An introduction to propensity score matching in STATA

Thomas G. Stewart Assistant Professor

This lecture is part 9 of the Propensity Scores and Related Methods Series presented and organized by Robert Greevy within Vanderbilt University's Center for Health Services Research.

NOTE 1

I reserve the right for these notes to be wrong, mistaken, or incomplete.

NOTE 2

These notes will continue to be updated as I

• expand the content
• generate more examples
• respond to helpful feedback regarding items in NOTE 1.

Please feel free to provide content and comments.

SOFTWARE

• StataCorp. 2015. Stata Statistical Software: Release 14. College Station, TX: StataCorp LP.

• E. Leuven and B. Sianesi. 2003. PSMATCH2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. (link). Version 4.0.11. To install in STATA, use command:

ssc install psmatch2

• Phil Clayton. 2013. TABLE1: module to create "table 1" of baseline characteristics for a manuscript. Version 1.1. To install in STATA, use command:

ssc install table1

REFERENCES

• Elizabeth A. Stuart. 2010. Matching Methods for Causal Inference: A Review and a Look Forward, Statistical Science, Vol. 25, No. 1, 1–21.

DATA FOR EXAMPLES AND DISCUSSION

To motivate the propensity score matching, I'll use the cattaneo2 dataset, a STATA example dataset. It can be loaded with the following command:

webuse cattaneo2

The data in cattaneo2 is a subset of data that was analysed in the following journal articles:

• Almond, D., Chay, K.Y., Lee, D.S., 2005. The costs of low birth weight, Quarterly Journal of Economics 120, 1031-1083.

• Cattaneo, M.D. 2010. Efficient semiparametric estimation of multi-valued treatment effects under ignorability, Journal of Econometrics, 155(2), 138-154.

The dataset included information about infant/mother/father characteristics from singleton births in Pennsylvania between 1989 and 1991. The original dataset included nearly 500,000 births. The STATA example dataset includes 4642 births.

RESEARCH QUESTION: What is the effect of maternal smoking during pregnancy on the infant's birthweight?

The dataset includes the following set of variables:

You can access the complete codebook with the command codebook after loading the data.

BIG PICTURE: BACKGROUND

BIG PICTURE: CHALLENGES

Differences in outcomes between the treated and untreated (or exposed and unexposed) may be the consequence of confounding variables and not the treatment (or exposure).

Dataset may include sub-groups for which a treatment effect should not be calculated because

• the sub-group may not be eligible for one treatment (a treatment effect should only be calculated in populations eligible for both treatments)
• though a sub-group may be eligible for both treatments, there may not be enough data for a comparison without extrapolation.

BIG PICTURE: SOLUTIONS

There are several methods for estimating a treatment effect with observational data. In this lecture series, you have been exposed (not randomly) to a family of methods which use the propensity score. The primary focus has been on propensity score matching.

STEPS (A SUMMARY OF STUART 2010)

1. Defining “closeness”: the distance measure used to determine whether an individual is a good match for another.
   1. Variables to include
      • Researchers should thus be liberal in terms of including variables that may be associated with treatment assignment and/or the outcomes.
      • One type of variable that should not be included in the matching process is any variable that may have been affected by the treatment of interest (Rosenbaum, 1984; Frangakis and Rubin, 2002; Greenland, 2003).
   2. Distance Measures
      • Exact
      • Mahalanobis
      • Propensity score / linear propensity score
        • With propensity score estimation, concern is not with the parameter estimates of the model, but rather with the resulting balance of the covariates (Augurzky and Schmidt, 2001).
2. Implementing a matching method, given that measure of closeness.

• Methods:
  1. k:1 Nearest Neighbor
     • Estimates Average Treatment Effect in the Treated (ATT or ATET)
     • May need a caliper
  2. Subclassification
  3. Full matching
  4. Weighting (IPTW)
• Assess Common Support
  • Examining the common support may indicate that it is not possible to reliably estimate the ATE.

3. Assessing the quality of the resulting matched samples, and perhaps iterating with steps 1 and 2 until well-matched samples result.
   • Perhaps the most important step in using matching methods is to diagnose the quality of the resulting matched samples
   • Tools:
     1. Histograms / Density Plots / ECDF
     2. Standardized Bias / Standardized difference in means
4. Analysis of the outcome and estimation of the treatment effect, given the matching done in step 3.
   1. After k:1 mathcing
      • May not need to account for matched pair
      • Must use weights if matching was with replacement
      • Use regression adjustment
   2. After subclassification
      • Aggregation weights determine estimation of ATT or ATE
      • Use regression adjustment

DEMONSTRATION