With genomewide SNP data now available, permutation tests have been suggested to obtain appropriately adjusted P–values [Churchill and Doerge, 1994]. The difficulty is that standard permutation tests only account for the markers actually tested, whereas the multiplicity spans the whole genome. This is important because although P–values are the usual output of classical tests, the real quantities of interest are the posterior odds for association or the closely related false–positive reporting probability [Wacholder et al., 2004] and positive predictive value [Ioannidis, 2005]. For a class of tests significant when a statistic T>t, the posterior odds may be expressed in terms of the prior odds as (1) where α, Beta are the type–1 and type–2 error rates of the test, respectively. Consideration of the prior odds is intrinsic to the Bayesian perspective, but it is also implicit in frequentist testing, if it is to be used responsibly.
