Random effects modelling versus logistic regression for the inclusion of cluster-level covariates in propensity score estimation: A Monte Carlo simulation and registry cohort analysis.

Purpose: Surgeon and hospital-related features, such as volume, can be associated with treatment choices and outcomes. Accounting for these covariates with propensity score (PS) analysis can be challenging due to the clustered nature of the data. We studied six different PS estimation strategies for clustered data using random effects modelling (REM) compared with logistic regression. Methods: Monte Carlo simulations were used to generate variable cluster-level confounding intensity [odds ratio (OR) = 1.01-2.5] and cluster size (20-1,000 patients per cluster). The following PS estimation strategies were compared: i) logistic regression omitting cluster-level confounders; ii) logistic regression including cluster-level confounders; iii) the same as ii) but including cross-level interactions; iv), v), and vi), similar to i), ii), and iii), respectively, but using REM instead of logistic regression. The same strategies were tested in a trial emulation of partial versus total knee replacement (TKR) surgery, where observational versus trial-based estimates were compared as a proxy for bias. Performance metrics included bias and mean square error (MSE). Results: In most simulated scenarios, logistic regression, including cluster-level confounders, led to the lowest bias and MSE, for example, with 50 clusters × 200 individuals and confounding intensity OR = 1.5, a relative bias of 10%, and MSE of 0.003 for (i) compared to 32% and 0.010 for (iv). The results from the trial emulation also gave similar trends. Conclusion: Logistic regression, including patient and surgeon-/hospital-level confounders, appears to be the preferred strategy for PS estimation.