of an appropriate ‘threshold’ for reporting possible associations as likely to be genuine. Here the mathematics is quite straightforward if we make the simplifying assumption that we have the same power to detect all true associations. Then we have18 Posterior odds for true association=Prior odds×Power∕Significance threshold That is, for a given significance threshold, the probability of a true association depends on the prior odds and, crucially, the power. A plausible estimate for the prior odds of true association at any specified locus might be of the order of 100,000:1 against, for example, on the basis of 1,000,000 ‘independent’ regions of the genome and an expectation of 10 detectable genes involved in the condition. (Other plausible estimates might vary from this by an order of magnitude or so in either direction.) Then, assuming a power of 0.5 and a significance threshold of 5×10-7, the posterior odds in favour of a ‘hit’ being a true association would be 10:1. However, if we relax this significance threshold by a factor of ten, or alternatively if the power were lower by a factor of 10, the posterior odds that a ‘hit’ is a true association would also be reduced by a factor of ten.
