A sequential testing approach to detecting multiple change points in the proportional hazards model

Abstract

The semi-parametric proportional hazards model has been widely adopted in clinical trials with time-to-event outcomes. A key assumption in the model is that the hazard ratio function is a constant over time, which is frequently violated as there is often a lag period before an experimental treatment reaches its full effect. One existing approach uses maximal score tests and Monte Carlo sampling to identify multiple change points in the hazard ratio function, which requires the number of change points that exist in the model to be known. We propose a sequential testing approach to detecting multiple change points in the hazard ratio function using likelihood ratio tests, and the distributions of the likelihood ratio statistics under the null hypothesis are evaluated via resampling. An important feature of the proposed approach is that the number of change points in the model is inferred from the data and does not need to be specified. Numerical results based on simulated clinical trials and a real time-to-event study show that the proposed approach can accurately detect the change points in the hazard ratio function.