Madsen and Browning proposed a statistic for testing a prespecified collapsed set of variants that leverages weighting of each variant by its frequency, thus allowing one to include variants of any frequency into the collapsed set.34 A score is calculated for each individual using that individual’s genotypes and the frequency-determined weights. The sum of ranks of the scores among the cases is then used as a summary statistic to be compared to the same statistic computed among the controls using permutation methods, in a manner analogous to the Wilcoxon rank test.39 Madsen and Browning showed that their proposed statistic is more powerful than either the CAST or CMC methods in a number of settings, but more work in this area is needed to clarify the advantages, if any, of each.34 Other strategies for testing groupwise frequency differences of genetic variations between cases and controls in an analogous manner to the CAST method have been proposed, although many have only been implemented in settings involving common variants. 34, 40, 4142
