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Designing Optimal, Data-Driven Policies from Multisite Randomized Trials

Published online by Cambridge University Press:  01 January 2025

Youmi Suk Open the ORCID record for Youmi Suk [Opens in a new window]  and
Chan Park
Youmi Suk*
Affiliation:
Teachers College, Columbia University
Chan Park
Affiliation:
University of Pennsylvania
*
Correspondence should be made to Youmi Suk, Department of Human Development, Teachers College, Columbia University, 525 West 120th Street, New York, NY10027, USA. Email: ysuk@tc.columbia.edu
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Abstract

Optimal treatment regimes (OTRs) have been widely employed in computer science and personalized medicine to provide data-driven, optimal recommendations to individuals. However, previous research on OTRs has primarily focused on settings that are independent and identically distributed, with little attention given to the unique characteristics of educational settings, where students are nested within schools and there are hierarchical dependencies. The goal of this study is to propose a framework for designing OTRs from multisite randomized trials, a commonly used experimental design in education and psychology to evaluate educational programs. We investigate modifications to popular OTR methods, specifically Q-learning and weighting methods, in order to improve their performance in multisite randomized trials. A total of 12 modifications, 6 for Q-learning and 6 for weighting, are proposed by utilizing different multilevel models, moderators, and augmentations. Simulation studies reveal that all Q-learning modifications improve performance in multisite randomized trials and the modifications that incorporate random treatment effects show the most promise in handling cluster-level moderators. Among weighting methods, the modification that incorporates cluster dummies into moderator variables and augmentation terms performs best across simulation conditions. The proposed modifications are demonstrated through an application to estimate an OTR of conditional cash transfer programs using a multisite randomized trial in Colombia to maximize educational attainment.

Keywords

optimal treatment regimesoptimal treatment rulespersonalized learningQ-learningweightingheterogeneous treatment effectsmultilevel dataclustered dataconditional cash transfer program

Information

Type
Application Reviews and Case Studies
Information
Psychometrika , Volume 88 , Issue 4 , December 2023 , pp. 1171 - 1196
Copyright
Copyright © 2023 The Author(s) under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-023-09937-2.

The manuscript was handled by the ARCS Editor Dr. Nidhi Kohli

References

References

Agniel, D., Almirall, D., Burkhart, Q., Grant, S., Hunter, S. B., Pedersen, E. R., Ramchand, R., & Griffin, B. A. (2020). Identifying optimal level-of-care placement decisions for adolescent substance use treatment. Drug and Alcohol Dependence, 212, 107991. https://doi.org/10.1016/j.drugalcdep.2020.107991CrossRefGoogle ScholarPubMed
Arboleda, F. L. T., & Valverde, M. (2021). The travels of a set of numbers: The multiple networks enabled by the Colombian ‘Estrato’ system. Social & Legal Studies, 30(5), 685–703. https://doi.org/10.1177/0964663920960536CrossRefGoogle Scholar
Athey, S., Tibshirani, J., & Wager, S. (2019). Generalized random forests. The Annals of Statistics, 47(2), 1148–1178. https://doi.org/10.1214/18-AOS1709CrossRefGoogle Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2019). Replication data for: Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia (tech. rep.). Inter-University Consortium for Political and Social Research. https://doi.org/10.3886/E113783V1Google Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2011). Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia. American Economic Journal: Applied Economics, 3(2), 167–195. https://doi.org/10.1257/app.3.2.167Google Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2011b). Replication data for: Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia [Ann Arbor, MI: Inter-University Consortium for Political and Social Research [distributor], 2019-10-12]. https://doi.org/10.3886/E113783V1 CrossRefGoogle Scholar
Barrera-Osorio, F., Linden, L. L., & Saavedra, J. E. (2019). Medium-and long-term educational consequences of alternative conditional cash transfer designs: Experimental evidence from Colombia. American Economic Journal: Applied Economics, 11(3), 54–91. https://doi.org/10.1257/app.20170008Google ScholarPubMed
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01CrossRefGoogle Scholar
Chakraborty, B., Laber, E. B., & Zhao, Y. (2013). Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme. Biometrics, 69(3), 714–723.CrossRefGoogle ScholarPubMed
Chakraborty, B., & Moodie, E. (2013). Statistical methods for dynamic treatment regimes. Springer. https://doi.org/10.1007/978-1-4614-7428-9 CrossRefGoogle ScholarPubMed
Chen, S., Tian, L., Cai, T., & Yu, M. (2017). A general statistical framework for subgroup identification and comparative treatment scoring. Biometrics, 73, 1199–1209. https://doi.org/10.1111/biom.12676CrossRefGoogle ScholarPubMed
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1–C68. https://doi.org/10.1111/ectj.12097CrossRefGoogle Scholar
Feller, A., & Gelman, A. (2015). Hierarchical models for causal effects. https://doi.org/10.1002/9781118900772.etrds0160 CrossRefGoogle Scholar
Firebaugh, G., Warner, C., & Massoglia, M. (2013). Fixed effects, random effects, and hybrid models for causal analysis. In Morgan, S. L. (Ed.), Handbook of causal analysis for social research (pp. 113–132). Springer. https://doi.org/10.1007/978-94-007-6094-3_7 CrossRefGoogle Scholar
Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference. Journal of Computational and Graphical Statistics, 20(1), 217–240. https://doi.org/10.1198/jcgs.2010.08162CrossRefGoogle Scholar
Huling, J. D., & Yu, M. (2021). Subgroup identification using the personalized package. Journal of Statistical Software, 98(5), 1–60. https://doi.org/10.18637/jss.v098.i05CrossRefGoogle Scholar
Imbens, G. W., & Rubin, D. B. (2015). Causal inference in statistics, social, and biomedical sciences. Cambridge University Press. https://doi.org/10.1017/cbo9781139025751 CrossRefGoogle Scholar
Kim, K., & Zubizarreta, J. R. (2023). Fair and robust estimation of heterogeneous treatment effects for policy learning. In Proceedings of the 40-th international conference on machine learning. https://doi.org/10.48550/arXiv.2306.03625 CrossRefGoogle Scholar
Kosorok, M. R., & Moodie, E. E. M. (2015). Adaptive treatment strategies in practice: Planning trials and analyzing data for personalized medicine. Society for Industrial and Applied Mathematics, Philadelphia, PA. https://doi.org/10.1137/1.9781611974188 CrossRefGoogle Scholar
Lee, Y., Nguyen, T. Q., & Stuart, E. A. (2021). Partially pooled propensity score models for average treatment effect estimation with multilevel data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 184(4), 1578–1598. https://doi.org/10.1111/rssa.12741CrossRefGoogle Scholar
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22. https://doi.org/10.1093/biomet/73.1.13CrossRefGoogle Scholar
Logan, B. R., Sparapani, R., McCulloch, R. E., & Laud, P. W. (2019). Decision making and uncertainty quantification for individualized treatments using Bayesian additive regression trees. Statistical Methods in Medical Research, 28(4), 1079–1093.CrossRefGoogle ScholarPubMed
Mitchell, S., Potash, E., Barocas, S., D’Amour, A., & Lum, K. (2021). Algorithmic fairness: Choices, assumptions, and definitions. Annual Review of Statistics and its Application, 8, 141–163. https://doi.org/10.1146/annurev-statistics-042720-125902CrossRefGoogle Scholar
Murphy, S. A. (2003). Optimal dynamic treatment regimes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 331–355. https://doi.org/10.1111/1467-9868.00389CrossRefGoogle Scholar
Murphy, S. A. (2005). An experimental design for the development of adaptive treatment strategies. Statistics in Medicine, 24(10), 1455–1481. https://doi.org/10.1002/sim.2022CrossRefGoogle ScholarPubMed
Murphy, S. A., Lynch, K. G., Oslin, D., McKay, J. R., & TenHave, T. (2007). Developing adaptive treatment strategies in substance abuse research. Drug and Alcohol Dependence, 88 S24–S30. https://doi.org/10.1016/j.drugalcdep.2006.09.008CrossRefGoogle ScholarPubMed
Murphy, S. A., Oslin, D. W., Rush, A. J., & Zhu, J. (2007). Methodological challenges in constructing effective treatment sequences for chronic psychiatric disorders. Neuropsychopharmacology, 32(2), 257–262. https://doi.org/10.1038/sj.npp.1301241CrossRefGoogle ScholarPubMed
Murray, T. A., Yuan, Y., & Thall, P. F. (2018). A Bayesian machine learning approach for optimizing dynamic treatment regimes. Journal of the American Statistical Association, 113(523), 1255–1267. https://doi.org/10.1080/01621459.2017.1340887CrossRefGoogle ScholarPubMed
Nabi, R., Malinsky, D., & Shpitser, I. (2019). Learning optimal fair policies. In Proceedings of the 36th international conference on machine learning (vol. 32, no. 1, pp. 4674–4682). https://doi.org/10.1609/aaai.v32i1.11553 CrossRefGoogle Scholar
Neyman, J. S. (1923). On the application of probability theory to agricultural experiments: Essay on principles. Section 9 (with discussion). Statistical Science, 4, 465–480.Google Scholar
Park, C., & Kang, H. (2022). Efficient semiparametric estimation of network treatment effects under partial interference [asac009]. Biometrika, 109(4), 1015–1031.CrossRefGoogle Scholar
Qian, M., & Murphy, S. A. (2011). Performance guarantees for individualized treatment rules. The Annals of Statistics, 39(2), 1180–1210. https://doi.org/10.1214/10-AOS864CrossRefGoogle ScholarPubMed
Raudenbush, S. W. (2009). Adaptive centering with random effects: An alternative to the fixed effects model for studying time-varying treatments in school settings. Education Finance and Policy, 4(4), 468–491. https://doi.org/10.1162/edfp.2009.4.4.468CrossRefGoogle Scholar
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1). Sage.Google Scholar
Raudenbush, S. W., & Schwartz, D. (2020). Randomized experiments in education, with implications for multilevel causal inference. Annual Review of Statistics and Its Application, 7(1), 177–208. https://doi.org/10.1146/annurev-statistics-031219-041205CrossRefGoogle Scholar
Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In Proceedings of the second Seattle symposium in biostatistics (pp. 189–326). https://doi.org/10.1007/978-1-4419-9076-1_11 CrossRefGoogle Scholar
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5), 688–701. https://doi.org/10.1037/h0037350CrossRefGoogle Scholar
Rubin, D. B. (1986). Comment: Which ifs have causal answers. Journal of the American Statistical Association, 81(396), 961–962. https://doi.org/10.2307/2289065Google Scholar
Stefanski, L. A., & Boos, D. D. (2002). The calculus of M-estimation. The American Statistician, 56(1), 29–38. https://doi.org/10.1198/000313002753631330CrossRefGoogle Scholar
Suk, Y. (2023). A within-group approach to ensemble machine learning methods for causal inference in multilevel studies. Journal of Educational and Behavioral Statistics. https://doi.org/10.3102/10769986231162096Google Scholar
Suk, Y., & Han, K. T. (2023). A psychometric framework for evaluating fairness in algorithmic decision making: Differential algorithmic functioning. Journal of Educational and Behavioral Statistics. https://doi.org/10.3102/10769986231171711Google Scholar
Suk, Y., & Kang, H. (2022). Robust machine learning for treatment effects in multilevel observational studies under cluster-level unmeasured confounding. Psychometrika, 87(1), 310–343. https://doi.org/10.1007/s11336-021-09805-xCrossRefGoogle ScholarPubMed
Suk, Y., & Kang, H. (2022). Tuning random forests for causal inference under cluster-level unmeasured confounding. Multivariate Behavioral Research. https://doi.org/10.1080/00273171.2021.1994364Google ScholarPubMed
Suk, Y., Kang, H., & Kim, J.-S. (2021). Random forests approach for causal inference with clustered observational data. Multivariate Behavioral Research, 56(6), 829–852. https://doi.org/10.1080/00273171.2020.1808437CrossRefGoogle ScholarPubMed
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.xCrossRefGoogle Scholar
Tsiatis, A. A., Davidian, M., Holloway, S. T., & Laber, E. B. (2019). Dynamic treatment regimes: Statistical methods for precision medicine. Hall/CRC. https://doi.org/10.1201/9780429192692 CrossRefGoogle Scholar
van der Vaart, A. W. (2000). Asymptotic statistics (Vol. 3). Cambridge University Press. https://doi.org/10.1017/cbo978051180225 Google Scholar
Wager, S., & Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523), 1228–1242. https://doi.org/10.1080/01621459.2017.1319839CrossRefGoogle Scholar
Watkins, C. J., & Dayan, P. (1992). Q-learning. Machine learning, 8(3), 279–292. https://doi.org/10.1023/a:1022676722315CrossRefGoogle Scholar
Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. The MIT press.Google Scholar
Zhang, B., Tsiatis, A. A., Davidian, M., Zhang, M., & Laber, E. (2012). Estimating optimal treatment regimes from a classification perspective. Stat, 1(1), 103–114. https://doi.org/10.1002/sta.411CrossRefGoogle ScholarPubMed
Zhao, Y., Zeng, D., Rush, A. J., & Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning. Journal of the American Statistical Association, 107(499), 1106–1118. https://doi.org/10.1080/01621459.2012.695674CrossRefGoogle ScholarPubMed
Agniel, D., Almirall, D., Burkhart, Q., Grant, S., Hunter, S. B., Pedersen, E. R., Ramchand, R., & Griffin, B. A. (2020). Identifying optimal level-of-care placement decisions for adolescent substance use treatment. Drug and Alcohol Dependence, 212, 107991. https://doi.org/10.1016/j.drugalcdep.2020.107991CrossRefGoogle ScholarPubMed
Arboleda, F. L. T., & Valverde, M. (2021). The travels of a set of numbers: The multiple networks enabled by the Colombian ‘Estrato’ system. Social & Legal Studies, 30(5), 685–703. https://doi.org/10.1177/0964663920960536CrossRefGoogle Scholar
Athey, S., Tibshirani, J., & Wager, S. (2019). Generalized random forests. The Annals of Statistics, 47(2), 1148–1178. https://doi.org/10.1214/18-AOS1709CrossRefGoogle Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2019). Replication data for: Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia (tech. rep.). Inter-University Consortium for Political and Social Research. https://doi.org/10.3886/E113783V1Google Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2011). Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia. American Economic Journal: Applied Economics, 3(2), 167–195. https://doi.org/10.1257/app.3.2.167Google Scholar
Barrera-Osorio, F., Bertrand, M., Linden, L. L., & Perez-Calle, F. (2011b). Replication data for: Improving the design of conditional transfer programs: Evidence from a randomized education experiment in Colombia [Ann Arbor, MI: Inter-University Consortium for Political and Social Research [distributor], 2019-10-12]. https://doi.org/10.3886/E113783V1 CrossRefGoogle Scholar
Barrera-Osorio, F., Linden, L. L., & Saavedra, J. E. (2019). Medium-and long-term educational consequences of alternative conditional cash transfer designs: Experimental evidence from Colombia. American Economic Journal: Applied Economics, 11(3), 54–91. https://doi.org/10.1257/app.20170008Google ScholarPubMed
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01CrossRefGoogle Scholar
Chakraborty, B., Laber, E. B., & Zhao, Y. (2013). Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme. Biometrics, 69(3), 714–723.CrossRefGoogle ScholarPubMed
Chakraborty, B., & Moodie, E. (2013). Statistical methods for dynamic treatment regimes. Springer. https://doi.org/10.1007/978-1-4614-7428-9 CrossRefGoogle ScholarPubMed
Chen, S., Tian, L., Cai, T., & Yu, M. (2017). A general statistical framework for subgroup identification and comparative treatment scoring. Biometrics, 73, 1199–1209. https://doi.org/10.1111/biom.12676CrossRefGoogle ScholarPubMed
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1–C68. https://doi.org/10.1111/ectj.12097CrossRefGoogle Scholar
Feller, A., & Gelman, A. (2015). Hierarchical models for causal effects. https://doi.org/10.1002/9781118900772.etrds0160 CrossRefGoogle Scholar
Firebaugh, G., Warner, C., & Massoglia, M. (2013). Fixed effects, random effects, and hybrid models for causal analysis. In Morgan, S. L. (Ed.), Handbook of causal analysis for social research (pp. 113–132). Springer. https://doi.org/10.1007/978-94-007-6094-3_7 CrossRefGoogle Scholar
Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference. Journal of Computational and Graphical Statistics, 20(1), 217–240. https://doi.org/10.1198/jcgs.2010.08162CrossRefGoogle Scholar
Huling, J. D., & Yu, M. (2021). Subgroup identification using the personalized package. Journal of Statistical Software, 98(5), 1–60. https://doi.org/10.18637/jss.v098.i05CrossRefGoogle Scholar
Imbens, G. W., & Rubin, D. B. (2015). Causal inference in statistics, social, and biomedical sciences. Cambridge University Press. https://doi.org/10.1017/cbo9781139025751 CrossRefGoogle Scholar
Kim, K., & Zubizarreta, J. R. (2023). Fair and robust estimation of heterogeneous treatment effects for policy learning. In Proceedings of the 40-th international conference on machine learning. https://doi.org/10.48550/arXiv.2306.03625 CrossRefGoogle Scholar
Kosorok, M. R., & Moodie, E. E. M. (2015). Adaptive treatment strategies in practice: Planning trials and analyzing data for personalized medicine. Society for Industrial and Applied Mathematics, Philadelphia, PA. https://doi.org/10.1137/1.9781611974188 CrossRefGoogle Scholar
Lee, Y., Nguyen, T. Q., & Stuart, E. A. (2021). Partially pooled propensity score models for average treatment effect estimation with multilevel data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 184(4), 1578–1598. https://doi.org/10.1111/rssa.12741CrossRefGoogle Scholar
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22. https://doi.org/10.1093/biomet/73.1.13CrossRefGoogle Scholar
Logan, B. R., Sparapani, R., McCulloch, R. E., & Laud, P. W. (2019). Decision making and uncertainty quantification for individualized treatments using Bayesian additive regression trees. Statistical Methods in Medical Research, 28(4), 1079–1093.CrossRefGoogle ScholarPubMed
Mitchell, S., Potash, E., Barocas, S., D’Amour, A., & Lum, K. (2021). Algorithmic fairness: Choices, assumptions, and definitions. Annual Review of Statistics and its Application, 8, 141–163. https://doi.org/10.1146/annurev-statistics-042720-125902CrossRefGoogle Scholar
Murphy, S. A. (2003). Optimal dynamic treatment regimes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 331–355. https://doi.org/10.1111/1467-9868.00389CrossRefGoogle Scholar
Murphy, S. A. (2005). An experimental design for the development of adaptive treatment strategies. Statistics in Medicine, 24(10), 1455–1481. https://doi.org/10.1002/sim.2022CrossRefGoogle ScholarPubMed
Murphy, S. A., Lynch, K. G., Oslin, D., McKay, J. R., & TenHave, T. (2007). Developing adaptive treatment strategies in substance abuse research. Drug and Alcohol Dependence, 88 S24–S30. https://doi.org/10.1016/j.drugalcdep.2006.09.008CrossRefGoogle ScholarPubMed
Murphy, S. A., Oslin, D. W., Rush, A. J., & Zhu, J. (2007). Methodological challenges in constructing effective treatment sequences for chronic psychiatric disorders. Neuropsychopharmacology, 32(2), 257–262. https://doi.org/10.1038/sj.npp.1301241CrossRefGoogle ScholarPubMed
Murray, T. A., Yuan, Y., & Thall, P. F. (2018). A Bayesian machine learning approach for optimizing dynamic treatment regimes. Journal of the American Statistical Association, 113(523), 1255–1267. https://doi.org/10.1080/01621459.2017.1340887CrossRefGoogle ScholarPubMed
Nabi, R., Malinsky, D., & Shpitser, I. (2019). Learning optimal fair policies. In Proceedings of the 36th international conference on machine learning (vol. 32, no. 1, pp. 4674–4682). https://doi.org/10.1609/aaai.v32i1.11553 CrossRefGoogle Scholar
Neyman, J. S. (1923). On the application of probability theory to agricultural experiments: Essay on principles. Section 9 (with discussion). Statistical Science, 4, 465–480.Google Scholar
Park, C., & Kang, H. (2022). Efficient semiparametric estimation of network treatment effects under partial interference [asac009]. Biometrika, 109(4), 1015–1031.CrossRefGoogle Scholar
Qian, M., & Murphy, S. A. (2011). Performance guarantees for individualized treatment rules. The Annals of Statistics, 39(2), 1180–1210. https://doi.org/10.1214/10-AOS864CrossRefGoogle ScholarPubMed
Raudenbush, S. W. (2009). Adaptive centering with random effects: An alternative to the fixed effects model for studying time-varying treatments in school settings. Education Finance and Policy, 4(4), 468–491. https://doi.org/10.1162/edfp.2009.4.4.468CrossRefGoogle Scholar
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1). Sage.Google Scholar
Raudenbush, S. W., & Schwartz, D. (2020). Randomized experiments in education, with implications for multilevel causal inference. Annual Review of Statistics and Its Application, 7(1), 177–208. https://doi.org/10.1146/annurev-statistics-031219-041205CrossRefGoogle Scholar
Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In Proceedings of the second Seattle symposium in biostatistics (pp. 189–326). https://doi.org/10.1007/978-1-4419-9076-1_11 CrossRefGoogle Scholar
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5), 688–701. https://doi.org/10.1037/h0037350CrossRefGoogle Scholar
Rubin, D. B. (1986). Comment: Which ifs have causal answers. Journal of the American Statistical Association, 81(396), 961–962. https://doi.org/10.2307/2289065Google Scholar
Stefanski, L. A., & Boos, D. D. (2002). The calculus of M-estimation. The American Statistician, 56(1), 29–38. https://doi.org/10.1198/000313002753631330CrossRefGoogle Scholar
Suk, Y. (2023). A within-group approach to ensemble machine learning methods for causal inference in multilevel studies. Journal of Educational and Behavioral Statistics. https://doi.org/10.3102/10769986231162096Google Scholar
Suk, Y., & Han, K. T. (2023). A psychometric framework for evaluating fairness in algorithmic decision making: Differential algorithmic functioning. Journal of Educational and Behavioral Statistics. https://doi.org/10.3102/10769986231171711Google Scholar
Suk, Y., & Kang, H. (2022). Robust machine learning for treatment effects in multilevel observational studies under cluster-level unmeasured confounding. Psychometrika, 87(1), 310–343. https://doi.org/10.1007/s11336-021-09805-xCrossRefGoogle ScholarPubMed
Suk, Y., & Kang, H. (2022). Tuning random forests for causal inference under cluster-level unmeasured confounding. Multivariate Behavioral Research. https://doi.org/10.1080/00273171.2021.1994364Google ScholarPubMed
Suk, Y., Kang, H., & Kim, J.-S. (2021). Random forests approach for causal inference with clustered observational data. Multivariate Behavioral Research, 56(6), 829–852. https://doi.org/10.1080/00273171.2020.1808437CrossRefGoogle ScholarPubMed
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.xCrossRefGoogle Scholar
Tsiatis, A. A., Davidian, M., Holloway, S. T., & Laber, E. B. (2019). Dynamic treatment regimes: Statistical methods for precision medicine. Hall/CRC. https://doi.org/10.1201/9780429192692 CrossRefGoogle Scholar
van der Vaart, A. W. (2000). Asymptotic statistics (Vol. 3). Cambridge University Press. https://doi.org/10.1017/cbo978051180225 Google Scholar
Wager, S., & Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523), 1228–1242. https://doi.org/10.1080/01621459.2017.1319839CrossRefGoogle Scholar
Watkins, C. J., & Dayan, P. (1992). Q-learning. Machine learning, 8(3), 279–292. https://doi.org/10.1023/a:1022676722315CrossRefGoogle Scholar
Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. The MIT press.Google Scholar
Zhang, B., Tsiatis, A. A., Davidian, M., Zhang, M., & Laber, E. (2012). Estimating optimal treatment regimes from a classification perspective. Stat, 1(1), 103–114. https://doi.org/10.1002/sta.411CrossRefGoogle ScholarPubMed
Zhao, Y., Zeng, D., Rush, A. J., & Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning. Journal of the American Statistical Association, 107(499), 1106–1118. https://doi.org/10.1080/01621459.2012.695674CrossRefGoogle ScholarPubMed
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