A unified method for monitoring and analysing controlled trials

Group sequential methods are becoming increasingly popular for monitoring and analysing large controlled trials, especially clinical trials. They not only allow trialists to monitor the data as it accumulates, but also reduce the expected sample size. Such methods are traditionally based on preserving the overall type I error by increasing the conservatism of the hypothesis tests performed at any single analysis. Using methods which are based on hypothesis testing in this way makes point estimation and the calculation of confidence intervals difficult and controversial. We describe a class of group sequential procedures based on a single parameter which reflects initial scepticism towards unexpectedly large effects. These procedures have good expected and maximum sample sizes, and lead to natural point and interval estimates of the treatment difference. Hypothesis tests, point estimates and interval estimates calculated using this procedure are consistent with each other, and tests and estimates made at the end of the trial are consistent with interim tests and estimates. This class of sequential tests can be considered in both a traditional group sequential manner or as a Bayesian solution to the problem.