Optimal Two-stage designs in Phase-II Clinical Trials.

Abstract

Two-stage designs have been widely used in phase II clinical trials. Such designs are desirable because they allow a decision to be made on whether a treatment is effective or not after the accumulation of the data at the end of each stage. Optimal fixed two-stage designs, where the sample size at each stage is fixed in advance, were proposed by Simon when the primary outcome is a binary response. We propose an adaptive two-stage design which allows the sample size at the second stage to depend on the results at the first stage. Using a Bayesian decision theoretic construct, we derive optimal adaptive two-stage designs. The optimality criterion is to minimize the expected sample size under the null hypothesis value. We further explore optimal adaptive designs that minimize the expected sample size at the alternative hypothesis, at a probability mid-point between the null and alternative hypotheses and a weighted combination of the null, alternative and mid-point value. We also construct an envelope function that gives the lowest expected sample size for any possible value of the response probability. The different designs are compared to Simon's design as well as the envelope function. The designs that minimize the expected sample size at the mid-point between the null and alternative hypotheses and the design that minimizes a weighted average of the response probabilities are closer to the envelope function. Results show that these designs perform better across a range of the response probability values, and generally surpass Simon's design.