Taking a chance: How likely am I to receive my preferred treatment in a clinical trial?

Researchers should ideally conduct clinical trials under a presumption of clinical equipoise, but in fact trial patients will often prefer one or other of the treatments being compared. Receiving an unblinded preferred treatment may affect the study outcome, possibly beneficially, but receiving a non-preferred treatment may induce 'reluctant acquiescence', and poorer outcomes. Even in blinded trials, patients' primary motivation to enrol may be the chance of potentially receiving a desirable experimental treatment, which is otherwise unavailable. Study designs with a higher probability of receiving a preferred treatment (denoted as 'concordance') will be attractive to potential participants, and investigators, because they may improve recruitment and hence enhance study efficiency. Therefore, it is useful to consider the concordance rates associated with various study designs. We consider this question with a focus on comparing the standard, randomised, two-arm, parallel group design with the two-stage randomised patient preference design and Zelen designs; we also mention the fully randomised and partially randomised patient preference designs. For each of these designs, we evaluate the concordance rate as a function of the proportions randomised to the alternative treatments, the distribution of preferences over treatments, and (for the Zelen designs) the proportion of patients who consent to receive their assigned treatment. We also examine the