Morgenthaler and Thilly30 were the first to describe a version of the collapsing approach in which the frequency of individuals carrying any one of a number of rare variants is contrasted between case and control groups. They termed this approach the ‘cohort allelic sums test’ or ‘CAST’ method and suggested the use of standard contingency table-based Chi-square or Fisher’s exact tests for obtaining p-values. The method as first proposed does not easily accommodate covariates, cannot be used with quantitative phenotypes, and does not consider weighting of the variants using, for example, variant frequency or functional annotations. Li and Leal considered an extension of the CAST method, which they termed the ‘Combined Multivariate and Collapsing (CMC)’ method.28 Here, rare variants are collapsed, as in the CAST method, and treated as a single set of variants whose frequency differences are then tested between groups. This testing could potentially be done simultaneously with frequency differences at other individual loci or among other collapsed sets using a summary distance-based Hotelling’s T-Squared statistic.28, 38 The CMC statistic has desirable properties in that it appropriately controls
