Causal Inference using Multivariate Generalized Linear Mixed-Effects Models with Longitudinal Data

Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; Zhou, Elliott, & Little, 2019) to incorporate multivariate generalized linear mixed-effects models. Unmeasured time-invariant factors are identified as subject-specific random effects in the assumed joint distribution of outcomes, time-varying confounders, and treatment assignments. Existing methods mostly assume no unmeasured confounding and focus on balancing the observed confounder distributions between different treatments, while our method allows the presence of time-invariant unmeasured confounding. We propose a sequential ignorability assumption based on treatment assignment heterogeneity, which is analogous to balancing the latent tendency toward each treatment due to unmeasured time-invariant factors beyond the observables. We use simulation studies to assess the sensitivity of the proposed method's performance to various model assumptions. The method is applied to observational clinical data to investigate the efficacy of continuously using mycophenolate in different subgroups of scleroderma patients who were treated with the drug.