Hypothesis Testing for an Extended Cox Model with Time-Varying Coefficients

Chongzhi Di, Fred Hutchinson Cancer Research Center
Ying Qing Chen, Fred Hutchinson Cancer Research Center
Takumi Saegusa, University of Washington

Abstract

In many randomized clinical trials, the log-rank test has routinely been used to detect a treatment effect under the Cox proportional hazards model for censored time-to-event outcomes. However, it may lose power substantially when the proportional hazards assumption does not hold. There are approaches to testing the proportionality, such as the smoothing spline-based score test by Lin, Zhang and Davidian (2006). In this paper, we consider an extended Cox model assuming time-varying treatment effect. We then use smoothing splines to model the time-varying treatment effect, and we propose spline-based score tests for the overall treatment effect. Our proposed tests take into account statistical evidence from both the magnitude and the shape of hazard ratio functions, and thus are omnibus and powerful against various types of alternatives. Simulation studies confirm that the proposed tests perform well in finite samples and are often more powerful than both the log-rank and the proportionality tests in many settings. We applied our methods to determine whether or not single-dose nevirapine, taken by HIV-1-infected pregnant woman, would improve their newborns’ 18-month survival in the HIVNET 012 Study conducted by the HIV Prevention Trial Network.