The analysis of sequential clinical trials

Abstract

SUMMARY The conduct of a sequential clinical trial is considered in two distinct stages, the planning of the trial and the analysis of the results. Tests based on straight line stopping boundaries are considered. The planning stage is described in terms of existing theory and results are presented which allow significance levels to be quoted and interval estimates to be given at the analysis stage. Tables for use in the calculation of significance levels are included. The accuracy of large sample results is assessed by means of computer simulation. We consider the comparison of two treatments using sequential tests based on straight line stopping boundaries. Two special cases which have optimal properties are described in ? 2. The results of traditional sequential analysis will be used only in the planning of the trial. The analysis of the data, including the terminal sample size as part of the data, will be viewed as a separate process, involving the ordinary tools of nonsequential statistics. Results on significance levels and interval estimation are presented in ? 3. Some similar results have been given for certain restricted procedures by Armitage (1960) and for repeated significance tests by Siegmund (1978). Repeated significance tests themselves are described in the second (1975) edition of Armitage's book. In ? 4 the problems of overshoot and overrunning are discussed. A trial will be said to overrun if some responses are observed after formal termination. If the state of the trial is not updated continuously, but at regular intervals such as once a week or once a month, some overrunning is likely. It is even more likely if patient response takes some time to manifest itself, so that when termination occurs some patients have already been treated but have not yet responded. Overrunning can be ignored in the planning of a trial, but all the data, including the 'extra' observations, can be included in the analysis. Previous work on