Change point detection for clustered survival data with marginal proportional hazards model

In survival analysis, models with a change point for independent survival data have been extensively studied. However, few works in the literature focus on clustered survival data with a change point, despite the prevalence of such survival data in clinical research. In this article, we propose the maximal score test, along with its normalized version, to detect the existence of change point effects for the marginal proportional hazards model. We establish the asymptotic distributions of the proposed test statistics under both the null and local alternative hypotheses. To approximate the critical points for the proposed tests, a simple Monte Carlo method is presented. Furthermore, when the null hypothesis of no change point effects is rejected, we propose maximum smoothed partial likelihood estimators for the unknown change point and the regression parameters and derive the asymptotic properties of the estimators. Extensive simulation studies are carried out to evaluate the finite sample performance of the proposed methods. Finally, we illustrate the proposed methods with applications to the breast cancer data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial.