Sample sizes for randomized controlled trials utilizing Bayesian response adaptive randomization for continuous outcomes

We describe a Bayesian approach for sample size estimation for multi-arm randomized controlled trials utilizing response adaptive randomization (RAR) for continuous outcomes. Assuming normally distributed treatment effects and unknown but common treatment variance, this design incorporates outcome data to estimate posterior distributions of treatment parameters, modifies allocation proportions to favor more effective treatments, and re-estimates the number of participants needed. The sample size should be sufficient to show that at least one group difference is greater than 0 (success), or that all effect sizes are smaller than a desired threshold (futility) at prespecified probabilities. Using simulations for a 4-arm trial, we compare sample sizes based on hypothesis testing to those using a Bayesian approach: [1] without interim analysis; [2] with interim analyses and non-adaptive randomization; [3] with interim analyses and RAR. We demonstrate that two interim analyses, conducted when outcomes are available among 25% and 50% of participants, could result in fewer enrolled participants. Especially for distinctly large treatment effects, RAR-based sample size estimates increase due to imbalanced allocation of participants. Application of the approach to two completed randomized controlled trials confirms these observations. We conclude that early and frequent interim analyses may reduce the number of participants needed for a conclusive trial where participant allocation does not change throughout the trial. For trial designs incorporating RAR, the within-trial patient benefits of allocating more patients to favorable arms with larger sample size requirements should be considered against the efficiency of equal group allocation.