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Propensity score (PS) methods have been increasingly used in recent yearswhen assessing treatment effects in nonrandomized studies. In terms ofstatistical methods, a number of new PS weighting methods were developed, andit was shown that they can outperform PS matching in efficiency of treatmenteffect estimation in different simulation settings. For assessing balance ofcovariates in treatment groups, PS weighting methods commonly use the weightedstandardized difference, despite some deficiencies of this measure like, forexample, the distribution of the weighted standardized difference depending onthe sample size and on the distribution of weights. We introduce the weightedz-difference as a balance measure in PS weighting analyses and demonstrate itsusage in a simulation study and by applying it to an example from cardiacsurgery. The weighted z-difference is computationally simple and can becalculated for continuous, binary, ordinal and nominal covariates. By usingQ-Q-plots we can compare the balance of PS weighted samples immediately to thebalance in perfectly matched PS samples and to the expected balance in arandomized trial.

Measuring covariate balance in weighted propensity score analyses by the weighted z-difference