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Optimal, two‐stage, adaptive enrichment designs for randomized trials, using sparse linear programming

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  • Michael Rosenblum
  • Ethan X. Fang
  • Han Liu

Abstract

Adaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. The goal is to learn which populations benefit from an experimental treatment. Two critical components of adaptive enrichment designs are the decision rule for modifying enrolment, and the multiple‐testing procedure. We provide a general method for simultaneously optimizing these components for two‐stage, adaptive enrichment designs. We minimize the expected sample size under constraints on power and the familywise type I error rate. It is computationally infeasible to solve this optimization problem directly because of its non‐convexity. The key to our approach is a novel, discrete representation of this optimization problem as a sparse linear program, which is large but computationally feasible to solve by using modern optimization techniques. We provide an R package that implements our method and is compatible with linear program solvers in several software languages. Our approach produces new, approximately optimal trial designs.

Suggested Citation

  • Michael Rosenblum & Ethan X. Fang & Han Liu, 2020. "Optimal, two‐stage, adaptive enrichment designs for randomized trials, using sparse linear programming," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 749-772, July.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:3:p:749-772
    DOI: 10.1111/rssb.12366
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    References listed on IDEAS

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    1. Walter Lehmacher & Gernot Wassmer, 1999. "Adaptive Sample Size Calculations in Group Sequential Trials," Biometrics, The International Biometric Society, vol. 55(4), pages 1286-1290, December.
    2. Michael Rosenblum & Han Liu & En-Hsu Yen, 2014. "Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1216-1228, September.
    3. S. M. Lewis & A. M. Dean, 2001. "Detection of interactions in experiments on large numbers of factors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 633-672.
    4. M. Rosenblum & M. J. van der Laan, 2011. "Optimizing randomized trial designs to distinguish which subpopulations benefit from treatment," Biometrika, Biometrika Trust, vol. 98(4), pages 845-860.
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    Citations

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    Cited by:

    1. Nigel Stallard, 2023. "Rejoinder to discussion on “Adaptive enrichment designs with a continuous biomarker”," Biometrics, The International Biometric Society, vol. 79(1), pages 36-38, March.
    2. Alessandro Baldi Antognini & Rosamarie Frieri & Maroussa Zagoraiou, 2023. "New insights into adaptive enrichment designs," Statistical Papers, Springer, vol. 64(4), pages 1305-1328, August.
    3. Rachael V. Phillips & Mark J. van der Laan, 2023. "Discussion on “Adaptive enrichment designs with a continuous biomarker” by Nigel Stallard," Biometrics, The International Biometric Society, vol. 79(1), pages 20-22, March.
    4. Christopher Jennison, 2023. "Discussion on “Adaptive enrichment designs with a continuous biomarker” by N. Stallard," Biometrics, The International Biometric Society, vol. 79(1), pages 26-30, March.
    5. Nigel Stallard, 2023. "Adaptive enrichment designs with a continuous biomarker," Biometrics, The International Biometric Society, vol. 79(1), pages 9-19, March.
    6. Ke Sun & Linglong Kong & Hongtu Zhu & Chengchun Shi, 2024. "Optimal Treatment Allocation Strategies for A/B Testing in Partially Observable Time Series Experiments," Papers 2408.05342, arXiv.org, revised Oct 2024.

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