title: Predictive Bayesian inference and dynamic treatment regimes.
abstract: While optimal dynamic treatment regimes (DTRs) can be estimated without specification of a predictive model, a model-based approach, combined with dynamic programming and Monte Carlo integration, enables direct probabilistic comparisons between the outcomes under the optimal DTR and alternative (dynamic or static) treatment regimes. The Bayesian predictive approach also circumvents problems related to frequentist estimators under the nonregular estimation problem. However, the model-based approach is susceptible to misspecification, in particular of the "null-paradox" type, which is due to the model parameters not having a direct causal interpretation in the presence of latent individual-level characteristics. Because it is reasonable to insist on correct inferences under the null of no difference between the alternative treatment regimes, we discuss how to achieve this through a "null-robust" reparametrization of the problem in a longitudinal setting. Since we argue that causal inference can be entirely understood as posterior predictive inference in a hypothetical population without covariate imbalances, we also discuss how controlling for confounding through inverse probability of treatment weighting can be justified and incorporated in the Bayesian setting.
authors.affiliation: Dalla Lana School of Public Health, University of Toronto, Toronto, Ontario M5T 3M7, Canada.
authors.forename: Olli
authors.initials: O
authors.lastname: Saarela
authors.affiliation: Department of Mathematics and Statistics, FI-00014 University of Helsinki, Finland.|National Institute for Health and Welfare, FI-00271 Helsinki, Finland.
authors.forename: Elja
authors.initials: E
authors.lastname: Arjas
authors.affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada.
authors.forename: David A
authors.initials: DA
authors.lastname: Stephens
authors.affiliation: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec H3A 1A2, Canada.
authors.forename: Erica E M
authors.initials: EE
authors.lastname: Moodie
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000188:drug therapy; D019380:Anti-HIV Agents / Q000627:therapeutic use; D001499:Bayes Theorem; D056808:Biostatistics / Q000379:methods*; D004358:Drug Therapy; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D015215:Zidovudine / Q000627:therapeutic use
chemical_list: D019380:Anti-HIV Agents; D015215:Zidovudine
keywords: Dynamic programming; Inverse probability of treatment weighting; Null-paradox; Optimal dynamic treatment regimes; Posterior predictive inference