The log-rank test has been widely used to test a treatment effect under the Cox model for censored time-to-event outcomes, though it may lose power substantially when the model's proportional hazards assumption does not hold. In this paper, we consider an extended Cox model that uses B-splines or smoothing splines to model a time-varying treatment effect and propose score test statistics for the treatment effect. Our proposed new tests combine statistical evidence from both the magnitude and the shape of the time-varying hazard ratio function, and thus are omnibus and powerful against various types of alternatives. In addition, the new testing framework is applicable to any choices of spline basis functions, including B-splines and smoothing splines. Simulation studies confirm that the proposed tests perform well in finite samples and were frequently more powerful than conventional tests alone in many settings. The new methods are applied to the HIVNET 012 Study, a randomized clinical trial to assess the efficacy of single-dose Nevirapin against mother-to-child HIV transmission conducted by the HIV Prevention Trial Network.
Clinical Trials | Survival Analysis
Saegusa, Takumi; Di, Chongzhi; and Chen, Ying Qing, "Hypothesis Testing for an Extended Cox Model with Time-Varying Coefficients" (October 2013). UW Biostatistics Working Paper Series. Working Paper 395.