title: On Bayesian estimation of marginal structural models.
abstract: The purpose of inverse probability of treatment (IPT) weighting in estimation of marginal treatment effects is to construct a pseudo-population without imbalances in measured covariates, thus removing the effects of confounding and informative censoring when performing inference. In this article, we formalize the notion of such a pseudo-population as a data generating mechanism with particular characteristics, and show that this leads to a natural Bayesian interpretation of IPT weighted estimation. Using this interpretation, we are able to propose the first fully Bayesian procedure for estimating parameters of marginal structural models using an IPT weighting. Our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities, answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in Bayesian inference of marginal treatment effects. The proposed approach is compared to existing methods in simulated data, and applied to an analysis of the Canadian Co-infection Cohort.
authors: Dalla Lana School of Public Health, University of Toronto, 155 College Street, 6th floor, Toronto, Ontario, Canada M5T 3M7.
authors: Olli
authors: O
authors: Saarela
authors: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6.
authors: David A
authors: DA
authors: Stephens
authors: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, 1020 Pine Avenue West, Montreal, Quebec, Canada H3A 1A2.
authors: Erica E M
authors: EE
authors: Moodie
authors: Department of Medicine, Division of Infectious Diseases, McGill University, 3650 Saint Urbain, Montreal, Quebec, Canada H2X 2P4.
authors: Marina B
authors: MB
authors: Klein
mesh_terms: D000465:Algorithms; D019380:Anti-HIV Agents / Q000008:administration & dosage; D001499:Bayes Theorem; D001699:Biometry; D002170:Canada; D015331:Cohort Studies; D018450:Disease Progression; D015658:HIV Infections / Q000150:complications / Q000188:drug therapy; D006526:Hepatitis C / Q000150:complications; D006801:Humans; D016013:Likelihood Functions; D008103:Liver Cirrhosis / Q000209:etiology; D015233:Models, Statistical; D011336:Probability
chemical_list: D019380:Anti-HIV Agents
keywords: Bayesian inference; Causal inference; Inverse probability weighting; Longitudinal data; Marginal structural models; Posterior predictive inference; Variance estimation