One-sample survival tests for non-proportional hazards in oncology clinical trial

Abstract: In oncology, well-powered time-to-event randomized clinical trials are challenging due to a limited number of patients (e.g, pediatric cancers or personalized medicine). Last decade, many one- or two-stage designs for single-arm trials (SATs) have emerged as an alternative to overcome this issue. These designs rely on the one-sample log-rank test (OSLRT) and its modified version (mOSLRT) to compare the survival curves of an experimental and an external control group under the proportional hazards (PH) assumption that may be violated. We extend Finkelstein's formulation of OSLRT as a score test under PH by using a piecewise exponential model with change-points (CPs) for early, middle and delayed treatment effects and an accelerated hazards model for crossing hazards. The restricted mean survival time (RMST) based test is adapted to SATs and we also construct a combination test procedure (max-Combo) with correction for multiple testing. The performance of the developed tests (score tests, RMST and max-Combo tests) are evaluated through a simulation study of early, middle, delayed effects and crossing hazards. Findings show that the score tests are as conservative as the OSLRT and have the highest power when the data generation matches with the model. The max-Combo test is an interesting approach when the time-dependent relative treatment effect and/or the values of CPs are unknown. Uncertainty on the survival curve estimate of the external control group and model misspecification may have a significant impact on performance. For illustration, we apply the developed tests on three real data examples.