Gene Set Analysis for time-to-event outcome with the Generalized Berk-Jones statistic

Gene set analysis evaluates the collective impact of groups of genes on an outcome of interest, such as disease occurrence. By incorporating biological knowledge through predefined gene sets, this approach enhances the interpretability of results and improves statistical power compared to gene-wise analyses. In the context of time-to-event data, existing methods are limited and fail to account for potentially strong correlations within gene sets. Given the strong performance of the Generalized Berk-Jones (GBJ) statistic, which effectively incorporates correlation within the test statistic, we adapted this method to the time-to-event framework using a Cox model. We then compared its performance with established methods, including the Wald test, global test, and global boost test. Our proposed method, sGBJ, shows an over-control of Type I error, leading to reduced statistical power compared to other methods in numerical studies. We further benchmarked these methods in two different real-world contexts: gliomas and breast cancer. The Wald test emerged as the most effective, identifying the largest number of significant pathways while maintaining appropriate control of Type I error in simulation settings. sGBJ closely followed demonstrating good performances, without a significant loss of statistical power in analyzing these two real-world biomedical datasets.