A test of homogeneity of Hardy-Weinberg disequilibrium across strata

For genotype data being sampled from several strata with different allele frequencies, it is necessary to verify the assumption of homogeneity of Hardy - Weinberg disequilibrium across strata before testing Hardy - Weinberg law across strata. In practice, disequilibrium can be measured via fixation coefficients (ie, ratios of genotypic frequencies) or disequilibrium coefficients (ie, differences of genotypic frequencies). Test for homogeneity of Hardy - Weinberg disequilibrium using data from several populations has been derived according to fixation coefficients. In this article, using the likelihood score theory extended to nuisance parameters, we derive a homogeneity score test for comparing disequilibrium coefficients across several independent strata. Simulation results demonstrate that the homogeneity score test performs satisfactorily in the sense that its empirical size seldom exceeds the pre-chosen nominal level by more than 10% even for small sample sizes. Corresponding power and sample size formulae are provided as well. We illustrate our test with a real glyoxalase genotype data set.