A Shrinkage Method for Testing the Hardy–Weinberg Equilibrium in Case‐Control Studies

Testing for the Hardy–Weinberg equilibrium (HWE) is often used as an initial step for checking the quality of genotyping. When testing the HWE for case‐control data, the impact of a potential genetic association between the marker and the disease must be controlled for otherwise the results may be biased. Li and Li [2008] proposed a likelihood ratio test (LRT) that accounts for this potential genetic association and it is more powerful than the commonly used control‐only χ² test. However, the LRT is not efficient when the marker is independent of the disease, and also requires numerical optimization to calculate the test statistic. In this article, we propose a novel shrinkage test for assessing the HWE. The proposed shrinkage test yields higher statistical power than the LRT when the marker is independent of or weakly associated with the disease, and converges to the LRT when the marker is strongly associated with the disease. In addition, the proposed shrinkage test has a closed form and can be easily used to test the HWE for large datasets that result from genome‐wide association studies. We compare the performance of the shrinkage test with existing methods using simulation studies, and apply the shrinkage test to a genome‐wide association dataset for Alzheimer's disease.