Bayesian propensity score analysis for clustered observational data
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Bayesian propensity score analysis for clustered observational data Qi Zhou1 · Catherine McNeal2 · Laurel A. Copeland3 · Justin P. Zachariah4 · Joon Jin Song5 Accepted: 14 July 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract Observational data with clustered structure may have confounding at one or more levels which when combined critically undermine result validity. We propose using multilevel models in Bayesian propensity score analysis to account for cluster and individual level confounding in the estimation of both propensity score and in turn treatment effect. In addition, our approach includes confounders in the outcome model for more flexibility to model outcome-covariate surface, minimizing the influence of feedback effect in Bayesian joint modeling of propensity score model and outcome model. In an extensive simulation study, we compare several propensity score analysis approaches with varying complexity of multilevel modeling structures. With each of proposed propensity score model, random intercept outcome model augmented with covariates adjustment well maintains the property of propensity score as balancing score and outperforms single level outcome model. To illustrate the proposed models, a case study is considered, which investigates the impact of lipid screening on lipid management in youth from three different health care systems. Keywords Bayesian inference · Multilevel modeling · Observational data · Propensity score · Stratification · Lipid management
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Joon Jin Song [email protected]
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School of Management, Xi’an Jiaotong University, No. 28 Xianning Road, Xi’an, Shaanxi 710049, China
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Department of Internal Medicine, Baylor Scott and White Health, 2401 S. 31 St., Temple, TX 76508, USA
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Center for Applied Health Research, Baylor Scott and White Health, 2102 Birdcreek Drive, Temple, TX 76502, USA
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Division of Pediatric Cardiology, Department of Pediatrics, Baylor College of Medicine, Texas Children’s Hospital, Houston, TX, USA
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Department of Statistical Science, Baylor University, P.O. Box 97140 , Waco, TX 76798-7140, USA
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Q. Zhou et al.
1 Introduction Randomized controlled trials when properly executed support causal inference since random assignment of study subjects to comparison groups is free of confounding. Since some investigations necessarily require passive observation and nonrandomized group assignment, identified statistical associations may be confounded with distributions of confounders due to lack of randomization. The method called propensity score, first proposed by Rosenbaum and Rubin (1983), is a popular confounding adjustment technique for approaching causal inference in observational studies. The propensity score is the conditional probability of obtaining treatment assignment based on observed covariates, typically estimated through logistic regression. Then the estimated score, which should now account for the differences in measured cofounder distributions among the compared groups, is used in the outcome model for treat
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