Estimating treatment effect in randomized trial after control to treatment crossover using external controls

In clinical trials, it is common to design a study that permits the administration of an experimental treatment to participants in the placebo or standard of care group post primary endpoint. This is often seen in the open-label extension phase of a phase III, pivotal study of the new medicine, where the focus is on assessing long-term safety and efficacy. With the availability of external controls, proper estimation and inference of long-term treatment effect during the open-label extension phase in the absence of placebo-controlled patients are now feasible. Within the framework of causal inference, we propose several difference-in-differences (DID) type methods and a synthetic control method (SCM) for the combination of randomized controlled trials and external controls. Our realistic simulation studies demonstrate the desirable performance of the proposed estimators in a variety of practical scenarios. In particular, DID methods outperform SCM and are the recommended methods of choice. An empirical application of the methods is demonstrated through a phase III clinical trial in rare disease.