Estimating treatment effects from a randomized clinical trial in the presence of a secondary treatment.

In randomized clinical trials involving survival time, a challenge that arises frequently, for example, in cancer studies (Manegold, Symanowski, Gatzemeier, Reck, von Pawel, Kortsik, Nackaerts, Lianes and Vogelzang, 2005. Second-line (post-study) chemotherapy received by patients treated in the phase III trial of pemetrexed plus cisplatin versus cisplatin alone in malignant pleural mesothelioma. Annals of Oncology 16, 923--927), is that subjects may initiate secondary treatments during the follow-up. The marginal structural Cox model and the method of inverse probability of treatment weighting (IPTW) have been proposed, originally for observational studies, to make causal inference on time-dependent treatments. In this paper, we adopt the marginal structural Cox model and propose an inferential method that improves the efficiency of the usual IPTW method by tailoring it to the setting of randomized clinical trials. The improvement in efficiency does not depend on any additional assumptions other than those required by the IPTW method, which is achieved by exploiting the knowledge that the study treatment is independent of baseline covariates due to randomization. The finite-sample performance of the proposed method is demonstrated via simulations and by application to data from a cancer clinical trial.