consider a cases-only procedure, followed by a simple likelihood for case-control data that is proportional to the full-retrospective likelihood. Finally, we consider a retrospective procedure for inference on haplotype-environment interaction effects in matched or finely-stratified case-control studies. Our methods are based on the assumptions that haplotypes and environmental covariates are independent in the target population and that disease is rare. We illustrate our approaches using case-control data from the Finland-United States Investigation of Non-Insulin Dependent Diabetes Mellitus (FUSION) genetic study and simulated data.