Group Sequential Clinical Trials: A Classical Evaluation of Bayesian Decision-Theoretic Designs

Bayesian decision-theoretic designs for a clinical trial comparing two treatments for a disease with binary outcomes are developed and evaluated. The probability of successful outcome with treatment i is denoted by pi , i = 1, 2, and prior knowledge regarding each pi is assumed to follow a beta distribution. The pi are assumed to be independent. To facilitate comparison with frequentist clinical trial designs, we take a hypothesis-testing approach. The null hypothesis is δ < δ 0, and the alternative hypothesis is δ > 0, where δ 0 is the minimum treatment effect sought by the trial and δ = p 2 - p 1 is the true treatment difference. We use a simple terminal loss function reflecting the hypothesis-testing goal of the trial, and the total cost of the trial is the final sample size plus the terminal loss function. The stopping and decision rules that minimize the expectation of the total cost are determined by backward induction. Monte Carlo simulation is used to compare Bayesian and frequentist error rates and mean sample sizes of these Bayesian designs with one-tailed classical group-sequential designs of Pocock and O'Brien-Fleming. As expected, the Bayesian decision-theoretic designs have smaller mean costs than the classical designs. More surprising, when the magnitude of the terminal loss function is chosen to yield frequentist error rates similar to those for classical designs, the mean sample sizes of the Bayesian designs are usually smaller.