Balancing statistical and ethical considerations in planning clinical trials: recommendations for response-adaptive randomization urn designs

During a clinical trial, balancing statistical and ethical considerations are important. Response-adaptive randomization methods use the information from past patients to increase the probability of the next patient receiving the better treatment while avoiding the statistical concern of selection bias. We compared three response-adaptive randomization urn designs, Randomized Play-the-Winner, Modified Play-the-Winner, and Birth-and-Death Urn with Immigration, to the traditional equal allocation design with respect to power and allocation of patients to the better treatment. Because these designs have been described separately, our motivation was to systematically compare them and provide recommendations. With simulations, we varied sample size and combinations of treatment and control success probabilities. We also compared the response-adaptive randomization designs using exact distribution algorithms and applied them to past clinical trial data that used an equal allocation design. We conclude that Modified Play-the-Winner tends to be unpredictable and can result in allocation of all of the patients to the better treatment. Randomized Play-the-Winner allocates more patients to the better treatment than Birth-and-Death Urn with Immigration, but Birth-and-Death Urn with Immigration is more consistent in its allocations. Randomized Play-the-Winner and Birth-and-Death Urn with Immigration produce allocations that have comparable powers to equal allocation design.