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. Genet. Epidemiol. 2006. © 2006 Wiley‐Liss, Inc.