On Bayesian Estimation of Marginal Structural Models

• Activity Number: 324
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Olli Saarela*+ and Erica Moodie and David Stephens
• Companies: McGill University and McGill University and McGill University
• Keywords: Causal inference ; Inverse probability weighting ; Longitudinal data ; Marginal structural models ; Posterior predictive inference

Abstract

Bayesian estimation of marginal causal contrasts is based on a full probability model specification and integration over intermediate variables and confounders. In contrast, marginal structural models, estimated using inverse probability of treatment (IPT) weighting, only require specification of a marginal outcome model, in addition to the treatment assignment model. Since it is often desirable to concentrate the modeling efforts on estimation of the weights, there is motivation to study Bayesian counterparts of IPT weighted methods, which would enable utilizing hierarchical or Bayesian non-parametric model specifications or variable selection in modeling of the treatment assignment, as well as incorporating uncertainty in the estimated weights. We review the existing Bayesian approaches, and propose an alternative based on posterior predictive distribution of the weighted estimator. We also outline how the posterior predictive approach can be utilized in testing modeling assumptions should one wish to model the outcome process. The methods are illustrated with simulations, with specific interest in variance estimation, and with data from the Canadian Co-infection Cohort study.