Double-adjustment in propensity score matching analysis: choosing a threshold for considering residual imbalance

• Published in: BMC medical research methodology Vol. 17; no. 1; pp. 78 - 8
• Main Authors: Nguyen, Tri-Long, Collins, Gary S., Spence, Jessica, Daurès, Jean-Pierre, Devereaux, P. J., Landais, Paul, Le Manach, Yannick
• Format: Journal Article
• Language: English
• Published: England BioMed Central 28.04.2017; BMC
• Subjects: Algorithms; Bias; Causal inference; Computer Simulation; Confounding; Covariate balance; Economic models; Human health and pathology; Humans; Life Sciences; Logistic Models; Medical research; Models, Statistical; Monte Carlo Method; Propensity Score; Random variables; Statistical methods; Surgery; Causal inference; Confounding; Covariate balance; Propensity score
• ISSN: 1471-2288; 1471-2288
• DOI: 10.1186/s12874-017-0338-0

Double-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. We 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. We 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. If 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.