title: Hypothesis testing for an extended cox model with time-varying coefficients.
abstract: The log-rank test has been widely used to test treatment effects 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 article, 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 choice of spline basis functions, including B-splines, and smoothing splines. Simulation studies confirm that the proposed tests performed well in finite samples and were frequently more powerful than conventional tests alone in many settings. The new methods were applied to the HIVNET 012 Study, a randomized clinical trial to assess the efficacy of single-dose Nevirapine against mother-to-child HIV transmission conducted by the HIV Prevention Trial Network.
authors.affiliation: Department of Biostatistics, University of Washington, Seattle, Washington 98195, U.S.A.
authors.forename: Takumi
authors.initials: T
authors.lastname: Saegusa
authors.affiliation: Public Health Sciences Division, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, U.S.A.
authors.forename: Chongzhi
authors.initials: C
authors.lastname: Di
authors.affiliation: Vaccine and Infectious Disease & Public Health Sciences Divisions, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109, U.S.A.
authors.forename: Ying Qing
authors.initials: YQ
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D015658:HIV Infections / Q000401:mortality* / Q000517:prevention & control*; D006801:Humans; D018445:Infectious Disease Transmission, Vertical / Q000517:prevention & control* / Q000706:statistics & numerical data; D015233:Models, Statistical; D019829:Nevirapine / Q000008:administration & dosage*; D011247:Pregnancy; D011251:Pregnancy Complications, Infectious / Q000188:drug therapy* / Q000401:mortality; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D019829:Nevirapine
keywords: Censoring; Clinical trials; HIV/AIDS; Log‐rank test; Score test