Binary treatments
- estimand = "ATO"
Li, F., Morgan, K. L., & Zaslavsky, A. M. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association, 113(521), 390–400. tools:::Rd_expr_doi("10.1080/01621459.2016.1260466")
- estimand = "ATM"
Li, L., & Greene, T. (2013). A Weighting Analogue to Pair Matching in Propensity Score Analysis. The International Journal of Biostatistics, 9(2). tools:::Rd_expr_doi("10.1515/ijb-2012-0030")
- estimand = "ATOS"
Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika, 96(1), 187–199. tools:::Rd_expr_doi("10.1093/biomet/asn055")
- Other estimands
Austin, P. C. (2011). An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies. Multivariate Behavioral Research, 46(3), 399–424. tools:::Rd_expr_doi("10.1080/00273171.2011.568786")
- Marginal mean weighting through stratification (MMWS)
Hong, G. (2010). Marginal mean weighting through stratification: Adjustment for selection bias in multilevel data. Journal of Educational and Behavioral Statistics, 35(5), 499–531. tools:::Rd_expr_doi("10.3102/1076998609359785")
Desai, R. J., Rothman, K. J., Bateman, B. . T., Hernandez-Diaz, S., & Huybrechts, K. F. (2017). A Propensity-score-based Fine Stratification Approach for Confounding Adjustment When Exposure Is Infrequent: Epidemiology, 28(2), 249–257. tools:::Rd_expr_doi("10.1097/EDE.0000000000000595")
Multinomial Treatments
- estimand = "ATO"
Li, F., & Li, F. (2019). Propensity score weighting for causal inference with multiple treatments. The Annals of Applied Statistics, 13(4), 2389–2415. tools:::Rd_expr_doi("10.1214/19-AOAS1282")
- estimand = "ATM"
Yoshida, K., Hernández-Díaz, S., Solomon, D. H., Jackson, J. W., Gagne, J. J., Glynn, R. J., & Franklin, J. M. (2017). Matching weights to simultaneously compare three treatment groups: Comparison to three-way matching. Epidemiology (Cambridge, Mass.), 28(3), 387–395. tools:::Rd_expr_doi("10.1097/EDE.0000000000000627")
- Other estimands
McCaffrey, D. F., Griffin, B. A., Almirall, D., Slaughter, M. E., Ramchand, R., & Burgette, L. F. (2013). A Tutorial on Propensity Score Estimation for Multiple Treatments Using Generalized Boosted Models. Statistics in Medicine, 32(19), 3388–3414. tools:::Rd_expr_doi("10.1002/sim.5753")
- Marginal mean weighting through stratification
Hong, G. (2012). Marginal mean weighting through stratification: A generalized method for evaluating multivalued and multiple treatments with nonexperimental data. Psychological Methods, 17(1), 44–60. tools:::Rd_expr_doi("10.1037/a0024918")