The International Journal of Biostatistics CAUSAL INFERENCE Cutting Feedback in Bayesian Regression Adjustment for the Propensity Score

McCandless, Gustafson and Austin (2009) describe a Bayesian approach to regression adjustment for the propensity score to reduce confounding. A unique property of the method is that the treatment and outcome models are combined via Bayes theorem. However, this estimation procedure can be problematic if the outcome model is misspecified. We observe feedback that can bias propensity score estimates. Building on new innovation in Bayesian computation, we propose a technique for cutting feedback in a Bayesian propensity analysis. We use the posterior distribution of the propensity scores as an input in the regression model for the outcome. The method is approximately Bayesian in the sense that it does not use the full likelihood for estimation. Nonetheless, it severs feedback between the treatment and outcome giving propensity score estimates that are free from bias but modeled with uncertainty. We illustrate the method in a matched cohort study investigating the effect of statins on primary stroke prevention.

[1]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[2]  J. Robins,et al.  Results of multivariable logistic regression, propensity matching, propensity adjustment, and propensity-based weighting under conditions of nonuniform effect. , 2006, American journal of epidemiology.

[3]  Zhiqiang Tan,et al.  A Distributional Approach for Causal Inference Using Propensity Scores , 2006 .

[4]  K. Rice,et al.  Equivalence Between Conditional and Mixture Approaches to the Rasch Model and Matched Case-Control Studies, With Applications , 2004 .

[5]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[6]  Lawrence C McCandless,et al.  Bayesian propensity score analysis for observational data , 2006, Statistics in medicine.

[7]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[8]  D B Rubin,et al.  Matching using estimated propensity scores: relating theory to practice. , 1996, Biometrics.

[9]  D. Rubin.  For objective causal inference, design trumps analysis , 2008, 0811.1640.

[10]  R. Hubbard,et al.  Effect of statins on a wide range of health outcomes: a cohort study validated by comparison with randomized trials. , 2009, British journal of clinical pharmacology.

[11]  J. Robins,et al.  Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. , 1997, Statistics in medicine.

[12]  J. Ibrahim,et al.  Prior elicitation, variable selection and Bayesian computation for logistic regression models , 1999 .

[13]  James O. Berger,et al.  Modularization in Bayesian analysis, with emphasis on analysis of computer models , 2009 .

[14]  M. Plummer,et al.  CODA: convergence diagnosis and output analysis for MCMC , 2006 .

[15]  J. Lunceford,et al.  Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study , 2004, Statistics in medicine.

[16]  M. May.  Bayesian Survival Analysis. , 2002 .

[17]  Beat Neuenschwander,et al.  Combining MCMC with ‘sequential’ PKPD modelling , 2009, Journal of Pharmacokinetics and Pharmacodynamics.

[18]  J. Rutishauser.  The role of statins in clinical medicine--LDL--cholesterol lowering and beyond. , 2006, Swiss medical weekly.