A sample size calculation of Bayesian design for superiority trials with rare events

Abstract

Traditional approaches used in sample calculation for superiority trials comparing two low proportions usually provide very large sample sizes. Furthermore, such calculations may be inaccurate due to asymptotic normality that is often assumed but may not hold in such cases. Bayesian approach could reduce sample size by integrating historical information prior to data collection. It allows also single arm design to be conducted e.g. when it would not be ethical to enroll participants into a control group. In this analysis, a 1:1 randomized two-arm Bayesian trial designed to test for superiority was compared in terms of power and Bayesian Type I error with 1) a single-arm Bayesian trial and 2) a two- arm frequentist trial. Via Monte Carlo simulations, sample sizes required and trial powers were compared for various scenarios of efficacy results, using various prior distributions. Our analysis was applied to a real-world case study in the area of a trial to test the efficacy of a strategy to reduce mother-to- child transmission of HIV. As a result, regardless of the prior distributions used, power to detect superiority was found systematically higher with single-arm Bayesian design compared to two-arm Bayesian design. However when the size of the effect becomes smaller, the power of a two-arm Bayesian design becomes higher than single-arm. In our case study, using the model predictive prior for the experimental arm (transmission rate decrease from 2.3% to 0.7%), power to detect superiority (RR<1) could reach 80% with optimistically as low as 50 subjects. In the two-arm frequentist design, using Farrington and Manning method, the power to demonstrate superiority of the experimental over control arm would be far below 80% with 350 subjects (34% power). Similarly, in a two-arm Bayesian design, the power would not reach 80% using a prior set identical to the predictive prior in the control arm or the inflated 170% coefficient of variation (CV). Finally, based on single-arm Bayesian design, power reaches 80% with 350 subjects when using the inflated 170% CV to the control arm predictive prior.