Bayesian design of single-arm phase II clinical trials with continuous monitoring

Bayesian designs are increasingly used to conduct phase II clinical trials. However, stopping boundaries in most Bayesian designs are defined from posterior credible intervals. The use of designs based on posterior credible intervals results in a loss of efficiency when compared to formal stopping rules based on Bayesian hypothesis tests. Such designs also introduce an unnecessary element of subjectivity in the interpretation of trial results.

We derive a new class of Bayesian designs based on formal hypothesis tests. The prior densities used to define the alternative hypotheses in these tests assign no mass to parameter values that are consistent with the null hypotheses and are called nonlocal alternative prior densities.

We show that Bayesian designs based on hypothesis tests and nonlocal alternative prior densities are more efficient than common Bayesian designs based on posterior credible intervals and common frequentist designs. In contrast to trial designs based on Bayesian credible intervals, we demonstrate that the mis-specification of the prior densities used to describe the anticipated effect of the experimental treatment in designs based on hypothesis tests cannot increase the expected weight of evidence in favor of the trial agent.

Extension of test-based designs to phase I-II designs and randomized phase II designs remains an open research question.

Phase II single-arm trials designed using Bayesian hypothesis tests with nonlocal alternatives provide better operating characteristics, use fewer patients per correct decision, and provide more directly interpretable results than other commonly used Bayesian and frequentist designs. Because the mis-specification of the prior density on the effect of the experimental agent decreases the expected weight of evidence that is collected in favor of the experimental treatment, the use of Bayesian hypothesis tests to design clinical trials also eliminates a potential source of bias often associated with trials designed using posterior credible intervals.