Sequential allocation rules for multi-armed clinical trials

A number of well-known sequential allocation rules are compared with a fixed-sample rule as procedures for determining which of k≥2 treatments with normal responses has the largest mean. For known variances, it is shown in the case k=2 how the parameters of the rules can be chosen so that they achieve a similar pattern of error probabilities. A simple modification of the rules is described to deal with the problem of unknown variences. Simulation indicates that the error probabilities for the modified rules are generally no larger than those for the fixed-sample rule. It is also shown that the rules extend naturally to the case of more than two treatments, with many of their important properties being preserved.