Estimation of causal effects with repeatedly measured outcomes in a Bayesian framework

Constructing causal inference methods to handle longitudinal data in observational studies is of high interest. In an observational setting, treatment assignment at each clinical visit follows a decision strategy where the treating clinician selects treatment based on current and past clinical measurements as well as treatment histories. These time-dependent structures, coupled with inherent correlations between and within each visit, add on to the data complexity. Despite recent interest in Bayesian causal methods, only a limited literature has explored approaches to handle longitudinal data and no method handles repeatedly measured outcomes. In this paper, we extended two Bayesian approaches: Bayesian estimation of marginal structural models and two-stage Bayesian propensity score analysis to handle a repeatedly measured outcome. Our proposed methods permit causal estimation of treatment effects at each visit. Time-dependent inverse probability of treatment weights are obtained from the Markov chain Monte Carlo samples of the posterior treatment assignment model for each follow-up visit. We use a simulation study to validate and compare the proposed methods and illustrate our approaches through a study of intravenous immunoglobulin therapy in treating newly diagnosed juvenile dermatomyositis.