The z-difference can be used to measure covariate balance in matched propensity score analyses

The propensity score (PS) method is increasingly used to assess treatment effects in nonrandomized trials. Although there are several methods to use the PS for analysis, matching treated and untreated patients by the PS is recommended by most researchers among other reasons because this allows assessing covariate balance before and after matching. Although the standardized difference is commonly applied to compute a measure of balance, it has two deficiencies: its distribution depends on the sample size and one cannot compare standardized differences for baseline covariates on different scales, that is, continuous, binary, ordinal, or nominal covariates.

We introduce the z-difference to measure covariate balance in matched PS analyses and illustrate it by a recent matched PS analysis from cardiac surgery.

The z-difference is simple to calculate, can be used with second moments for continuous covariates, and in most cases can also be computed from published data. Its full advantage emerges after displaying z-differences in a Q-Q plot, which allows balance comparisons with respect to (1) a randomized trial and (2) a perfectly matched PS analysis in the sense of Rubin and Thomas.

The z-difference can be used to measure covariate balance in matched PS analyses.