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Maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects

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  • Chengchun Shi
  • Rui Song
  • Wenbin Lu
  • Bo Fu

Abstract

A salient feature of data from clinical trials and medical studies is inhomogeneity. Patients not only differ in baseline characteristics, but also in the way that they respond to treatment. Optimal individualized treatment regimes are developed to select effective treatments based on patient's heterogeneity. However, the optimal treatment regime might also vary for patients across different subgroups. We mainly consider patients’ heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups. We propose a new maximin projection learning method for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation. Based on estimated optimal treatment regimes for all subgroups, the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming problem, which can be efficiently computed by interior point methods. Consistency and asymptotic normality of the estimator are established. Numerical examples show the reliability of the methodology proposed.

Suggested Citation

  • Chengchun Shi & Rui Song & Wenbin Lu & Bo Fu, 2018. "Maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 681-702, September.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:4:p:681-702
    DOI: 10.1111/rssb.12273
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    Cited by:

    1. Shi, Chengchun & Wan, Runzhe & Song, Ge & Luo, Shikai & Zhu, Hongtu & Song, Rui, 2023. "A multiagent reinforcement learning framework for off-policy evaluation in two-sided markets," LSE Research Online Documents on Economics 117174, London School of Economics and Political Science, LSE Library.
    2. Chengchun Shi & Sheng Zhang & Wenbin Lu & Rui Song, 2022. "Statistical inference of the value function for reinforcement learning in infinite‐horizon settings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 765-793, July.
    3. Shi, Chengchun & Luo, Shikai & Le, Yuan & Zhu, Hongtu & Song, Rui, 2022. "Statistically efficient advantage learning for offline reinforcement learning in infinite horizons," LSE Research Online Documents on Economics 115598, London School of Economics and Political Science, LSE Library.
    4. Gao, Yuhe & Shi, Chengchun & Song, Rui, 2023. "Deep spectral Q-learning with application to mobile health," LSE Research Online Documents on Economics 119445, London School of Economics and Political Science, LSE Library.
    5. Zhou, Yunzhe & Qi, Zhengling & Shi, Chengchun & Li, Lexin, 2023. "Optimizing pessimism in dynamic treatment regimes: a Bayesian learning approach," LSE Research Online Documents on Economics 118233, London School of Economics and Political Science, LSE Library.
    6. Qiong Zhang & Amin Khademi & Yongjia Song, 2022. "Min-Max Optimal Design of Two-Armed Trials with Side Information," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 165-182, January.
    7. Shi, Chengchun & Zhang, Shengxing & Lu, Wenbin & Song, Rui, 2022. "Statistical inference of the value function for reinforcement learning in infinite-horizon settings," LSE Research Online Documents on Economics 110882, London School of Economics and Political Science, LSE Library.

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