On Bayesian estimation of marginal structural models
Corresponding Author
Olli Saarela
Dalla Lana School of Public Health, University of Toronto, 155 College Street, 6th floor, Toronto, Ontario, Canada M5T 3M7
email: [email protected]Search for more papers by this authorDavid A. Stephens
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Search for more papers by this authorErica E. M. Moodie
Department of Epidemiology, Biostatistics and Occupational Health, McGill University, 1020 Pine Avenue West, Montreal, Quebec, Canada H3A 1A2
Search for more papers by this authorMarina B. Klein
Department of Medicine, Division of Infectious Diseases, McGill University, 3650 Saint Urbain, Montreal, Quebec, Canada H2X 2P4
Search for more papers by this authorCorresponding Author
Olli Saarela
Dalla Lana School of Public Health, University of Toronto, 155 College Street, 6th floor, Toronto, Ontario, Canada M5T 3M7
email: [email protected]Search for more papers by this authorDavid A. Stephens
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Search for more papers by this authorErica E. M. Moodie
Department of Epidemiology, Biostatistics and Occupational Health, McGill University, 1020 Pine Avenue West, Montreal, Quebec, Canada H3A 1A2
Search for more papers by this authorMarina B. Klein
Department of Medicine, Division of Infectious Diseases, McGill University, 3650 Saint Urbain, Montreal, Quebec, Canada H2X 2P4
Search for more papers by this authorSummary
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.
Supporting Information
Additional Supporting Information may be found in the online version of this article.
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| biom12269-sup-0001-SuppData.pdf133.3 KB | Supplementary Materials. |
| biom12269-sup-0001-SuppData_Code.zip11.2 KB | Supplementary Materials Code. |
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