Exact tests of Hardy-Weinberg equilibrium and homogeneity of disequilibrium across strata

Detecting departures from Hardy-Weinberg equilibrium (HWE) of marker-genotype frequencies is a crucial first step in almost all human genetic analyses. When a sample is stratified by multiple ethnic groups, it is important to allow the marker-allele frequencies to differ over the strata. In this situation, it is common to test for HWE by using an exact test within each stratum and then using the minimum P value as a global test. This approach does not account for multiple testing, and, because it does not combine information over strata, it does not have optimal power. Several approximate methods to combine information over strata have been proposed, but most of them sum over strata a measure of departure from HWE; if the departures are in different directions, then summing can diminish the overall evidence of departure from HWE. An exact stratified test is more appealing because it uses the probability of genotype configurations across the strata as evidence for global departures from HWE. We developed an exact stratified test for HWE for diallelic markers, such as single-nucleotide polymorphisms (SNPs), and an exact test for homogeneity of Hardy-Weinberg disequilibrium. By applying our methods to data from Perlegen and HapMap - a combined total of more than five million SNP genotypes, with three to four strata and strata sizes ranging from 23 to 60 subjects - we illustrate that the exact stratified test provides more-robust and more-powerful results than those obtained by either the minimum of exact test P values over strata or approximate stratified tests that sum measures of departure from HWE. Hence, our new methods should be useful for samples composed of multiple ethnic groups.