Sequential estimation for two-stage and three-stage clinical trials

A clinical trial setting is considered in which two treatments are available for a particular ailment. The responses to the treatments are normally distributed with unknown means and a common known variance. A two-stage trial and a three-stage trial are studied. In the two-stage trial, patients are randomised equally in the first stage, and the better treatment at the end of this stage is used exclusively in the second stage. The three-stage trial permits a second randomised stage before a single treatment is selected. For these designs, the exact bias and variance of the estimated treatment difference at the end of the trial are derived. These quantities are also derived when there are time trends in the data. Numerical results indicate that the presence of time trends can seriously bias the estimated treatment difference and can also lead to an increase in its variance.