A note on exact tests of Hardy-Weinberg equilibrium

Abstract

Deviations from Hardy-Weinberg equilibrium (HWE) can indicate inbreeding, population stratification, and even problems in genotyping. In samples of affected individuals, these deviations can also provide evidence for association. Tests of HWE are commonly performed using a simple chi2 goodness-of-fit test. We show that this chi2 test can have inflated type I error rates, even in relatively large samples (e.g., samples of 1,000 individuals that include approximately 100 copies of the minor allele). On the basis of previous work, we describe exact tests of HWE together with efficient computational methods for their implementation. Our methods adequately control type I error in large and small samples and are computationally efficient. They have been implemented in freely available code that will be useful for quality assessment of genotype data and for the detection of genetic association or population stratification in very large data sets.

Figure 1

Type I error rates as a function of minor-allele counts for rare alleles, for samples of either 100 or 1,000 chromosomes and corresponding to a significance threshold of α=0.05, 0.01, or 0.001. Results are plotted as a function of the number of minor alleles in the sample for the exact P_HWE statistic (red) and for the asymptotic χ² test statistic (blue). A gray line denotes the nominal error rate. Note that the Y-axes in figures 1 and 2 differ.

Figure 2

Type I error rates as a function of minor-allele counts for common alleles, for samples of either 100 or 1,000 chromosomes and corresponding to a significance threshold of α=0.05, 0.01, or 0.001. Results are plotted as a function of the number of minor alleles in the sample for the exact P_HWE statistic (red) and for the asymptotic χ² test statistic (blue). A gray line denotes the nominal error rate. Note that the Y-axes in figures 1 and 2 differ.