The PSMATCH Procedure
Features of the PSMATCH Procedure
You can use the PSMATCH procedure to create propensity scores (PS) for observations from treated and control groups by fitting a binary logistic regression model. Alternatively, you can input propensity scores that have already been created by using a different model or even a different approach such as a tree-based method. For example, you can input propensity scores that have been computed by the LOGISTIC procedure using a binary probit model or by the HPSPLIT procedure using a classification tree.
By default, the PSMATCH procedure uses the propensity scores to computes weights for the observations. Various types of weights are available, depending on whether the outcome analysis will use the weights to estimate the average treatment effect at the population level (ATE) or the average treatment effect for subjects who receive treatment (ATT). For more information about propensity score weighting, see the section Propensity Score Weighting.
The PSMATCH procedure optionally creates strata of observations that have similar propensity scores. For more information, see the section Propensity Score Stratification.
The PSMATCH procedure optionally matches observations in the treated and control groups. The procedure provides three strategies for propensity score matching.
Greedy nearest neighbor matching selects the control unit nearest to each treated unit. Greedy nearest neighbor matching is done sequentially for treated units and without replacement.
Optimal matching selects all control units that match each treated unit by minimizing the total absolute difference in propensity score across all matches. Optimal matching selects all matches simultaneously and without replacement. Three methods for optimal matching are available: fixed ratio matching, variable ratio matching, and full matching.
Matching with replacement selects the control unit that best matches each treated unit. Each control unit can be matched to more than one treated unit, but it can only be matched to the same treated unit once.
For all three matching methods, you can specify a caliper width, which imposes a restriction on the quality of the matches. The difference in propensity score between the treated unit and its matching control unit must be less than or equal to the caliper width. For more information about these methods, see the section Matching Methods.
Matching can be based on the difference in the logit of the propensity score (LPS), as well as the difference in the propensity score (PS). Furthermore, matching can be based on Mahalanobis distance that is computed from a set of continuous covariates (possibly including LPS and LS).
The PSMATCH procedure provides various ways to assess how well the distributions of variables are balanced between the treated and control groups. These variables include the propensity score, the logit of the propensity score, variables used in the logistic regression model, and other variables in the data set. The assessments include the following:
differences in the distributions of the variables between the treated and control groups after weighting, stratification, and matching
standardized mean differences in the variables between the treated and control groups after weighting, stratification, and matching
percentage reductions of absolute differences after weighting, stratification, and matching.
When you use stratification, the differences are also computed within each stratum. For more information about these statistics, see the section Variable Balance Assessment.
The PSMATCH procedure also provides various plots for assessing balance. These plots include the following:
bar charts for classification variables
box plots for continuous variables
CDF plots for continuous variables
cloud plots for continuous variables, which are scatter plots in which the points are jittered to prevent overplotting
cloud plots for inverse probability of treatment weights and ATT weights
a standardized mean differences plot that summarizes differences between the treated and control groups
When you use stratification, these plots are also produced for each stratum.
The PSMATCH procedures saves propensity scores and weights in an output data set that contains a sample that has been adjusted either by weighting, stratification, or matching. If the sample is stratified, you can save the strata identification in the output data set. If the sample is matched, you can save the matching identification in the output data set.
Provided that the distributions of the variables in the adjusted sample are well balanced between the treated and control groups, the output data set serves as input for a subsequent outcome analysis that incorporates weights or strata or that is based on matched observations. Although the PSMATCH procedure itself does not provide this analysis, many other SAS/STAT procedures can be used for this purpose.