Causal inference using multivariate generalized linear mixed-effects models

Dynamic prediction of causal effects under different treatment regimens is an essential problem in precision medicine. It is challenging because the actual mechanisms of treatment assignment and effects are unknown in observational studies. We propose a multivariate generalized linear mixed-effects model and a Bayesian g-computation algorithm to calculate the posterior distribution of subgroup-specific intervention benefits of dynamic treatment regimes. Unmeasured time-invariant factors are included as subject-specific random effects in the assumed joint distribution of outcomes, time-varying confounders, and treatment assignments. We identify a sequential ignorability assumption conditional on treatment assignment heterogeneity, that is, analogous to balancing the latent treatment preference due to unmeasured time-invariant factors. We present a simulation study to assess the proposed method's performance. The method is applied to observational clinical data to investigate the efficacy of continuously using mycophenolate in different subgroups of scleroderma patients.