Omnibus permutation tests of the association of an ensemble of genetic markers with disease in case-control studies.

An omnibus permutation test of the overall null hypothesis can be used to assess the association of an entire ensemble of genetic markers with disease in case-control studies. In this approach, p-values for univariate marker-specific Armitage trend tests are combined to form a scalar statistic, which is then used in a permutation test to determine an overall p-value. Two previously described competing methods utilize either a standard two-sample Hotelling's T2 statistic or a global U statistic that is a weighted sum of univariate U statistics. In contrast to Hotelling's test, omnibus tests are much less sensitive to missing data, and utilize all available data. In contrast to the global U test, omnibus tests do not require that the direction of the effects of the individual markers on the risk of disease be correctly specified in advance; in fact, any combination of one- and two-sided univariate tests can be used. Simulations show that, even under circumstances favoring the competing tests (no missing data; direction of effects known), omnibus permutation tests based on Fisher's combining function or the Anderson-Darling statistic typically have power comparable to or greater than Hotelling's and the global U tests.