Multi-Armed Angle-Based Direct Learning for Estimating Optimal Individualized Treatment Rules With Various Outcomes

References

• Audibert, J.-Y., Tsybakov, A. B., (2007), “Fast Learning Rates for Plug-in Classifiers,” The Annals of Statistics, 35, 608–633. DOI: 10.1214/009053606000001217.
   Web of Science ®Google Scholar
• Bach, F. R., Lanckriet, G. R., and Jordan, M. I. (2004), “Multiple Kernel Learning, Conic Duality, and the SMO Algorithm,” in Proceedings of the Twenty-First International Conference on Machine Learning, p. 6. Banff, Alberta, Canada: ACM.
   Google Scholar
• Bai, X., Tsiatis, A. A., Lu, W., and Song, R. (2016), “Optimal Treatment Regimes for Survival Endpoints Using a Locally-Efficient Doubly-Robust Estimator From a Classification Perspective,” Lifetime Data Analysis, 23, 1–20.
   Web of Science ®Google Scholar
• Baron, G., Perrodeau, E., Boutron, I., and Ravaud, P. (2013), “Reporting of Analyses From Randomized Controlled Trials With Multiple Arms: A Systematic Review,” BMC Medicine, 11, 84. DOI: 10.1186/1741-7015-11-84.
   PubMed Web of Science ®Google Scholar
• Beck, A., and Teboulle, M. (2009), “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems,” SIAM Journal on Imaging Sciences, 2, 183–202. DOI: 10.1137/080716542.
   Web of Science ®Google Scholar
• Bickel, P. J., Ritov, Y., and Tsybakov, A. B. (2009), “Simultaneous Analysis of Lasso and Dantzig Selector,” The Annals of Statistics, 1705–1732. DOI: 10.1214/08-AOS620.
   Web of Science ®Google Scholar
• Breheny, P., and Huang, J. (2015), “Group Descent Algorithms for Nonconvex Penalized Linear and Logistic Regression Models With Grouped Predictors,” Statistics and Computing, 25, 173–187. DOI: 10.1007/s11222-013-9424-2.
   PubMed Web of Science ®Google Scholar
• Breiman, L., and Friedman, J. H. (1997), “Predicting Multivariate Responses in Multiple Linear Regression,” Journal of the Royal Statistical Society, Series B, 59, 3–54. DOI: 10.1111/1467-9868.00054.
   Google Scholar
• Chen, S., Tian, L., Cai, T., and Yu, M. (2017), “A General Statistical Framework for Subgroup Identification and Comparative Treatment Scoring,” Biometrics, 73, 1199–1209. DOI: 10.1111/biom.12676.
   PubMed Web of Science ®Google Scholar
• Cui, Y., Zhu, R., Kosorok, M. (2017), “Tree Based Weighted Learning for Estimating Individualized Treatment Rules With Censored Data,” Electronic Journal of Statistics, 11, 3927–3953. DOI: 10.1214/17-EJS1305.
   PubMed Web of Science ®Google Scholar
• Fan, C., Lu, W., Song, R., and Zhou, Y. (2017), “Concordance-Assisted Learning for Estimating Optimal Individualized Treatment Regimes,” Journal of the Royal Statistical Society, Series B, 79, 1565–1582. DOI: 10.1111/rssb.12216.
   Google Scholar
• Foster, J. C., Taylor, J. M., and Ruberg, S. J. (2011), “Subgroup Identification From Randomized Clinical Trial Data,” Statistics in Medicine, 30, 2867–2880. DOI: 10.1002/sim.4322.
   PubMed Web of Science ®Google Scholar
• Goldberg, Y., and Kosorok, M. R. (2012), “Q-learning With Censored Data,” Annals of Statistics, 40, 529–560. DOI: 10.1214/12-AOS968.
   PubMed Web of Science ®Google Scholar
• Hammer, S. M., Katzenstein, D. A., Hughes, M. D., Gundacker, H., Schooley, R. T., Haubrich, R. H., Henry, W. K., Lederman, M. M., Phair, J. P., Niu, M. (1996), “A Trial Comparing Nucleoside Monotherapy With Combination Therapy in HIV-infected Adults With cd4 Cell Counts From 200 to 500 Per Cubic Millimeter,” New England Journal of Medicine, 335, 1081–1090. DOI: 10.1056/NEJM199610103351501.
   PubMed Web of Science ®Google Scholar
• Jiang, R., Lu, W., Song, R., and Davidian, M. (2017), “On Estimation of Optimal Treatment Regimes for Maximizing t-year Survival Probability,” Journal of the Royal Statistical Society, Series B, 79, 1165–1185. DOI: 10.1111/rssb.12201.
   Google Scholar
• Kakuda, T. N. (2000), “Pharmacology of Nucleoside and Nucleotide Reverse Transcriptase Inhibitor-induced Mitochondrial Toxicity,” Clinical Therapeutics, 22, 685–708. DOI: 10.1016/S0149-2918(00)90004-3.
   PubMed Web of Science ®Google Scholar
• Laber, E., and Zhao, Y. (2015), “Tree-Based Methods for Individualized Treatment Regimes,” Biometrika, 102, 501–514. DOI: 10.1093/biomet/asv028.
   PubMed Web of Science ®Google Scholar
• Liu, Y., Wang, Y., Kosorok, M. R., Zhao, Y., and Zeng, D. (2016), “Robust Hybrid Learning for Estimating Personalized Dynamic Treatment Regimens,” arXiv:1611.02314.
   Google Scholar
• Lounici, K., Pontil, M., Tsybakov, A. B., and Van De Geer, S. (2009), “Taking Advantage of Sparsity in Multi-task Learning,” arXiv:0903.1468.
   Google Scholar
• Lu, W., Zhang, H. H., and Zeng, D. (2013),“Variable Selection for Optimal Treatment Decision,” Statistical Methods in Medical Research, 22(5), 493–504. DOI: 10.1177/0962280211428383.
   PubMed Web of Science ®Google Scholar
• Meier, L., Van De Geer, S., and Bühlmann, P. (2008), “The Group Lasso for Logistic Regression,” Journal of the Royal Statistical Society, Series B, 70, 53–71. DOI: 10.1111/j.1467-9868.2007.00627.x.
   Google Scholar
• Murphy, S. A. (2003), “Optimal Dynamic Treatment Regimes,” Journal of the Royal Statistical Society, Series B, 65, 331–355. DOI: 10.1111/1467-9868.00389.
   Google Scholar
• Murphy, S. A. (2005), “A Generalization Error for q-Learning,” Journal of Machine Learning Research, 6, 1073–1097.
   PubMed Web of Science ®Google Scholar
• Nesterov, Y. (2013), Introductory Lectures on Convex Optimization: A Basic Course (vol. 87), New York: Springer Science & Business Media.
   Google Scholar
• Qi, Z., and Liu, Y. (2018), “D-learning to Estimate Optimal Individual Treatment Rules,” Electronic Journal of Statistics, 12, 3601–3638. DOI: 10.1214/18-EJS1480.
   Web of Science ®Google Scholar
• Qian, M., and Murphy, S. A. (2011), “Performance Guarantees for Individualized Treatment Rules,” Annals of Statistics, 39, 1180–1210. DOI: 10.1214/10-AOS864.
   PubMed Web of Science ®Google Scholar
• Robins, J. M. (2004), “Optimal Structural Nested Models for Optimal Sequential Decisions,” in Proceedings of the Second Seattle Symposium in Biostatistics, New York, NY: Springer, pp. 189–326.
   Google Scholar
• Rohde, A., Tsybakov, A. B. (2011), “Estimation of High-dimensional Low-rank Matrices,” The Annals of Statistics, 39, 887–930. DOI: 10.1214/10-AOS860.
   Web of Science ®Google Scholar
• Tao, Y., and Wang, L. (2017), “Adaptive Contrast Weighted Learning for Multi-stage Multi-treatment Decision-making,” Biometrics, 73, 145–155. DOI: 10.1111/biom.12539.
   PubMed Web of Science ®Google Scholar
• L. Tian, 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,” Journal of the American Statistical Association, 109, 1517–1532. DOI: 10.1080/01621459.2014.951443.
   PubMed Web of Science ®Google Scholar
• Toh, K.-C., and Yun, S. (2010), “An Accelerated Proximal Gradient Algorithm for Nuclear Norm Regularized Linear Least Squares Problems,” Pacific Journal of Optimization, 6, 615–640.
   Web of Science ®Google Scholar
• Watkins, C. J. (1989), “Learning From Delayed Rewards,” PhD thesis, University of Cambridge, UK.
   Google Scholar
• Watkins, C. J., and Dayan, P. (1992), “Q-learning,” Machine Learning, 8, 279–292. DOI: 10.1007/BF00992698.
   Web of Science ®Google Scholar
• Wu, T. T., and Lange, K. (2010), “Multicategory Vertex Discriminant Analysis for High-dimensional Data,” The Annals of Applied Statistics, 4, 1698–1721. DOI: 10.1214/10-AOAS345.
   Web of Science ®Google Scholar
• Zhang, B., Tsiatis, A. A., Laber, E. B., and Davidian, M. (2012), “A Robust Method for Estimating Optimal Treatment Regimes,” Biometrics, 68, 1010–1018. DOI: 10.1111/j.1541-0420.2012.01763.x.
   PubMed Web of Science ®Google Scholar
• Zhang, C., and Liu, Y. (2014), “Multicategory Angle-based Large-margin Classification,” Biometrika, 101, 625–640. DOI: 10.1093/biomet/asu017.
   PubMed Web of Science ®Google Scholar
• Zhang, Y., Laber, E. B., Tsiatis, A., and Davidian, M. (2015), “Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes,” Biometrics, 71, 895–904. DOI: 10.1111/biom.12354.
   PubMed Web of Science ®Google Scholar
• Zhao, Y., Zeng, D., Rush, A. J., and Kosorok, M. R. (2012b), “Estimating Individualized Treatment Rules Using Outcome Weighted Learning,” Journal of the American Statistical Association, 107, 1106–1118. DOI: 10.1080/01621459.2012.695674.
   PubMed Web of Science ®Google Scholar
• Zhao, Y.-Q., Zeng, D., Laber, E. B., and Kosorok, M. R. (2015a), “New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes,” Journal of the American Statistical Association, 110, 583–598. DOI: 10.1080/01621459.2014.937488.
   PubMed Web of Science ®Google Scholar
• Zhao, Y.-Q., Zeng, D., Laber, E. B., Song, R., Yuan, M., and Kosorok, M. R. (2015b), “Doubly Robust Learning for Estimating Individualized Treatment With Censored Data,” Biometrika, 102, 151–168. DOI: 10.1093/biomet/asu050.
   PubMed Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar