Gene set analysis for GWAS: Assessing the use of modified Kolmogorov-Smirnov statistics

We discuss the use of modified Kolmogorov-Smirnov (KS) statistics in the context of gene set analysis and review corresponding null and alternative hypotheses. Especially, we show that, when enhancing the impact of highly significant genes in the calculation of the test statistic, the corresponding test can be considered to infer the classical self-contained null hypothesis. We use simulations to estimate the power for different kinds of alternatives, and to assess the impact of the weight parameter of the modified KS statistic on the power. Finally, we show the analogy between the weight parameter and the genesis and distribution of the gene-level statistics, and illustrate the effects of differential weighting in a real-life example.