A Bayesian latent class approach to causal inference with longitudinal data

Bayesian methods are becoming increasingly in demand in clinical and public health comparative effectiveness research. Limited literature has explored parametric Bayesian causal approaches to handle time-dependent treatment and time-dependent covariates. In this article, building on to the work on Bayesian g-computation, we propose a fully Bayesian causal approach, implemented using latent confounder classes which represent the patient's disease and health status. Our setting is suitable when the latent class represents a true disease state that the physician is able to infer without misclassification based on manifest variables. We consider a causal effect that is confounded by the visit-specific latent class in a longitudinal setting and formulate the joint likelihood of the treatment, outcome and latent class models conditionally on the class indicators. The proposed causal structure with latent classes features dimension reduction of time-dependent confounders. We examine the performance of the proposed method using simulation studies and compare the proposed method to other causal methods for longitudinal data with time-dependent treatment and time-dependent confounding. Our approach is illustrated through a study of the effectiveness of intravenous immunoglobulin in treating newly diagnosed juvenile dermatomyositis.