A Simple Approximation to Bias in Gene–Environment Interaction Estimates When a Case Might Not Be the Case

Case–control genetic association studies are often used to examine the role of the genetic basis in complex diseases, such as cancer and neurodegenerative diseases. The role of the genetic basis might vary by nongenetic (environmental) measures, what is traditionally defined as gene–environment interactions (G×E). A commonly overlooked complication is that the set of clinically diagnosed cases might be contaminated by a subset with a nuisance pathologic state that presents with the same symptoms as the pathologic state of interest. The genetic basis of the pathologic state of interest might differ from that of the nuisance pathologic state. Often, frequencies of the pathologically defined states within the clinically diagnosed set of cases vary by the environment. We derive a simple and general approximation to bias in G×E parameter estimates when the presence of the nuisance pathologic state is ignored. We then perform extensive simulation studies to show that ignoring the presence of the nuisance pathologic state can result in substantial bias in G×E estimates and that the approximation we derived is reasonably accurate in finite samples. We demonstrate the applicability of the proposed approximation in a study of Alzheimer’s disease.