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Response-adaptive randomisation (RAR) can considerably improve the chances ofa successful treatment outcome for patients in a clinical trial by skewing theallocation probability towards better performing treatments as dataaccumulates. There is considerable interest in using RAR designs in drugdevelopment for rare diseases, where traditional designs are not feasible orethically objectionable. In this paper we discuss and address a major criticismof RAR: the undesirable type I error inflation due to unknown time trends inthe trial. Time trends can appear because of changes in the characteristics ofrecruited patients - so-called "patient drift". Patient drift is a realisticconcern for clinical trials in rare diseases because these typically recruitpatients over a very long period of time. We compute by simulations how largethe type I error inflation is as a function of the time trend magnitude inorder to determine in which contexts a potentially costly correction isactually necessary. We then assess the ability of different correction methodsto preserve type I error in this context and their performance in terms ofother operating characteristics, including patient benefit and power. We makerecommendations of which correction methods are most suitable in the raredisease context for several RAR rules, differentiating between the two-armedand the multi-armed case. We further propose a RAR design for multi-armedclinical trials, which is computationally cheap and robust to several timetrends considered.

Response adaptive designs for binary responses: how to offer patient benefit while being robust to time trends?