Case-control versus case-only estimates of gene-environment interactions with common and misclassified clinical diagnosis

Genetic studies provide valuable information to assess if the effect of genetic variants varies by the nongenetic "environmental" variables, what is traditionally defined to be gene-environment interaction (GxE). A common complication is that multiple disease states present with the same set of symptoms, and hence share the clinical diagnosis. Because (a) disease states might have distinct genetic bases; and (b) frequencies of the disease states within the clinical diagnosis vary by the environmental variables, analyses of association with the clinical diagnosis as an outcome variable might result in false positive or false negative findings. We develop estimates for this setting to be able to assess GxE in a case-only study and we compare the case-control and case-only estimates. We report extensive simulation studies that evaluate empirical properties of the estimates and show the application to a study of Alzheimer's disease.