The PSMATCH Procedure

Propensity score analysis assumes that the true propensity scores are known. When the propensity scores are estimated—as is usually the case in practice—you need to assess how well the distributions of the propensity scores (or the logit propensity scores) and the adjusted variables are balanced between the treatment group and the control group.

The ASSESS statement in the PSMATCH procedure provides a variety of statistical measures and graphical displays for comparing these distributions. You can make these assessments for all the observations in the data set, the observations in the support region, or the matched observations (if you specify a MATCH statement).

Two statistical measures for variable balance assessment are the standardized difference between the treatment and control groups and the variance ratio. For good variable balance, the absolute standardized difference should be less than or equal to 0.25, and the variance ratio should be between 0.5 and 2 (Rubin 2001, p. 174; Stuart 2010, p. 11).

Note that in addition to the threshold of 0.25 for the standardized difference, a smaller threshold of 0.1 has also been used to indicate meaningful imbalance in the variables (Normand et al. 2001; Mamdani et al. 2005; Austin 2009).

The standardized difference is computed by dividing the mean difference by an estimate of its standard deviation. Two estimates of the standard deviation are available:

For binary classification variables, the mean is taken to be the average proportion p of the first classification level, and the variance is computed as (Austin, Grootendorst, and Anderson 2007, p. 737).

If you specify a STRATA statement, then stratum-specific standardized mean differences are computed for observations in the support region.

The PSMATCH procedure displays the standardized differences in plots. You can also request box plots for continuous variables, bar charts for binary classification variables, and cloud plots for both continuous and binary classification variables. These plots are also produced by stratum if you specify a STRATA statement.

The next three subsections describe how standardized mean differences and variance ratios are computed for all observations, observations in the support region, and matched observations.