Sequential procedures for comparing several medical treatments

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Abstract
The use of sequential methods in clinical trials allows inferior treatments to be eliminated early. From an ethical point of view, the advantages are substantial. However, early stopping induces estimation bias and a deterioration in precision because of reduced sample sizes. This paper considers the problem of determining which of k ≥ 2 treatments with Bernoulli responses has the highest probability of success. Two sequential procedures are investigated and compared with a fixed—sample procedure. Various properties are derived and illustrated for the cases k =2,3 and 5. It is shown that the sequential procedures can achieve a pattern of error probabilities equivalent to the fixed—sample procedure for a much lower level of expected successes lost. Approximations for the bias and standard deviation of estimators of treatment differences are obtained by using results about the distribution of stopping times for a normal process.

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