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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):673-689; doi:10.1093/biomet/asm049
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Copyright © 2007 Biometrika Trust

Articles

Optimal adaptive randomized designs for clinical trials

Yi Cheng

Department of Mathematical Sciences, Indiana University, South Bend, Indiana 46634, U.S.A.

Donald A. Berry

Biostatistics Department, The University of Texas, M. D. Anderson Cancer Center, Houston, Texas 77030, U.S.A.

ycheng{at}iusb.edu

dberry{at}mdanderson.org

Received for publication 1 July 2005. Revision received 1 January 2007.

Optimal decision-analytic designs are deterministic. Such designs are appropriately criticized in the context of clinical trials because they are subject to assignment bias. On the other hand, balanced randomized designs may assign an excessive number of patients to a treatment arm that is performing relatively poorly. We propose a compromise between these two extremes, one that achieves some of the good characteristics of both. We introduce a constrained optimal adaptive design for a fully sequential randomized clinical trial with k arms and n patients. An r-design is one for which, at each allocation, each arm has probability at least r of being chosen, 0 <= r <= 1/k. An optimal design among all r-designs is called r-optimal. An r1-design is also an r2-design if r1 >= r2. A design without constraint is the special case r = 0 and a balanced randomized design is the special case r = 1/k. The optimization criterion is to maximize the expected overall utility in a Bayesian decision-analytic approach, where utility is the sum over the utilities for individual patients over a ‘patient horizon’ N. We prove analytically that there exists an r-optimal design such that each patient is assigned to a particular one of the arms with probability 1 – (k – 1)r, and to the remaining arms with probability r. We also show that the balanced design is asymptotically r-optimal for any given r, 0 <= r < 1/k, as N/n -> {infty}. This implies that every r-optimal design is asymptotically optimal without constraint. Numerical computations using backward induction for k = 2 arms show that, in general, this asymptotic optimality feature for r-optimal designs can be accomplished with moderate trial size n if the patient horizon N is large relative to n. We also show that, in a trial with an r-optimal design, r < 1/2, fewer patients are assigned to an inferior arm than when following a balanced design, even for r-optimal designs having the same statistical power as a balanced design. We discuss extensions to various clinical trial settings.

Key Words: Backward induction • Balanced design • Decision theory • Induction • Jensen's inequality • Martingale convergence theorem • Multiple arms • Optimal design • Randomized sequential allocation



References

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    Berry D. A. Bayesian statistics and the efficiency and ethics of clinical trials. Statist. Sci. (2004) 19:175–87.[CrossRef]

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    Berry D. A., Fristedt B. Bandit Problems, Sequential Allocation of Experiments (1985) London: Chapman and Hall.

    Cheng Y., Su F., Berry D. A. Choosing sample size for a clinical trial using decision analysis. Biometrika (2003) 90:923–36.[Abstract/Free Full Text]

    Colton T. A model for selecting one of two medical treatments. J. Am. Statist. Assoc. (1963) 58:388–400.[CrossRef][Web of Science]

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    Rubin D. B. Estimating causal effects of treatments in randomized and non-randomized studies. J. Educ. Psychol. (1974) 66:688–701.[CrossRef][Web of Science]


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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
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Google Scholar
Right arrow Articles by Cheng, Y.
Right arrow Articles by Berry, D. A.
Right arrow Search for Related Content
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Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?