A simple approximation to bias in the genetic effect estimates when multiple disease states share a clinical diagnosis

Case-control genome-wide association studies (CC-GWAS) might provide valuable clues to the underlying pathophysiologic mechanisms of complex diseases, such as neurodegenerative disease and cancer. A commonly overlooked complication is that multiple distinct disease states might present with the same set of symptoms and hence share a clinical diagnosis. These disease states can only be distinguished based on a biomarker evaluation that might not be feasible in the whole set of cases in the large number of samples that are typically needed for CC-GWAS. Instead, the biomarkers are measured on a subset of cases. Or an external reliability study estimates the frequencies of the disease states of interest within the clinically diagnosed set of cases. These frequencies often vary by the genetic and/or nongenetic variables. We derive a simple approximation that relates the genetic effect estimates obtained in a traditional logistic regression model with the clinical diagnosis as the outcome variable to the genetic effect estimates in the relationship to the true disease state of interest. We performed simulation studies to assess the accuracy of the approximation that we have derived. We next applied the derived approximation to the analysis of the genetic basis of the innate immune system of Alzheimer's disease.