Flexible propensity score estimation strategies for clustered data in observational studies

Existing studies have suggested superior performance of nonparametric machine learning over logistic regression for propensity score estimation. However, it is unclear whether the advantages of nonparametric propensity score modeling are carried to settings where there is clustering of individuals, especially when there is unmeasured cluster-level confounding. In this work we examined the performance of logistic regression (all main effects), Bayesian additive regression trees and generalized boosted modeling for propensity score weighting in clustered settings, with the clustering being accounted for by including either cluster indicators or random intercepts. We simulated data for three hypothetical observational studies of varying sample and cluster sizes. Confounders were generated at both levels, including a cluster-level confounder that is unobserved in the analyses. A binary treatment and a continuous outcome were generated based on seven scenarios with varying relationships between the treatment and confounders (linear and additive, nonlinear/nonadditive, nonadditive with the unobserved cluster-level confounder). Results suggest that when the sample and cluster sizes are large, nonparametric propensity score estimation may provide better covariate balance, bias reduction, and 95% confidence interval coverage, regardless of the degree of nonlinearity or nonadditivity in the true propensity score model. When the sample or cluster sizes are small, however, nonparametric approaches may become more vulnerable to unmeasured cluster-level confounding and thus may not be a better alternative to multilevel logistic regression. We applied the methods to the National Longitudinal Study of Adolescent to Adult Health data, estimating the effect of team sports participation during adolescence on adulthood depressive symptoms.