Bayes factors for genome-wide association studies: comparison with P-values

Abstract

The Bayes factor is a summary measure that provides an alternative to the P-value for the ranking of associations, or the flagging of associations as "significant". We describe an approximate Bayes factor that is straightforward to use and is appropriate when sample sizes are large. We consider various choices of the prior on the effect size, including those that allow effect size to vary with the minor allele frequency (MAF) of the marker. An important contribution is the description of a specific prior that gives identical rankings between Bayes factors and P-values, providing a link between the two approaches, and allowing the implications of the use of P-values to be more easily understood. As a summary measure of noteworthiness P-values are difficult to calibrate since their interpretation depends on MAF and, crucially, on sample size. A consequence is that a consistent decision-making procedure using P-values requires a threshold for significance that reduces with sample size, contrary to common practice.