A more flexible alternative to the sum statistic is the truncated product of p-values. Here, the product is formed of all the p-values lower than a preset threshold [31], or the K smallest p-values [32]. When the individual tests have the same distribution, the rank truncated product has equivalent power to the sum statistic, but is more balanced when the tests have different distributions. This will occur, for example, when conducting haplotype-based tests on regions of different sizes, leading to tests with different degrees of freedom. Analytic distributions are known for independent tests, which have been used in simulation studies to show improved power for combined evidence methods compared with traditional corrections [31,32]. The present authors prefer the truncated product to the sum statistic on account of its balanced combination of different test, and also prefer to truncate on rank rather than threshold because the number of true gene effects is fixed across studies, whereas their p-values are random [32].
