  Response-adaptive randomisation (RAR) can considerably improve the chances of
a successful treatment outcome for patients in a clinical trial by skewing the
allocation probability towards better performing treatments as data
accumulates. There is considerable interest in using RAR designs in drug
development for rare diseases, where traditional designs are not feasible or
ethically objectionable. In this paper we discuss and address a major criticism
of RAR: the undesirable type I error inflation due to unknown time trends in
the trial. Time trends can appear because of changes in the characteristics of
recruited patients - so-called "patient drift". Patient drift is a realistic
concern for clinical trials in rare diseases because these typically recruit
patients over a very long period of time. We compute by simulations how large
the type I error inflation is as a function of the time trend magnitude in
order to determine in which contexts a potentially costly correction is
actually necessary. We then assess the ability of different correction methods
to preserve type I error in this context and their performance in terms of
other operating characteristics, including patient benefit and power. We make
recommendations of which correction methods are most suitable in the rare
disease context for several RAR rules, differentiating between the two-armed
and the multi-armed case. We further propose a RAR design for multi-armed
clinical trials, which is computationally cheap and robust to several time
trends considered.
