Some results on estimation for two-stage clinical trials

A clinical trial setting is considered in which two treatments are available for a particular ailment. A two—stage trial is studied, in which 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. For exponential and Bernoulli responses, the exact bias and variance of the estimated treatment difference at the end of the trial are derived. Corresponding results for normal responses with unequal variances are also obtained, and the numerical accuracy of a normal approximation is investigated. The results indicate that the bias in estimation can be up to 25% when the size of the first stage is small, reducing to less than 7% for moderate first—stage sizes. For both exponential and Bernoulli responses, a normal approximation works well for moderate first—stage sizes, with the approximation for Bernoulli responses being slightly better.