Bayesian Propensity Score Analysis for Observational Data

Abstract

Propensity scores analysis (PSA) involves regression adjustment for the estimated propensity scores, and the method can be used for estimating causal effects from observational data. However, confidence intervals for the treatment effect may be falsely precise because PSA ignores uncertainty in the estimated propensity scores. We propose Bayesian propensity score analysis (BPSA) for observational studies with a binary treatment, binary outcome and measured confounders. The method uses logistic regression models with the propensity score as a latent variable. The first regression models the relationship between the outcome, treatment and propensity score, while the second regression models the relationship between the propensity score and measured confounders. Markov chain Monte Carlo is used to study the posterior distribution of the exposure effect. We demonstrate BPSA in an observational study of the effect of statin therapy on all-cause mortality in patients discharged from Ontario hospitals following acute myocardial infarction. The results illustrate that BPSA and PSA may give different inferences despite the large sample size. We study performance using Monte Carlo simulations. Synthetic datasets are generated using competing models for the outcome variable and various fixed parameter values. The results indicate that if the outcome regression model is correctly specified, in the sense that the outcome risk within treatment groups is a smooth function of the propensity score, then BPSA permits more efficient estimation of the propensity scores compared to PSA. BPSA exploits prior information about the relationship be-Dedication xi 6 Conclusion 6.1 Summary 112 6.2 Future Research Bibliography Appendices A Computing the limiting estimates for PSA v List of Tables 1.1 Baseline characteristics of patients discharged alive from hospital following acute myocardial infarction 4.1 Log ORs for the association between Y and (X, C) 4.2 Point estimates for 7, the log ORs for the association between X and C.

Propensity score weighting with multilevel data

“…Note that here the standard error calculation does not take into account the uncertainty in estimating the propensity score. More discussions on this can be found in McCandless et al [28].…”

Variation in New Zealand hospital outcomes: combining hierarchical Bayesian modeling and propensity score methods for hospital performance comparisons

“…Exploring sensitivity to possibly unobserved confounding is likely to move the analysis to one in which the propensity score is regarded as an unknown. Although there has been some work allowing for uncertainty in the propensity score this has primarily been aimed at accommodating parameter uncertainty for a propensity score model fitted to fully observed covariates (McCandless et al 2009a;McCandless et al 2009b). Since propensity score theory is worked out under the assumption of a known propensity score (Imbens 2000;Rosenbaum and Rubin 1983) it is unclear to what extent basic results such as weak ignorability conditional on the propensity score apply in the context of an uncertain propensity score.…”

Moment Conditions and Bayesian Non-Parametrics

“…Thus the propensity scores and the ATE can be estimated jointly (e.g. McCandless et al (2009), Zigler et al (2013) and Zigler and Dominici (2014)).…”