Bias in parameter estimates due to omitting gene–environment interaction terms in case‐control studies

Genetic studies are continuing to generate volumes and variety of data that can be used to examine the genetic effects. Often the effect of a genetic variant varies by nongenetic measures, what is traditionally defined as gene–environment interaction (G×E). If the G×E term is neglected, estimates of the main effects can be substantially biased. We derive a general and convenient approximation to the magnitude of bias in the estimates due to omitting the G×E term. We show that the approximation is reasonably accurate in finite samples. We then apply the approximation in a study of Alzheimer's disease.