Re-randomisation trials in multi-episode settings: Estimands and independence estimators

Often patients may require treatment on multiple occasions. The re-randomisation design can be used in such multi-episode settings, as it allows patients to be re-enrolled and re-randomised for each new treatment episode they experience. We propose a set of estimands that can be used in multi-episode settings, focusing on issues unique to multi-episode settings, namely how each episode should be weighted, how the patient's treatment history in previous episodes should be handled, and whether episode-specific effects or average effects across all episodes should be used. We then propose independence estimators for each estimand, and show the manner in which many re-randomisation trials have been analysed in the past (a simple comparison between all intervention episodes vs. all control episodes) corresponds to a per-episode added-benefit estimand, that is, the average effect of the intervention across all episodes, over and above any benefit conferred from the intervention in previous episodes. We show this estimator is generally unbiased, and describe when other estimators will be unbiased. We conclude that (i) consideration of these estimands can help guide the choice of which analysis method is most appropriate; and (ii) the re-randomisation design with an independence estimator can be a useful approach in multi-episode settings.