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Robust learning for optimal treatment decision with NP-dimensionality

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  • Shi, Chengchun
  • Song, Rui
  • Lu, Wenbin

Abstract

In order to identify important variables that are involved in making optimal treatment decision, Lu, Zhang and Zeng (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the misspecification of the conditional mean model. Two problems arise: (i) in a world of explosively big data, effective methods are needed to handle ultra-high dimensional data set, for example, with the dimension of predictors is of the non-polynomial (NP) order of the sample size; (ii) both the propensity score and conditional mean models need to be estimated from data under NP dimensionality. In this paper, we propose a robust procedure for estimating the optimal treatment regime under NP dimensionality. In both steps, penalized regressions are employed with the non-concave penalty function, where the conditional mean model of the response given predictors may be misspecified. The asymptotic properties, such as weak oracle properties, selection consistency and oracle distributions, of the proposed estimators are investigated. In addition, we study the limiting distribution of the estimated value function for the obtained optimal treatment regime. The empirical performance of the proposed estimation method is evaluated by simulations and an application to a depression dataset from the STAR*D study.

Suggested Citation

  • Shi, Chengchun & Song, Rui & Lu, Wenbin, 2016. "Robust learning for optimal treatment decision with NP-dimensionality," LSE Research Online Documents on Economics 102114, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:102114
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    File URL: http://eprints.lse.ac.uk/102114/
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    References listed on IDEAS

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    1. Baqun Zhang & Anastasios A. Tsiatis & Eric B. Laber & Marie Davidian, 2012. "A Robust Method for Estimating Optimal Treatment Regimes," Biometrics, The International Biometric Society, vol. 68(4), pages 1010-1018, December.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    5. White, Halbert, 1983. "Corrigendum [Maximum Likelihood Estimation of Misspecified Models]," Econometrica, Econometric Society, vol. 51(2), pages 513-513, March.
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    Cited by:

    1. Hyung G. Park & Danni Wu & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2023. "Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 397-418, July.
    2. Muxuan Liang & Menggang Yu, 2023. "Relative contrast estimation and inference for treatment recommendation," Biometrics, The International Biometric Society, vol. 79(4), pages 2920-2932, December.
    3. Hyung Park & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2021. "A constrained single‐index regression for estimating interactions between a treatment and covariates," Biometrics, The International Biometric Society, vol. 77(2), pages 506-518, June.
    4. Hyung Park & Thaddeus Tarpey & Eva Petkova & R. Todd Ogden, 2024. "A high-dimensional single-index regression for interactions between treatment and covariates," Statistical Papers, Springer, vol. 65(7), pages 4025-4056, September.
    5. Hyung Park & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2023. "Functional additive models for optimizing individualized treatment rules," Biometrics, The International Biometric Society, vol. 79(1), pages 113-126, March.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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