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Implementing optimal allocation in sequential binary response experiments. (English) Zbl 1284.62496

Summary: For sequential experiments with \(K\) treatments, we establish two formal optimization criteria to find optimal allocation strategies. Both criteria involve the sample sizes on each treatment and a concave noncentrality parameter from a multivariate test. We show that these two criteria are equivalent. We apply this result to specific questions: (1) How do we maximize power of a multivariate test of homogeneity with binary response?, and (2) for fixed power, how do we minimize expected treatment failures? Because the solutions depend on unknown parameters, we describe a response-adaptive randomization procedure that “targets” the optimal allocation and provides increases in power along the lines of 2–4% over complete randomization for equal allocation. The increase in power contradicts the conclusions of other authors who have explored other randomization procedures for \(K = 2\) and have found that the variability induced by randomization negates any benefit of targeting an optimal allocation.

MSC:

62K99 Design of statistical experiments
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