Tutorial: Introduction to Propensity Score Methods with R

Overview

The use of propensity score methods (Rosenbaum & Rubin, 1983) for estimating causal effects in observational studies or certain kinds of quasi-experiments has been increasing in the social sciences (Thoemmes & Kim, 2011) and in medical research (Austin, 2008) in the last decade. Propensity score analysis (PSA) attempts to adjust selection bias that occurs due to the lack of randomization. Analysis is typically conducted in two phases where in phase I, the probability of placement in the treatment is estimated to identify matched pairs or clusters so that in phase II, comparisons on the dependent variable can be made between matched pairs or within clusters. R (R Core Team, 2012) is ideal for conducting PSA given its wide availability of the most current statistical methods vis-à-vis add-on packages as well as its superior graphics capabilities.

Goals

The proposed workshop will provide participants with a theoretical overview of propensity score methods as well as illustrations and discussion of PSA applications. Methods used in phase I of PSA (i.e. models or methods for estimating propensity scores) include logistic regression, classification trees, and matching. Discussions on appropriate comparisons and estimations of effect size and confidence intervals in phase II will also be covered. The use of graphics for diagnosing covariate balance as well as summarizing overall results will be emphasized. Lastly, the extension of PSA methods for multilevel data will also be presented.

Outline

• Theoretical overview of propensity score methods
• Phase I of PSA - Adjusting for selection bias by modeling treatment placement
  • Stratification using logistic regression and classification trees; also random forests
  • Propensity score matching
  • Checking covariate balance
• Phase II of PSA - Estimating effects re: response variables
  • Dependent sample tests and confidence intervals.
  • Visualizing results
  • Sensitivity analysis
  • Analysis of multilevel data

Prerequisites

Basic knowledge of regression models and statistics.

Intended Audience

This tutorial is intended for anyone who wished to use propensity score models for estimating causal effects in observational studies.

Workshop Materials

Materials will include slides, R scripts, and data and will be made available on the website below.

Related Links

http://jason.bryer.org/talks/psaworkshop.html

R Packages

• MatchIt (Ho, Imai, King, & Stuart, 2011) Nonparametric Preprocessing for Parametric Causal Inference
• Matching (Sekhon, 2011) Multivariate and Propensity Score Matching Software for Causal Inference
• party (Hothorn, Hornik, & Zeileis, 2006) A Laboratory for Recursive Partytioning
• multilevelPSA (Bryer & Pruzek, 2011) Multilevel Propensity Score Analysis
• PSAgraphics (Helmreich & Pruzek, 2009) An R Package to Support Propensity Score Analysis
• rpart (Therneau, Atkinson, & Ripley, 2012) Recursive Partitioning
• rbounds (Keele, 2010) An Overview of rebounds: An R Package for Rosenbaum bounds sensitivity analysis with matched data.

References

Rosenbaum, P.R. (2010). Design of Observational Studies. New York: Springer. Austin, P. C. (2011). Comparing paired vs non-paired statistical methods of analyses when making inferences about absolute risk reductions in propensity-score matched samples. Statistics in Medicine, 30.

Bryer, J. (2011). multilevelPSA: Multilevel propensity score analysis [Computer software manual]. Retrieved from http://github.com/jbryer/multilevelPSA

Bryer, J., & Pruzek, R.M. (2011). An international comparison of private and public schools using multilevel propensity score methods and graphics (Abstract). Multivariate Behavioral Research, 46(6), 1010-1011.

Helmreich, J. E., & Pruzek, R. M. (2009). PSAgraphics: An R package to support propensity score analysis. Journal of Statistical Software, 29(6). Available from http://www.jstatsoft.org/v29/i06/paper

Ho, D.E., Imai, K., King, G., and Stuart, E.A (2011). MatchIt: Nonparametric Preprocessing for Parametric Causal Inference. Journal of Statistical Software 42(8). Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651--674.

R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Rosenbaum, P.R. (2005). Sensitivity analysis in observational studies. In B.S. Everitt & D.C. Howell Encyclopedia of Statistics in Behavioral Science, pp. 1809-1814. Chichester: John Wiley & Sons.

Rosenbaum, P.R. (2012). Testing one hypothesis twice in observational studies. Biometrika. Sekhon, J.S. (2011). Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching Package for R. Journal of Statistical Software, 42(7), 1-52. Shadish, W.R., Clark, M.H., & Steiner, P.M. (2008). Can nonrandomized experiments yield accurate answers? A randomized experiment comparing random and nonrandom assignments. Journal of the American Statistical Association, 103(484). 1334-1356.

Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Science, 25, 1-21. Stuart, E.A., & Rubin, D.B. (2007). Best practices in quasi-experimental designs: Matching methods for causal inference. Chapter 11 (pp. 155-176) in J. Osborne (Ed.). Best Practices in Quantitative Social Science. Thousand Oaks, CA: Sage Publications.

Therneau, T., Atkinson, B., & Ripley, B. (2012). rpart: Recursive Partitioning. R package version 4.0-1. Thoemmes, F. J., & Kim, E. S. (2011). A systematic review of propensity score methods in the social sciences. Multivariate Behavioral Research, 46, 90-118.