To compare strength of association evidence between sets of variants within the same gene or across different genes, an extension of the gene-set approach can be implemented. Sum statistics are obtained as previously described for each group of variants, then calibrated by the respective number of variants. The difference between the two proportional sum statistics is the test statistic of interest,DF=1J∑jWF,j−1K∑kWF,k,where the j = 1,…,J and k = 1,…,K subscripts index the competing sets of variants, and the F subscript indicates that the variant-specific joint location-scale statistics are obtained by Fisher’s method (although other methods of combining such as minP could be used as well). The significance of DF can be evaluated with the phenotype-permutation approach as described above.