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A Bayesian Decision-Theoretic Model of Sequential Experimentation with Delayed Response

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  • Stephen Chick
  • Martin Forster
  • Paolo Pertile

Abstract

We solve a Bayesian decision-theoretic model of a sequential experiment in which the real-valued primary end point is observed with delay. The solution yields a unified policy defining the optimal 'do notexperiment'/'fixed sample size experiment'/'sequential experiment' regions as a function of the prior mean. The model can value the expected benefits accruing to study units, the fixed costs of switching from control to treatment, and allows the number of study units to benefit from a stopping decision to fall as the number of study units recruited to the experiment rises. We apply the model to the field of medical statistics, using data from a published trial investigating the clinical- and cost-effectiveness of drug-eluting stents versus bare metal stents. We demonstrate the model’s superiority over alternative trial designs when judged according to the maximisation of the net benefits of the trial, minus sampling costs, and we investigate how the size of the delay determines the optimal choice of trial design. The optimal policy also performs well when judged according to the probability of making the correct selection of health technology.

Suggested Citation

  • Stephen Chick & Martin Forster & Paolo Pertile, 2015. "A Bayesian Decision-Theoretic Model of Sequential Experimentation with Delayed Response," Discussion Papers 15/09, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:15/09
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    References listed on IDEAS

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    1. Paolo Pertile & Martin Forster & Davide La Torre, 2010. "Optimal sequential sampling rules for the economic evaluation of health technologies," Discussion Papers 10/24, Department of Economics, University of York.
    2. S. A. Murphy, 2003. "Optimal dynamic treatment regimes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 331-355, May.
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    4. Ahuja, Vishal & Birge, John R., 2016. "Response-adaptive designs for clinical trials: Simultaneous learning from multiple patients," European Journal of Operational Research, Elsevier, vol. 248(2), pages 619-633.
    5. Jennifer L. Kirk & Michael P. Fay, 2014. "An Introduction to Practical Sequential Inferences via Single-Arm Binary Response Studies Using the binseqtest R Package," The American Statistician, Taylor & Francis Journals, vol. 68(4), pages 230-242, November.
    6. Stephen E. Chick & Noah Gans, 2009. "Economic Analysis of Simulation Selection Problems," Management Science, INFORMS, vol. 55(3), pages 421-437, March.
    7. Paolo Pertile & Martin Forster & Davide La Torre, 2014. "Optimal Bayesian sequential sampling rules for the economic evaluation of health technologies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(2), pages 419-438, February.
    8. Dimitris Bertsimas & Adam J. Mersereau, 2007. "A Learning Approach for Interactive Marketing to a Customer Segment," Operations Research, INFORMS, vol. 55(6), pages 1120-1135, December.
    9. Brezzi, Monica & Lai, Tze Leung, 2002. "Optimal learning and experimentation in bandit problems," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 87-108, November.
    10. Stephen E. Chick & Peter Frazier, 2012. "Sequential Sampling with Economics of Selection Procedures," Management Science, INFORMS, vol. 58(3), pages 550-569, March.
    11. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    12. Lisa V. Hampson & Christopher Jennison, 2013. "Group sequential tests for delayed responses (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 3-54, January.
    13. Marina Roshini Sooriyarachchi & John Whitehead & Kim Bolland & Anne Whitehead, 2003. "Incorporating Data Received after a Sequential Trial Has Stopped into the Final Analysis: Implementation and Comparison of Methods," Biometrics, The International Biometric Society, vol. 59(3), pages 701-709, September.
    14. Felipe Caro & Jérémie Gallien, 2007. "Dynamic Assortment with Demand Learning for Seasonal Consumer Goods," Management Science, INFORMS, vol. 53(2), pages 276-292, February.
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    Cited by:

    1. Nikhil Bhat & Vivek F. Farias & Ciamac C. Moallemi & Deeksha Sinha, 2020. "Near-Optimal A-B Testing," Management Science, INFORMS, vol. 66(10), pages 4477-4495, October.
    2. Williamson, S. Faye & Jacko, Peter & Jaki, Thomas, 2022. "Generalisations of a Bayesian decision-theoretic randomisation procedure and the impact of delayed responses," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    3. Panos Kouvelis & Joseph Milner & Zhili Tian, 2017. "Clinical Trials for New Drug Development: Optimal Investment and Application," Manufacturing & Service Operations Management, INFORMS, vol. 19(3), pages 437-452, July.
    4. Andres Alban & Stephen E. Chick & Martin Forster, 2020. "Value-based clinical trials: selecting trial lengths and recruitment rates in different regulatory contexts," Discussion Papers 20/01, Department of Economics, University of York.
    5. Thijssen, Jacco J.J. & Bregantini, Daniele, 2017. "Costly sequential experimentation and project valuation with an application to health technology assessment," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 202-229.
    6. Vishal Ahuja & John R. Birge, 2020. "An Approximation Approach for Response-Adaptive Clinical Trial Design," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 877-894, October.

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    More about this item

    Keywords

    Bayesian Inference; Clinical Trials; Delayed Observations; Sequential Experimentation;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • I10 - Health, Education, and Welfare - - Health - - - General

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