Comparison of statistics in association tests of genetic markers for survival outcomes

Computationally efficient statistical tests are needed in association testing of large scale genetic markers for survival outcomes. In this study, we explore several test statistics based on the Cox proportional hazards model for survival data. First, we consider the classical partial likelihood-based Wald and score tests. A revised way to compute the score statistics is explored to improve the computational efficiency. Next, we propose a Cox-Snell residual-based score test, which allows us to handle the controlling variables more conveniently. We also illustrated the incorporation of these three tests into a permutation procedure to adjust for the multiple testing. In addition, we examine a simulation-based approach proposed by Lin (2005) to adjust for multiple testing. We presented the comparison of these four statistics in terms of type I error, power, family-wise error rate, and computational efficiency under various scenarios via extensive simulation.