The propensity score-based marginal mean weighting through stratification (MMWS) method removes selection bias associated with a large number of covariates by equating the pretreatment composition between treatment groups (Hong, 2010a, 2012, 2015; Huang et al, 2005).

Unlike propensity score matching and stratification that are mostly restricted to evaluations of binary treatments, the MMWS method is flexible for evaluating binary and multivalued treatments by approximating a completely randomized experiment. In evaluating whether the treatment effects differ across subpopulations defined by individual characteristics or treatment settings, researchers may assign weights within each subpopulation in order to approximate a randomized block design. To investigate whether one treatment moderates the effect of another concurrent treatment, researchers may assign weights to the data to approximate a factorial randomized design. The method can also be used to assess whether the effect of an initial treatment is amplified or weakened by a subsequent treatment or to identify an optimal treatment sequence through approximating a sequential randomized experiment.

Even though such analyses can similarly be conducted through inverse-probability-of-treatment weighting (IPTW) that has been increasingly employed in epidemiological research (Hernán, Brumbeck, & Robins, 2000; Robins, Hernán, & Brumback, 2000), IPTW is known for bias and imprecision in estimation especially when the propensity score models are misspecified in their functional forms (Hong, 2010a; Kang & Schafer, 2007; Schafer & Kang, 2008; Waernbaum, 2012). In contrast, the nonparametric MMWS method displays a relatively high level of robustness despite such misspecifications and also gains efficiency, as indicated by simulation results (Hong, 2010a).

A free stand-alone MMWS software program for evaluating a binary treatment has the following features:

− Import Stata or SPSS data file
− Multiple imputation of missing data
− Initial screening of multicollinearity
− Variable selection for the propensity score model
− Determine common support with or without a caliper
− Flexible stratification of the sample
− MMWS computation (exportable as a Stata or SPSS file)
− Balance checking
− Weighted estimation of the treatment effect
− Sensitivity analysis

Download MMWS Users Manual for the stand-alone MMWS software

A stand-alone MMWS program for a multivalued treatment is currently under construction.

Stata users may use an MMWS module in their analysis.

MMWS Workshop Materials: This web site provides the SPSS, Stata, SAS, and R code that Hong and her colleagues have previously used in workshops and graduate courses.


Hernán, M. A., Brumback, B. B., & Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology, 11(5), 561-570.

Hong, G. (2010a). Marginal mean weighting through stratification: Adjustment for selection bias in multilevel data. Journal of Educational and Behavioral Statistics, 35(5), 499-531.

Hong, G. (2012). Marginal mean weighting through stratification: A generalized method for evaluating multi-valued and multiple treatments with non-experimental data. Psychological Methods, 17(1), 44-60.

Hong, G. (2015). Causality in a social world: Moderation, mediation, and spill-over. West Sussex, UK: John Wiley & Sons, Inc.

Huang, I. C., Diette, G. B., Dominici, F., Frangakis, C. & Wu, A.W., (2005). Variations of physician group profiling indicators for asthma care. American Journal of Managed Care, 11(1), 38-44.

Kang, J. D., & Schafer, J. L. (2007). Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical science, 22(4), 523-539.

Robins, J. M., Hernán, M. A., & Brumback, B. B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550-560.

Schafer, J. L., & Kang, J. (2008). Average causal effects from nonrandomized studies: A practical guide and simulated example. Psychological Methods, 13(4), 279-313.

Waernbaum, I. (2012). Model misspecification and robustness in causal inference: Comparing matching with doubly robust estimation. Statistics in Medicine, 31, 1572-1581.