Tymofyeyev, Yevgen; Rosenberger, William F.; Hu, Feifang Implementing optimal allocation in sequential binary response experiments. (English) Zbl 1284.62496 J. Am. Stat. Assoc. 102, No. 477, 224-234 (2007). 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. Cited in 38 Documents MSC: 62K99 Design of statistical experiments PDFBibTeX XMLCite \textit{Y. Tymofyeyev} et al., J. Am. Stat. Assoc. 102, No. 477, 224--234 (2007; Zbl 1284.62496) Full Text: DOI