The PSMATCH Procedure
Propensity Score Analysis
In a randomized study, the potential outcomes within treatment and control groups are unrelated to treatment assignment because individuals are randomly assigned to the groups. Consequently the treatment assignment given the variables X is strongly ignorable.
Rosenbaum and Rubin (1983) defined treatment assignment to be strongly ignorable when two conditions are met. The first condition (unconfoundedness) states that the potential outcomes 
and the treatment assignment (T) are conditionally independent given the observed baseline variables:
This condition is called the "no unmeasured confounders" assumption because it assumes that all the variables that affect both the outcome and the treatment assignment have been measured. The second condition (probabilistic assignment) states that there is a positive probability that a subject receives each treatment:
When the treatment assignment in an observational study is assumed to be strongly ignorable, Rosenbaum and Rubin (1983, p. 43) showed that unbiased estimates of average treatment effects can be obtained by conditioning on the propensity score e(x), which is the probability of the treatment assignment conditional on a set of observed variables X:
At any value of the propensity score e(x), the difference between the treatment and control means is an unbiased estimate of the average treatment effect at e(x). Consequently, matching on the propensity score and propensity score stratification also produce unbiased estimates of treatment effects (Rosenbaum and Rubin 1983, p. 44).
Furthermore, the propensity score is a balancing score. At each value of the propensity score, the distributions of the variables X are the same in the treated and control groups (Rosenbaum and Rubin 1983, p. 44; Stuart 2010, p. 6). Thus, the treatment assignment T and observed variables X are conditionally independent given the propensity score Rosenbaum (2010, p. 72):
Propensity score analysis attempts to replicate the properties of a randomized trial with respect to the observed variables X. The steps involved in this analysis are described in the section Process of Propensity Score Analysis.
The following subsections describe the support region and the propensity score methods that are available in the PSMATCH procedure.
Support Region
For stratification and matching, the PSMATCH procedure selects observations whose propensity scores lie in a support region that can be defined in several ways:
Selecting all available observations. You can request this definition by specifying REGION=ALLOBS in the PROC PSMATCH statement.
Selecting observations whose propensity scores lie in a specified range. You can request this definition by specifying REGION=ALLOBS and then additionally specifying range options.
Selecting observations whose propensity scores lie in the region of common support for the propensity scores for observations in the treated and control groups. You can request this definition by specifying REGION=CS. This region can be extended by specifying the EXTEND suboption.
Selecting observations whose propensity scores lie in the region of propensity scores for observations in the treated group. You can request this definition by specifying REGION=TREATED. This region can be extended by specifying the EXTEND suboption.
In combination with the REGION= option, you can specify the OUT(OBS=REGION) option in the OUTPUT statement to request that only observations in the support region be included in the output data set. You can specify this combination even without the use of stratification or matching. For example, you can use the REGION=ALLOBS(PMSIN=0.1 PSMAX=0.9) option to include only observations whose propensity scores are greater than or equal to 0.1 and less than or equal to 0.9 in the output data set.
Propensity Score Methods
You can use the propensity score methods in the PSMATCH procedure to create an output data set that contains a sample that has been adjusted (either by matching, stratification, or weighting) so that the distributions of the variables are balanced between the treated and control groups. The two groups differ only randomly in their observed or measured variables, as in a randomized study. You can then use the output data set in an outcome analysis to estimate the effect of the treatment.
The following propensity score methods are available in the PSMATCH procedure:
weighting, which creates weights that are appropriate for estimating the ATE and ATT
stratification, which creates strata based on propensity scores
matching, which matches treated units with control units
Note that the outcome variable is not involved in these methods. For more information about these methods, see the sections Propensity Score Weighting, Propensity Score Stratification, and Matching Process.