Testing departure from Hardy-Weinberg proportions.

The Hardy-Weinberg principle, one of the most important principles in population genetics, was originally developed for the study of allele frequency changes in a population over generations. It is now, however, widely used in studies of human diseases to detect inbreeding, populations stratification, and genotyping errors. For assessment of deviation from the Hardy-Weinberg proportions in data, the most popular approaches include the asymptotic Pearson's chi-square goodness-of-fit test and the exact test. The Pearson's chi-square goodness-of-fit test is simple and straightforward, but it is very sensitive to small sample size or rare allele frequency. The exact test of Hardy-Weinberg proportions is preferable in these situations. The exact test can be performed through complete enumeration of heterozygote genotypes or on the basis of the Markov chain Monte Carlo procedure. In this chapter, we describe the Hardy-Weinberg principle and the commonly used Hardy-Weinberg proportions tests and their applications, and we demonstrate how the chi-square test and exact test of Hardy-Weinberg proportions can be performed step-by-step using the popular software programs SAS, R, and PLINK, which have been widely used in genetic association studies, along with numerical examples. We also discuss recent approaches for testing Hardy-Weinberg proportions in case-control study designs that are better than traditional approaches for testing Hardy-Weinberg proportions in controls only. Finally, we note that deviation from the Hardy-Weinberg proportions in affected individuals can provide evidence for an association between genetic variants and diseases.