Gene-environment interactions in case-control studies with silent disease

Genome-wide association studies (GWAS) often measure gene-environment interactions (G x E). We consider the problem of accurately estimating a G x E in a case-control GWAS when a subset of the controls have silent, or undiagnosed, disease and the frequency of the silent disease varies by the environmental variable. We show that using case-control status without accounting for misdiagnosis can lead to biased estimates of the G x E. We further propose a pseudolikelihood approach to remove the bias and accurately estimate how the relationship between the genetic variant and the true disease status varies by the environmental variable. We demonstrate our method in extensive simulations and apply our method to a GWAS of prostate cancer.