title: The z-difference can be used to measure covariate balance in matched propensity score analyses.
abstract: OBJECTIVE
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  The z-difference can be used to measure covariate balance in matched PS analyses.
authors: Institute of Medical Epidemiology, Biostatistics, and Informatics, Faculty of Medicine, Martin Luther University of Halle-Wittenberg, Magdeburger Str. 8, 06097 Halle (Saale), Germany. Electronic address: oliver.kuss@medizin.uni-halle.de.
authors: Oliver
authors: O
authors: Kuss
mesh_terms: D000368:Aged; D000704:Analysis of Variance; D006348:Cardiac Surgical Procedures; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D057216:Propensity Score; D016032:Randomized Controlled Trials as Topic; D016896:Treatment Outcome
keywords: Covariate balance; Propensity score; Propensity score matching; Q–Q plot; Standardized difference; z-Difference