Adapting the logical basis of tests for Hardy-Weinberg equilibrium to the real needs of association studies in human and medical genetics

The standard procedure to assess genetic equilibrium is a χ² test of goodness-of-fit. As is the case with any statistical procedure of that type, the null hypothesis is that the distribution underlying the data is in agreement with the model. Thus, a significant result indicates incompatibility of the observed data with the model, which is clearly at variance with the aim in the majority of applications: to exclude the existence of gross violations of the equilibrium condition. In current practice, we try to avoid this basic logical difficulty by increasing the significance bound to the P-value (e.g. from 5 to 10%) and inferring compatibility of the data with Hardy Weinberg Equilibrium (HWE) from an insignificant result. Unfortunately, such direct inversion of a statistical testing procedure fails to produce a valid test of the hypothesis of interest, namely, that the data are in sufficiently good agreement with the model under which the P-value is calculated. We present a logically unflawed solution to the problem of establishing (approximate) compatibility of an observed genotype distribution with HWE. The test is available in one- and two-sided versions. For both versions, we provide tools for exact power calculation. We demonstrate the merits of the new approach through comparison with the traditional χ² goodness-of-fit test in 2×60 genotype distributions from 43 published genetic studies of complex diseases where departure from HWE was noted in either the case or control sample. In addition, we show that the new test is useful for the analysis of genome-wide association studies.