In this work, we focus on improving two major aspects of pathway enrichment analysis (Fig 1). First, we incorporate numerical and analytic solutions for the p-value estimation of the MOCS and SOCS statistics. This removes the need for phenotype permutations or Monte Carlo simulations, thereby making the score computation faster. Second, we developed a rigorous type I error control strategy and implemented a modified Fisher method to compute parameter-free pathway scores[19]. While some elements of our algorithm have been proposed in other fields of statistical genetics[20,21], the novelty of our method lies in the unique combination of sophisticated analytical methods employed for pathway analysis, which results in improved computational speed, precision, type I error control and power.
