Joint mixed-effects models for causal inference with longitudinal data.

Causal inference with observational longitudinal data and time-varying exposures is complicated due to the potential for time-dependent confounding and unmeasured confounding. Most causal inference methods that handle time-dependent confounding rely on either the assumption of no unmeasured confounders or the availability of an unconfounded variable that is associated with the exposure (eg, an instrumental variable). Furthermore, when data are incomplete, validity of many methods often depends on the assumption of missing at random. We propose an approach that combines a parametric joint mixed-effects model for the study outcome and the exposure with g-computation to identify and estimate causal effects in the presence of time-dependent confounding and unmeasured confounding. G-computation can estimate participant-specific or population-average causal effects using parameters of the joint model. The joint model is a type of shared parameter model where the outcome and exposure-selection models share common random effect(s). We also extend the joint model to handle missing data and truncation by death when missingness is possibly not at random. We evaluate the performance of the proposed method using simulation studies and compare the method to both linear mixed- and fixed-effects models combined with g-computation as well as to targeted maximum likelihood estimation. We apply the method to an epidemiologic study of vitamin D and depressive symptoms in older adults and include code using SAS PROC NLMIXED software to enhance the accessibility of the method to applied researchers.