Objectives: The propensity score (PS) is a balancing score. Following PS matching, balance checking usually relies on estimating separately the standardized absolute mean difference for each baseline characteristic. The average standardized absolute mean difference and the Mahalanobis distances have been proposed to summarize the information across the covariates. However, they might be minimized when nondesirable variables such as instrumental variables (IV) are included in the PS model. We propose a new weighted summary balance measure that takes into account, for each covariate, its strength of association with the outcome.
Study design and setting: This new measure was evaluated using a simulation study to assess whether minimization of the measure coincided with minimally biased estimates. All measures were then applied to a real data set from an observational cohort study.
Results: Contrarily to the other measures, our proposal was minimized when including the confounders, which coincided with minimal bias and mean squared error, but increased when including an IV in the PS model. Similar findings were observed in the real data set.
Conclusion: A balance measure taking into account the strength of association between the covariates and the outcome may be helpful to identify the most parsimonious PS model.
Keywords: Balance; Causal inference; Instrumental variables; Propensity score; Propensity score matching; Standardized mean difference.
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