Balance measures for propensity score methods: a clinical example on beta-agonist use and the risk of myocardial infarction.

PURPOSE: Propensity score (PS) methods aim to control for confounding by balancing confounders between exposed and unexposed subjects with the same PS. PS balance measures have been compared in simulated data but limited in empirical data. Our objective was to compare balance measures in clinical data and assessed the association between long-acting inhalation beta-agonist (LABA) use and myocardial infarction.
METHODS: We estimated the relationship between LABA use and myocardial infarction in a cohort of adults with a diagnosis of asthma or chronic obstructive pulmonary disorder from the Utrecht General Practitioner Research Network database. More than two thousand PS models, including information on the observed confounders age, sex, diabetes, cardiovascular disease and chronic obstructive pulmonary disorder status, were applied. The balance of these confounders was assessed using the standardised difference (SD), Kolmogorov-Smirnov (KS) distance and overlapping coefficient. Correlations between these balance measures were calculated. In addition, simulation studies were performed to assess the correlation between balance measures and bias.
RESULTS: LABA use was not related to myocardial infarction after conditioning on the PS (median heart rate = 1.14, 95%CI = 0.47-2.75). When using the different balance measures for selecting a PS model, similar associations were obtained. In our empirical data, SD and KS distance were highly correlated balance measures (r = 0.92). In simulations, SD, KS distance and overlapping coefficient were similarly correlated to bias (e.g. r = 0.55, r = 0.52 and r = -0.57, respectively, when conditioning on the PS).
CONCLUSIONS: We recommend using the SD or the KS distance to quantify the balance of confounder distributions when applying PS methods.