Cumulative Hazard Ratio Estimation for Treatment Regimes in Sequentially Randomized Clinical Trials

The proportional hazards model is widely used in survival analysis to allow adjustment for baseline covariates. The proportional hazard assumption may not be valid for treatment regimes that depend on intermediate responses to prior treatments received, and it is not clear how such a model can be adapted to clinical trials employing more than one randomization. Besides, since treatment is modified post-baseline, the hazards are unlikely to be proportional across treatment regimes. Although Lokhnygina and Helterbrand (Biometrics 63: 422-428, 2007) introduced the Cox regression method for two-stage randomization designs, their method can only be applied to test the equality of two treatment regimes that share the same maintenance therapy. Moreover, their method does not allow auxiliary variables to be included in the model nor does it account for treatment effects that are not constant over time. In this article, we propose a model that assumes proportionality across covariates within each treatment regime but not across treatment regimes. Comparisons among treatment regimes are performed by testing the log ratio of the estimated cumulative hazards. The ratio of the cumulative hazard across treatment regimes is estimated using a weighted Breslow-type statistic. A simulation study was conducted to evaluate the performance of the estimators and proposed tests.