Journal
BIOMETRICAL JOURNAL
Volume 57, Issue 6, Pages 941-958Publisher
WILEY-BLACKWELL
DOI: 10.1002/bimj.201400153
Keywords
Dynamic programming; Inverse probability of treatment weighting; Null-paradox; Optimal dynamic treatment regimes; Posterior predictive inference
Funding
- Natural Sciences and Engineering Research Council (NSERC) of Canada
- Fonds de recherche du Quebec-Sante (FRQ-S)
- National Cancer Institute (NCI)
- National Heart, Lung, and Blood Institute (NHLBI)
- National Institute on Deafness and Communication Disorders (NIDCD)
- [UL1-TR000424]
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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.
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