A seamless phase II/III design with sample-size re-estimation

A main objective in clinical trials is to find the best treatment in a given finite class of competing treatments and then to show superiority of this treatment against a control treatment. Traditionally, the best treatment is estimated in a phase II trial. Then in an independent phase III trial, superiority of this treatment, estimated as best in the first trial, is to be shown against the control treatment by a size alpha test. In this paper we investigate a competing adaptive two-stage test procedure for a seamless phase II/III trial. We assume that the variance is unknown and include therefore the calculation of the total sample size based on the first-stage-variance estimation. We derive formulae for the expected number of patients. These formulae depend on the unknown variance only, not on the other unknown parameters. Using a prior for the unknown variance, we can determine the two-stage test procedure of size alpha and power 1 - beta that is optimal in that it needs a minimal number of observations. The results are illustrated by a numerical example that indicates the superiority of the adaptive procedure over the traditional approach.