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Theory and Methods Special Issue on Precision Medicine and Individualized Policy Discovery

Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve With High-Dimensional Covariates

, &
Pages 309-321 | Received 29 Apr 2019, Accepted 22 Sep 2020, Published online: 09 Mar 2021

References

  • Breheny, P., and Huang, J. (2011), “Coordinate Descent Algorithms for Nonconvex Penalized Regression, With Applications to Biological Feature Selection,” The Annals of Applied Statistics, 5, 232–253. DOI: 10.1214/10-AOAS388.
  • Cai, T., Tian, L., Wong, P. H., and Wei, L. J. (2011), “Analysis of Randomized Comparative Clinical Trial Data for Personalized Treatment Selections,” Biostatistics, 12, 270–282. DOI: 10.1093/biostatistics/kxq060.
  • Chen, G., Zeng, D., and Kosorok, M. R. (2016), “Personalized Dose Finding Using Outcome Weighted Learning,” Journal of the American Statistical Association, 111, 1509–1547. DOI: 10.1080/01621459.2016.1148611.
  • Chen, X., and Christensen, T. M. (2015), “Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions,” Journal of Econometrics, 188, 447–465. DOI: 10.1016/j.jeconom.2015.03.010.
  • de Boor, C. (2001), A Practical Guide to Splines, Applied Mathematical Sciences, New York: Springer-Verlag.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360. DOI: 10.1198/016214501753382273.
  • Fan, J., and Lv, J. (2011), “Nonconcave Penalized Likelihood With NP-Dimensionality,” IEEE Transactions on Information Theory, 57, 5467–5484. DOI: 10.1109/TIT.2011.2158486.
  • Han, K., Zhou, X.-H., and Liu, B. (2017), “CSTE Curve for Selection the Optimal Treatment When Outcome Is Binary,” Scientia Sinica Mathematica, 47, 497–514.
  • Huang, Y. (2015), “Identifying Optimal Biomarker Combinations for Treatment Selection Through Randomized Controlled Trials,” Clinical Trials, 12, 348–56. DOI: 10.1177/1740774515580126.
  • Huang, Y., and Fong, Y. (2014), “Identifying Optimal Biomarker Combinations for Treatment Selection via a Robust Kernel Method,” Biometrics, 70, 891–901. DOI: 10.1111/biom.12204.
  • Janes, H., Brown, M. D., Huang, Y., and Pepe, M. S. (2014), “An Approach to Evaluating and Comparing Biomarkers for Patient Treatment Selection,” The International Journal of Biostatistics, 10, 99–121. DOI: 10.1515/ijb-2012-0052.
  • Jiang, B., and Liu, J. (2014), “Variable Selection for General Index Models via Sliced Inverse Regression,” The Annals of Statistics, 42, 1751–1786. DOI: 10.1214/14-AOS1233.
  • Jiang, B., Song, R., Li, J., and Zeng, D. (2019), “Entropy Learning for Dynamic Treatment Regimes,” Statistica Sinica, 29, 1633–1655.
  • Kang, C., Janes, H., and Huang, Y. (2014), “Combining Biomarkers to Optimize Patient Treatment Recommendations,” Biometrics, 70, 695–707. DOI: 10.1111/biom.12191.
  • Kosorok, M. R., and Laber, E. B. (2019), “Precision Medicine,” Annual Review of Statistics and Its Application, 6, 263–286. DOI: 10.1146/annurev-statistics-030718-105251.
  • Laber, E. B., and Qian, M. (2019), “Generalization Error for Decision Problems,” Wiley StatsRef: Statistics Reference Online (accepted).
  • Laber, E. B., and Zhao, Y. Q. (2015), “Tree-Based Methods for Individualized Treatment Regimes,” Biometrika, 102, 501–514. DOI: 10.1093/biomet/asv028.
  • Liu, R., Yang, L., and Härdle, W. K. (2013), “Oracally Efficient Two-Step Estimation of Generalized Additive Model,” Journal of the American Statistical Association, 108, 619–631. DOI: 10.1080/01621459.2013.763726.
  • Luckett, D. J., Laber, E. B., Kahkoska, A. R., Maahs, D. M., Mayer-Davis, E., and Kosorok, M. R. (2020), “Estimating Dynamic Treatment Regimes in Mobile Health Using V-Learning,” Journal of the American Statistical Association, 115, 692–706. DOI: 10.1080/01621459.2018.1537919.
  • Ma, S., and He, X. (2016), “Inference for Single-Index Quantile Regression Models With Profile Optimization,” The Annals of Statistics, 44, 1234–1268. DOI: 10.1214/15-AOS1404.
  • Ma, S., and Song, P. X.-K. (2015), “Varying Index Coefficient Models,” Journal of the American Statistical Association, 110, 341–356. DOI: 10.1080/01621459.2014.903185.
  • Ma, S., and Yang, L. (2011), “A Jump-Detecting Procedure Based on Spline Estimation,” Journal of Nonparametric Statistics, 23, 67–81. DOI: 10.1080/10485250903571978.
  • Ma, Y., and Zhou, X.-H. (2014), “Treatment Selection in a Randomized Clinical Trial via Covariate-Specific Treatment Effect Curves,” Statistical Methods in Medical Research, 26, 124–141. DOI: 10.1177/0962280214541724.
  • Neykov, M., Liu, J., and Cai, T. (2016), “L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models With Gaussian Designs,” Journal of Machine Learning Research, 17, 1–37.
  • Qian, M., and Murphy, S. A. (2011), “Performance Guarantees for Individualized Treatment Rules,” The Annals of Statistics, 39, 1180–1210. DOI: 10.1214/10-AOS864.
  • Radchenko, P. (2015), “High Dimensional Single Index Models,” Journal of Multivariate Analysis, 139, 266–282. DOI: 10.1016/j.jmva.2015.02.007.
  • Rubin, D. B. (2005), “Causal Inference Using Potential Outcomes,” Journal of the American Statistical Association, 100, 322–331. DOI: 10.1198/016214504000001880.
  • Rubin, D. B., and van der Laan, M. J. (2012), “Statistical Issues and Limitations in Personalized Medicine Research With Clinical Trials,” The International Journal of Biostatistics, 8, 18. DOI: 10.1515/1557-4679.1423.
  • Shi, C., Fan, A., Song, R., and Lu, W. (2018), “High-Dimensional a-Learning for Optimal Dynamic Treatment Regimes,” The Annals of Statistics, 46, 925–957. DOI: 10.1214/17-AOS1570.
  • Song, R., Luo, S., Zeng, D., Zhang, H., Lu, W., and Li, Z. (2017), “Semiparametric Single-Index Model for Estimating Optimal Individualized Treatment Strategy,” Electronic Journal of Statistics, 11, 364–384. DOI: 10.1214/17-EJS1226.
  • Stone, C. (1985), “Additive Regression and Other Nonparametric Models,” The Annals of Statistics, 13, 689–705. DOI: 10.1214/aos/1176349548.
  • Taylor, J. M. G., Cheng, W., and Foster, J. C. (2015), “Reader Reaction to ‘a Robust Method for Estimating Optimal Treatment Regimes’ by Zhang et al. (2012),” Biometrics, 71, 267–273. DOI: 10.1111/biom.12228.
  • Wager, S., and Athey, S. (2018), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association, 113, 1228–1242. DOI: 10.1080/01621459.2017.1319839.
  • Wang, H., Li, B., and Leng, C. (2009), “Shrinkage Tuning Parameter Selection With a Diverging Number of Parameters,” Journal of the Royal Statistical Society, Series B, 71, 671–683. DOI: 10.1111/j.1467-9868.2008.00693.x.
  • Wang, L., and Yang, L. (2007), “Spline-Backfitted Kernel Smoothing of Nonlinear Additive Autoregression Model,” The Annals of Statistics, 35, 2474–2503. DOI: 10.1214/009053607000000488.
  • Watson, M. W., and Engle, R. F. (1983), “Alternative Algorithms for the Estimation of Dynamic Factor, Mimic and Varying Coefficient Regression Models,” Journal of Econometrics, 23, 385–400. DOI: 10.1016/0304-4076(83)90066-0.
  • Wu, T. (2016), “Set Valued Dynamic Treatment Regimes,” Ph.D. thesis, The University of Michigan.
  • Zhang, B., Tsiatis, A. A., Davidian, M., Zhang, M., and Laber, E. (2012), “Estimating Optimal Treatment Regimes From a Classification Perspective,” Stat, 1, 103–114. DOI: 10.1002/sta.411.
  • Zhang, B., and Zhang, M. (2018), “C-Learning: A New Classification Framework to Estimate Optimal Dynamic Treatment Regimes,” Biometrics, 74, 891–899. DOI: 10.1111/biom.12836.
  • Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
  • Zhang, Y., Laber, E. B., Davidian, M., and Tsiatis, A. A. (2018), “Interpretable Dynamic Treatment Regimes,” Journal of the American Statistical Association, 113, 1541–1549. DOI: 10.1080/01621459.2017.1345743.
  • Zhao, Y., Zeng, D., Rush, A. J., and Kosorok, M. R. (2012), “Estimating Individualized Treatment Rules Using Outcome Weighted Learning,” Journal of the American Statistical Association, 107, 1106–1118. DOI: 10.1080/01621459.2012.695674.
  • Zheng, S., Liu, R., Yang, L., and Härdle, W. K. (2016), “Statistical Inference for Generalized Additive Models: Simultaneous Confidence Corridors and Variable Selection,” TEST, 25, 607–626. DOI: 10.1007/s11749-016-0480-8.
  • Zhou, X., Mayer-Hamblett, N., Khan, U., and Kosorok, M. R. (2017), “Residual Weighted Learning for Estimating Individualized Treatment Rules,” Journal of the American Statistical Association, 112, 169–187. DOI: 10.1080/01621459.2015.1093947.
  • Zhou, X.-H., and Ma, Y. B. (2012), “BATE Curve in Assessment of Clinical Utility of Predictive Biomarkers,” Science China Mathematics, 55, 1529–1552. DOI: 10.1007/s11425-012-4473-0.
  • Zhu, K., Huang, Y., and Zhou, X.-H. (2018), “Tree-Based Ensemble Methods for Individualized Treatment Rules,” Biostatistics & Epidemiology, 2, 61–83.
  • Zhu, W., Zeng, D., and Song, R. (2019), “Proper Inference for Value Function in High-Dimensional Q-Learning for Dynamic Treatment Regimes,” Journal of the American Statistical Association, 114, 1404–1417. DOI: 10.1080/01621459.2018.1506341.