Adaptive two-stage test procedures to find the best treatment in clinical trials
1 Faculty of Mathematics and Geography, Catholic University of Eichstätt-Ingolstadt, D-85071 Eichstätt, Germany wolfgang.bischoff{at}ku-eichstaett.de, 2 AstraZeneca, Clinical Science, S-15185 Södertälje, Sweden frank.miller{at}astrazeneca.com
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. The traditional procedure estimates the best treatment in a first trial. Then in an independent second trial superiority of this treatment, estimated as best in the first trial, is to be shown against the control treatment by a size 
test. In this paper we investigate these two trials of this traditional procedure as a two-stage test procedure. Additionally we introduce competing two-stage group-sequential test procedures. Then we derive formulae for the expected number of patients. These formulae depend on unknown parameters. When we have a prior for the unknown parameters we can determine the two-stage test procedure of size and power ß that is optimal, in that it needs a minimal number of observations. The results are illustrated by a numerical example, which indicates the superiority of the group-sequential procedures.
Key Words: Adaptive design; Bayes procedure; Clinical trial; Expected number of patients with respect to a prior; Group-sequential test; Two-stage test; Unknown variance
Received August 2002. Revised July 2004.