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

Case-control genome-wide association (CC-GWAS) studies might provide valuable clues to the underlying pathophysiologic mechanisms of complex diseases, such as neurodegenerative disease, 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 in a biomarker evaluation that might not be feasible on 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 frequencies of the disease states of interest within the clinically diagnosed set of cases. These frequencies often vary by the genetic and/or non-genetic variables. We derive a simple approximation that relates the genetic effect estimates obtained in a logistic regression model with the clinical diagnosis as an outcome variable to the estimates in the relationship to the true disease state of interest. We performed simulation studies to assess accuracy of the approximation that we’ve derived. We next applied the derived approximation to the analysis of the genetic basis of innate immune system of Alzheimer’s disease.