The Annals of Applied Statistics

Variable selection for estimating the optimal treatment regimes in the presence of a large number of covariates

Baqun Zhang and Min Zhang

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Abstract

Most existing methods for optimal treatment regimes, with few exceptions, focus on estimation and are not designed for variable selection with the objective of optimizing treatment decisions. In clinical trials and observational studies, often numerous baseline variables are collected and variable selection is essential for deriving reliable optimal treatment regimes. Although many variable selection methods exist, they mostly focus on selecting variables that are important for prediction (predictive variables) instead of variables that have a qualitative interaction with treatment (prescriptive variables) and hence are important for making treatment decisions. We propose a variable selection method within a general classification framework to select prescriptive variables and estimate the optimal treatment regime simultaneously. In this framework, an optimal treatment regime is equivalently defined as the one that minimizes a weighted misclassification error rate and the proposed method forward sequentially select prescriptive variables by minimizing this weighted misclassification error. A main advantage of this method is that it specifically targets selection of prescriptive variables and in the meantime is able to exploit predictive variables to improve performance. The method can be applied to both single- and multiple-decision point setting. The performance of the proposed method is evaluated by simulation studies and application to a clinical trial.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 4 (2018), 2335-2358.

Dates
Received: August 2017
Revised: October 2017
First available in Project Euclid: 13 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1542078047

Digital Object Identifier
doi:10.1214/18-AOAS1154

Mathematical Reviews number (MathSciNet)
MR3875703

Keywords
C-learning classification high-dimensional data misclassification error personalized medicine dynamic treatment regime variable selection

Citation

Zhang, Baqun; Zhang, Min. Variable selection for estimating the optimal treatment regimes in the presence of a large number of covariates. Ann. Appl. Stat. 12 (2018), no. 4, 2335--2358. doi:10.1214/18-AOAS1154. https://projecteuclid.org/euclid.aoas/1542078047


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References

  • Bang, H. and Robins, J. M. (2005). Doubly robust estimation in missing data and causal inference models. Biometrics 61 962–972.
  • Barrett, J. K., Henderson, R. and Rosthøj, C. (2014). Doubly robust estimation of optimal dynamic treatment regimes. Stat. Biosci. 6 244–260.
  • Biernot, P. and Moodie, E. E. M. (2010). A comparison of variable selection approaches for dynamic treatment regimes. Int. J. Biostat. 6 Article ID 6.
  • Brinkley, J., Tsiatis, A. and Anstrom, K. J. (2010). A generalized estimator of the attributable benefit of an optimal treatment regime. Biometrics 66 512–522.
  • Chakraborty, B., Murphy, S. and Strecher, V. (2010). Inference for non-regular parameters in optimal dynamic treatment regimes. Stat. Methods Med. Res. 19 317–343.
  • Fan, A., Lu, W. and Song, R. (2016). Sequential advantage selection for optimal treatment regime. Ann. Appl. Stat. 10 32–53.
  • Geng, Y., Zhang, H. H. and Lu, W. (2015). On optimal treatment regimes selection for mean survival time. Stat. Med. 34 1169–1184.
  • Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA.
  • Gunter, L., Zhu, J. and Murphy, S. A. (2011). Variable selection for qualitative interactions. Stat. Methodol. 8 42–55.
  • Kang, C., Janes, H. and Huang, Y. (2014). Combining biomarkers to optimize patient treatment recommendations. Biometrics 70 695–720.
  • Keller, M. B., McCullough, J. P., Klein, D. N., Arnow, B., Dunner, D. L., Gelenberg, A. J., Marekowitz, J. C., Nemeroff, C. B., Russell, J. M., Thase, M. E., Trivedi, M. H. and Zajecka, J. (2000). A comparison of nefazodone, the cognitive behavioral-analysis system of psychotherapy, and their combination for treatment of chronic depression. N. Engl. J. Med. 342 331–336.
  • Lu, W., Zhang, H. H. and Zeng, D. (2013). Variable selection for optimal treatment decision. Stat. Methods Med. Res. 22 493–504.
  • Mebane, W. R. and Sekhon, J. S. (2011). Genetic optimization using derivatives: The rgenoud package for R. J. Stat. Softw. 42 1–26.
  • Moodie, E. E. M., Richardson, T. S. and Stephens, D. A. (2007). Demystifying optimal dynamic treatment regimes. Biometrics 63 447–455.
  • Murphy, S. A. (2003). Optimal dynamic treatment regimes. J. R. Stat. Soc. Ser. B. Stat. Methodol. 65 331–366.
  • Peto, R. (1982). Statistical aspects of cancer trials. In Treatment of Cancer (K. Halnan, ed.) 867–871. Chapman, London.
  • Qian, M. and Murphy, S. A. (2011). Performance guarantees for individualized treatment rules. Ann. Statist. 39 1180–1210.
  • Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In Proceedings of the Second Seattle Symposium in Biostatistics (D. Y. Halnan and P. J. Halnan, eds.). Lect. Notes Stat. 179 189–326. Springer, New York.
  • Robins, J., Orellana, L. and Rotnitzky, A. (2008). Estimation and extrapolation of optimal treatment and testing strategies. Stat. Med. 27 4678–4721.
  • Schulte, P. J., Tsiatis, A. A., Laber, E. B. and Davidian, M. (2014). $Q$- and $A$-learning methods for estimating optimal dynamic treatment regimes. Statist. Sci. 29 640–661.
  • Tian, L., Alizadeh, A. A., Gentles, A. J. and Tibshirani, R. (2014). A simple method for estimating interactions between a treatment and a large number of covariates. J. Amer. Statist. Assoc. 109 1517–1532.
  • Watkins, C. J. C. H. and Dayan, P. (1992). Q-learning. Mach. Learn. 8 279–292.
  • Young, J. G., Cain, L. E., Robins, J. M., O’Reilly, E. J. and Hernán, M. A. (2011). Comparative effectiveness of dynamic treatment regimes: An application of the parametric g-formula. Stat. Biosci. 3 119–143.
  • Zhang, B. and Zhang, M. (2015). C-learning: A new classification framework to estimate optimal dynamic treatment regimes. Working Paper 116, Dept. Biostatistics, Univ. Michigan, Working Paper Series.
  • Zhang, B. and Zhang, M. (2018). Supplement to “Variable selection for estimating the optimal treatment regimes in the presence of a large number of covariates.” DOI:10.1214/18-AOAS1154SUPP.
  • Zhang, B., Tsiatis, A. A., Laber, E. B. and Davidian, M. (2012a). A robust method for estimating optimal treatment regimes. Biometrics 68 1010–1018.
  • Zhang, B., Tsiatis, A. A., Davidian, M., Zhang, M. and Laber, E. (2012b). Estimating optimal treatment regimes from a classification perspective. Stat. 1 103–114.
  • Zhang, B., Tsiatis, A. A., Laber, E. B. and Davidian, M. (2013). Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions. Biometrika 100 681–694.
  • Zhao, Y., Zeng, D., Rush, A. J. and Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning. J. Amer. Statist. Assoc. 107 1106–1118.
  • Zhao, Y.-Q., Zeng, D., Laber, E. B. and Kosorok, M. R. (2015). New statistical learning methods for estimating optimal dynamic treatment regimes. J. Amer. Statist. Assoc. 110 583–598.

Supplemental materials

  • Additional results. We provide additional simulation and data analysis results.