Abstract
BackgroundDouble-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. However, it is not always possible to include all covariates in adjustment. We aimed to find the optimal imbalance threshold for entering covariates into regression.MethodsWe conducted a series of Monte Carlo simulations on virtual populations of 5,000 subjects. We performed PS 1:1 nearest-neighbor matching on each sample. We calculated standardized mean differences across groups to detect any remaining imbalance in the matched samples. We examined 25 thresholds (from 0.01 to 0.25, stepwise 0.01) for considering residual imbalance. The treatment effect was estimated using logistic regression that contained only those covariates considered to be unbalanced by these thresholds.ResultsWe showed that regression adjustment could dramatically remove residual confounding bias when it included all of the covariates with a standardized difference greater than 0.10. The additional benefit was negligible when we also adjusted for covariates with less imbalance. We found that the mean squared error of the estimates was minimized under the same conditions.ConclusionIf covariate balance is not achieved, we recommend reiterating PS modeling until standardized differences below 0.10 are achieved on most covariates. In case of remaining imbalance, a double adjustment might be worth considering.
Highlights
Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching
Approximating completely randomized experiment, a fundamental step in PS matching analysis is to ensure that the covariate balance across the treatment groups is achieved, by using diagnostics that have been described in the literature [5, 6]
The correction provided by the doublerobust approach varied with the Standardized mean difference (SMD) threshold value used to choose the unbalanced covariates for regression adjustment
Summary
Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. It is not always possible to include all covariates in adjustment. Propensity score (PS) matching analysis is a popular method for estimating the treatment effect in observational studies [1,2,3]. Defined as the conditional probability of receiving the treatment of interest given a set of confounders, the PS aims to balance confounding covariates across treatment groups [4]. Approximating completely randomized experiment, a fundamental step in PS matching analysis is to ensure that the covariate balance across the treatment groups is achieved, by using diagnostics that have been described in the literature [5, 6]. If balance is achieved across all of the confounders, the treatment effect can be estimated without bias. Any unbalanced covariates can be adjusted within the PS-matched sample [8]
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