Various methods have been developed to aggregate SNP summary statistics into gene scores[3,11,12]. A common aggregation method is to use only the most significant SNP within a window encompassing the gene of interest, for example by assigning the maximum-of-chi-squares (MOCS) as the gene score statistic[3,13] (the contributing chi-squared values can be obtained from SNP p-values by using the inverse chi-squared quantile transformation). Another method is to combine results for all SNPs in the gene region, for example by using the sum-of-chi-squares (SOCS) statistic[14]. Both the MOCS and SOCS statistics are confounded by several properties of the gene. Specifically, in both cases it is important to correct for gene size and LD structure to obtain a well-calibrated p-value for the statistic. In the remainder of this paper, we also refer to the p-values of the MOCS and the SOCS statistics as max and sum gene scores, respectively. P-values can be estimated by phenotype label permutation, but this method is both computationally intensive and requires access to genotype data of the actual study, which are rarely shared[15]. Thus, one often has access
