Estimating efficacy in trials with selective crossover

When one arm in a trial has a worse early endpoint such as recurrence, a data‐monitoring committee might recommend that all participants are offered the apparently superior treatment. The resultant crossover makes it difficult to measure differences between arms thereafter, including for longer‐term endpoints such as mortality and disease‐specific mortality. In this paper, we consider estimators of the efficacy of treatment on those who would not cross over if randomised to the apparently inferior arm. Binomial and proportional hazards maximum likelihood estimators are developed. The binomial estimator is applied to analysis of a breast cancer treatment trial and compared with intention‐to‐treat and inverse probability weighting estimators. Full and partial likelihood proportional‐hazard model estimators are assessed through computer simulations, where they had similar bias and variance. The new efficacy estimators extend those for all‐or‐none compliance to this important problem. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd