  A causal decomposition analysis allows researchers to determine whether the
difference in a health outcome between two groups can be attributed to a
difference in each group's distribution of one or more modifiable mediator
variables. With this knowledge, researchers and policymakers can focus on
designing interventions that target these mediator variables. Existing methods
for causal decomposition analysis either focus on one mediator variable or
assume that each mediator variable is conditionally independent given the group
label and the mediator-outcome confounders. In this paper, we propose a
flexible causal decomposition analysis method that can accommodate multiple
correlated and interacting mediator variables, which are frequently seen in
studies of health behaviors and studies of environmental pollutants. We extend
a Monte Carlo-based causal decomposition analysis method to this setting by
using a multivariate mediator model that can accommodate any combination of
binary and continuous mediator variables. Furthermore, we state the causal
assumptions needed to identify both joint and path-specific decomposition
effects through each mediator variable. To illustrate the reduction in bias and
confidence interval width of the decomposition effects under our proposed
method, we perform a simulation study. We also apply our approach to examine
whether differences in smoking status and dietary inflammation score explain
any of the Black-White differences in incident diabetes using data from a
national cohort study.
