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Clinical trial design enabling epsilon-optimal treatment rules

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  • Charles F. Manski
  • Aleksey Tetenov

Abstract

Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesians have argued that trials should be designed to maximize subjective expected utility in settings of clinical interest. This perspective is compelling given a credible prior distribution on treatment response, but Bayesians have struggled to provide guidance on specification of priors. We use the frequentist statistical decision theory of Wald (1950) to study design of trials under ambiguity. We show that epsilon-optimal rules exist when trials have large enough sample size. An epsilon-optimal rule has expected welfare within epsilon of the welfare of the best treatment in every state of nature. Equivalently, it has maximum regret no larger than epsilon. We consider trials that draw predetermined numbers of subjects at random within groups stratified by covariates and treatments. The principal analytical findings are simple sufficient conditions on sample sizes that ensure existence of epsilon-optimal treatment rules when outcomes are bounded. These conditions are obtained by application of Hoeffding (1963) large deviations inequalities to evaluate the performance of empirical success rules.

Suggested Citation

  • Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling epsilon-optimal treatment rules," Carlo Alberto Notebooks 430, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:430
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    References listed on IDEAS

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    1. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    2. Yi Cheng, 2003. "Choosing sample size for a clinical trial using decision analysis," Biometrika, Biometrika Trust, vol. 90(4), pages 923-936, December.
    3. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
    4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    5. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    6. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    7. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    8. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

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