Sequential trials stopping rules

S. Zohar, A. Latouche, M. Taconnet, and S. Chevret, Software to compute and conduct sequential Bayesian phase I or II dose-ranging clinical trials with stopping rules. Comput Methods Programs Biomed 72 117-125 (2003). 

Naive estimators associated with sequential tests may also be biased in the sense that the expectation of standard fixed trial estimators taken over all possible trials run to the same stopping rule may not be equal to the true treatment effect. Adjustments for estimators and associated intervals are possible but raise similar issues to those discussed under section 19.2.1. For example, suppose that we have a fixed parallel-group trial and calculate, as a conventional treatment estimate, the difference between the mean outcomes in each group. Suppose we then notice, however, on looking at the results for the patients ordered over time, that had we run this trial as a given sequential trial with three looks at equal intervals, then we would have stopped exactly at the point dictated by the fixed trial, which happens to correspond to the second look of the sequential trial. Had we carried out the sequential trial we should have adjusted the treatment estimator, but since we have carried out a fixed trial we shall not. 

If it is considered desirable and feasible to run a double-blind trial in a given indication, the fact that a sequential trial is being run with repeated looks at accumulating data has the capacity, as O Neill (1993) puts it, to influence parts of the trial conduct such as types of patients entered, definitions of endpoints, exclusion criteria etc. (p. 606). Sometimes the data-monitoring board is kept in the dark as to which treatment is which and results are presented to it without revealing the treatment labels. This is not always possible for example, where an asymmetric stopping rule is being used, as may be the case when trials can be stopped for lack of efficacy. 

Sequential trial. (A somewhat unfortunate term since nearly all patients are recruited sequentially and in this sense nearly all trials would be sequential.) A clinical trial in which the results are analysed at various intervals with the intention of stopping the trial when a conclusive result has been reached. A stopping rule is usually defined in advance. In frequentist statistics it is necessary to make an adjustment to the results of an otherwise standard analysis to take the stopping rule into account. Such an adjustment is not necessary in Bayesian statistics, although the stopping rule itself ought to be at least partly dependent on the prior distribution so that, for this reason alone, the posterior distribution will vary with the stopping rule. 

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