Rational inferences about departures from Hardy-Weinberg equilibrium

Previous studies have explored the use of departure from Hardy-Weinberg equilibrium (DHW) for fine mapping Mendelian disorders and for general fine mapping. Other studies have used Hardy-Weinberg tests for genotyping quality control. To enable investigators to make rational decisions about whether DHW is due to genotyping error or to underlying biology, we developed an analytic framework and software to determine the parameter values for which DHW might be expected for common diseases. We show analytically that, for a general disease model, the difference between population and Hardy-Weinberg-expected genotypic frequencies (Delta) at the susceptibility locus is a function of the susceptibility-allele frequency (q), heterozygote relative risk (beta), and homozygote relative risk (gamma). For unaffected control samples, Delta is a function of risk in nonsusceptible homozygotes (alpha), the population prevalence of disease (K-p), q, beta, and gamma. We used these analytic functions to calculate D and the number of cases or controls needed to detect DHW for a range of genetic models consistent with common diseases (1.1 <= gamma <= 10 and 0.005 <= K-p <= 0.2). Results suggest that significant DHW can be expected in relatively small samples of patients over a range of genetic models. We also propose a goodness-of-fit test to aid investigators in determining whether a DHW observed in the context of a case-control study is consistent with a genetic disease model. We illustrate how the analytic framework and software can be used to help investigators interpret DHW in the context of association studies of common diseases.