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Biometrika 1981 68(1):119-132; doi:10.1093/biomet/68.1.119
© 1981 by Biometrika Trust
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Sequential medical trials involving paired data

HERMAN CHERNOFF and A. JOHN PETKAU

Department of Mathematics, Massachusetts Institute of Technology Cambridge
Department of Mathematics, University of British Columbia Vancouver

A general approach to sequential decision-theoretic problems is illustrated with Anscombe's formulation of the problem of comparing two treatments in a medical trial. The Bayes sequential procedure for a continuous time verion of the problem is explicitly determined. Suboptimal procedures are proposed and evaluated; asymptotic results and numerical descriptions are provided. The continuous time version is found to provide accurate approximations even for clinical trials involving relatively small horizon sizes.

Key Words: Bayes risk • Clinical trials • Decision theory • Free boundary problem • Optimal stopping • Wiener process


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