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Choosing sample size for a clinical trial using decision analysis

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  • Yi Cheng

Abstract

Consider designing a clinical trial in stages, with two treatments and N exchangeable patients to be treated. Responses are dichotomous. The problem is to decide how large each stage should be and how many patients should be assigned to each treatment during each stage. Information is updated during and after each stage using Bayes' theorem. In planning stage j, responses from selections in stages 1 to j - 1 are available, but interim responses in stage j are not available. Our analytical results consider two stages for two scenarios, when one treatment arm is known and when both treatment arms are unknown. The dominant term for the length of the first stage in an optimal design for general N is found explicitly. In both scenarios the order of magnitude of the length of the first stage is the square root of N. The finite-N performance of asymptotically optimal allocation is compared with that of the true optimal allocation. Our numerical study also shows that, for a trial of three stages with one known arm, the optimal first-stage sample size is asymptotically proportional to the cube root of N. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Yi Cheng, 2003. "Choosing sample size for a clinical trial using decision analysis," Biometrika, Biometrika Trust, vol. 90(4), pages 923-936, December.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:923-936
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    Cited by:

    1. Andrew Willan, 2011. "Sample Size Determination for Cost-Effectiveness Trials," PharmacoEconomics, Springer, vol. 29(11), pages 933-949, November.
    2. Isakov, Leah & Lo, Andrew W. & Montazerhodjat, Vahid, 2019. "Is the FDA too conservative or too aggressive?: A Bayesian decision analysis of clinical trial design," Journal of Econometrics, Elsevier, vol. 211(1), pages 117-136.
    3. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling epsilon-optimal treatment rules," Carlo Alberto Notebooks 430, Collegio Carlo Alberto.
    4. Charles F. Manski, 2005. "Fractional Treatment Rules for Social Diversification of Indivisible Private Risks," NBER Working Papers 11675, National Bureau of Economic Research, Inc.
    5. Charles F. Manski, 2021. "Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald," Econometrica, Econometric Society, vol. 89(6), pages 2827-2853, November.
    6. Charles F. Manski, 2019. "Meta-Analysis for Medical Decisions," NBER Working Papers 25504, National Bureau of Economic Research, Inc.
    7. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling ε-optimal treatment rules," CeMMAP working papers 60/15, Institute for Fiscal Studies.
    8. Elea McDonnell Feit & Ron Berman, 2019. "Test & Roll: Profit-Maximizing A/B Tests," Marketing Science, INFORMS, vol. 38(6), pages 1038-1058, November.

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