  Heterogeneity and comorbidity are two interwoven challenges associated with
various healthcare problems that greatly hampered research on developing
effective treatment and understanding of the underlying neurobiological
mechanism. Very few studies have been conducted to investigate heterogeneous
causal effects (HCEs) in graphical contexts due to the lack of statistical
methods. To characterize this heterogeneity, we first conceptualize
heterogeneous causal graphs (HCGs) by generalizing the causal graphical model
with confounder-based interactions and multiple mediators. Such confounders
with an interaction with the treatment are known as moderators. This allows us
to flexibly produce HCGs given different moderators and explicitly characterize
HCEs from the treatment or potential mediators on the outcome. We establish the
theoretical forms of HCEs and derive their properties at the individual level
in both linear and nonlinear models. An interactive structural learning is
developed to estimate the complex HCGs and HCEs with confidence intervals
provided. Our method is empirically justified by extensive simulations and its
practical usefulness is illustrated by exploring causality among psychiatric
disorders for trauma survivors.
