A Monte Carlo approach for change‐point detection in the Cox proportional hazards model

Detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis. The testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test. In the presence of random censoring and/or covariates, however, the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice. Moreover, a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged. In this paper, we consider maximal score tests for detecting change point(s) in the Cox proportional hazards model with censored data. We propose to use a simple Monte Carlo approach for assessing the statistical significance of tests. The proposed approach is applicable for testing a single change point in the Cox model with covariates and sample stratifications over various types of candidate regions, including discrete time-point sets or disjoint intervals. We also show that the proposed test statistics and the Monte Carlo procedure are well applicable under situations with multiple change points. Simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite-sample performance of the proposed approach.

[1]  S. Piantadosi,et al.  Placebo-controlled trial of safety and efficacy of intraoperative controlled delivery by biodegradable polymers of chemotherapy for recurrent gliomas , 1995, The Lancet.

[2]  Hung T. Nguyen,et al.  Estimation in change-point hazard rate models , 1984 .

[3]  V. Farewell,et al.  On testing for a constant hazard against a change-point alternative. , 1982, Biometrics.

[4]  Hans-Georg Müller,et al.  CHANGE-POINT MODELS FOR HAZARD FUNCTIONS , 1994 .

[5]  Yi-Ching Yao.  Maximum likelihood estimation in hazard rate models with a change-point , 1986 .

[6]  Z. Ying,et al.  A resampling method based on pivotal estimating functions , 1994 .

[7]  Z. Ying,et al.  Checking the Cox model with cumulative sums of martingale-based residuals , 1993 .

[8]  O. Pons.  Estimation in a Cox regression model with a change-point according to a threshold in a covariate , 2003 .

[9]  David E. Matthews,et al.  Asymptotic Score-Statistic Processes and Tests for Constant Hazard Against a Change-Point Alternative , 1985 .

[10]  D. Cox.  Regression Models and Life-Tables , 1972 .

[11]  D. Zucker,et al.  Weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment , 1990 .

[12]  V. Farewell,et al.  On a singularity in the likelihood for a change-point hazard rate model , 1985 .

[13]  Steven G. Self,et al.  Asymptotic Distribution Theory for Cox-Type Regression Models with General Relative Risk Form , 1983 .

[14]  X H Liu,et al.  The Cox proportional hazards model with change point: an epidemiologic application. , 1990, Biometrics.