A hybrid generalized propensity score approach for observational studies

References

• Breiman, L. 1996. Bagging predictors. Machine Learning 24 (2):123–40. doi:10.1007/BF00058655.
   Web of Science ®Google Scholar
• Breiman, L. 2001. Random forests. Machine Learning 45 (1):5–32. doi:10.1023/A:1010933404324.
   Web of Science ®Google Scholar
• Crump, R., V. J. Hotz, G. W. Imbens, and O. A. Mitnik. 2009. Dealing with limited overlap in estimation of average treatment effects. Biometrika 96 (1):187–99. doi:10.1093/biomet/asn055.
   Web of Science ®Google Scholar
• D’Agostino, R. B. Jr. 1998. Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Statistics in Medicine 17 (19):2265–81. doi:10.1002/(SICI)1097-0258(19981015)17:19<2265::AID-SIM918>3.0.CO;2-B.
   PubMed Web of Science ®Google Scholar
• Feng, P., X.-H. Zhou, Q.-M. Zou, M.-Y. Fan, and X.-S. Li. 2012. Generalized Propensity score for estimating the average treatment effect of multiple treatments. Statistics in Medicine 31 (7):681–97. doi:10.1002/sim.4168.
   PubMed Web of Science ®Google Scholar
• Friedman, J., T. Hastie, and R. Tibshirani. 2000. Additive logistic regression: A statistical view of boosting. The Annals of Statistics 28 (2):337–407. doi:10.1214/aos/1016218223.
   Web of Science ®Google Scholar
• Friedman, J. H. 2001. Greedy function approximation: A gradient boosting machine. The Annals of Statistics 29 (5):1189–232. doi:10.1214/aos/1013203451.
   Web of Science ®Google Scholar
• Friedman, J. H. 2002. Stochastic gradient boosting. Computational Statistics & Data Analysis 38 (4):367–78. doi:10.1016/S0167-9473(01)00065-2.
   Web of Science ®Google Scholar
• Ghosh, D. 2018. Relaxed covariate overlap and margin-based causal effect estimation. Statistics in Medicine 37 (28):4252–65. doi:10.1002/sim.7919.
   PubMed Web of Science ®Google Scholar
• Greenwell, B., B. Boehmke, and J. Cunningham, & GBM Developers. 2018. gbm: Generalized Boosted Regression Models. R package version 2.1.3. Accessed October 6, 2018. https://cran.r-project.org/web/packages/gbm/
   Google Scholar
• Hastie, T., R. Tibshirani, and J. Friedman. 2009. The Elements of Statistical Learning: Data Mining, Inference and Prediction. 2nd ed. New York: Springer.
   Google Scholar
• James, G., D. Witten, T. Hastie, and R. Tibshirani. 2013. An Introduction to Statistical Learning with Application in R. 1st ed. New York: Springer
   Google Scholar
• Imbens, G. W. 2000. The role of the propensity score in estimating dose-response functions. Biometrika 87 (3):706–10. doi:10.1093/biomet/87.3.706.
   Web of Science ®Google Scholar
• Lee, B. K., J. Lessler, and E. A. Stuart. 2010. Improving propensity score weighting using machine learning. Statistics in Medicine 29 (3):337–46. doi:10.1002/sim.3782.
   PubMed Web of Science ®Google Scholar
• Lin, L., Y. Zhu, and L. Chen. 2019. Causal inference for multi-level treatments with machine-learned propensity scores. Health Services and Outcomes Research Methodology 19 (2-3):106–26. doi:10.1007/s10742-018-0187-2.
   Web of Science ®Google Scholar
• Liaw, A., and M. Wiener. 2018. randomForest: Breiman and Cutler’s Random Forests for Classification and Regression. R package version 4.6-14. Accessed October 6, 18. https://cran.r-project.org/web/packages/randomForest/
   Google Scholar
• Luo, W., Y. Zhu, and D. Ghosh. 2017. On estimating regression-based causal effects using sufficient dimension reduction. Biometrika 104 (1):51–65.
   Web of Science ®Google Scholar
• Peters, A., T. Hothorn, B. D. Ripley, T. Therneau, and B. Atkinson. 2018. ipred: Improved Predictors. R package version 0.9-7. Accessed October 6, 2018. https://cran.r-project.org/web/packages/nnet/
   Google Scholar
• R Core Team 2018. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Ripley, B., and W. Venables. 2016. nnet: Feed-Forward Neural Networks and Multinomial Log-Linear Models. R package version 7.3.12. Accessed October 6, 2018. https://cran.r-project.org/web/packages/nnet/
   Google Scholar
• Rosenbaum, P. R., and D. B. Rubin. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70 (1):41–55. doi:10.1093/biomet/70.1.41.
   Web of Science ®Google Scholar
• Tu, C., W. Y. Koh, and S. Jiao. 2013. Using generalized doubly robust estimator to estimate average treatments of multiple treatments in observational studies. Journal of Statistical Computation and Simulation 83 (8):1518–26. doi:10.1080/00949655.2012.663375.
   Web of Science ®Google Scholar
• Watkins, S., M. Jonsson-Funk, M. A. Brookhart, S. A. Rosenberg, T. M. O'Shea, and J. Daniels. 2013. An empirical comparison of tree-based methods for propensity score estimation. Health Services Research 48 (5):1798–817. doi:10.1111/1475-6773.12068.
   PubMed Web of Science ®Google Scholar
• Wooldridge, J. M. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed. Massachusetts: The MIT Press.
   Google Scholar
• Wyss, R., A. R. Ellis, M. A. Brookhart, C. J. Girman, M. J. Funk, R. LoCasale, and T. Sturmer. 2014. The role of prediction modelling in propensity score estimation: An evaluation of logistic regression, bCART, and the covariate-balancing propensity score. American Journal of Epidemiology 180 (6):645–55. doi:10.1093/aje/kwu181.
   PubMed Web of Science ®Google Scholar
• Xie, Y., Y. Zhu, C. A. Cotton, and P. Wu. 2019. A model averaging approach for estimating propensity scores by optimizing balance. Statistical Methods in Medical Research 28 (1):84–101. doi:10.1177/0962280217715487.
   PubMed Web of Science ®Google Scholar