Bayesian graphical modelling for heterogeneous causal effects

Our motivation stems from current medical research aiming at personalized treatment using a molecular-based approach. The goal is to develop a more precise and targeted decision making process, relative to traditional treatments based primarily on clinical diagnoses. A challenge we address is evaluating treatment effects for individuals affected by Glioblastoma (GBM), a brain cancer where targeted therapy is essential to improve patients' prospects. Specifically, we consider the pathway associated to cytokine TGF-beta, whose abnormal signalling activity has been found to be linked to the progression of GBM and other tumors. We analyze treatment effects within a causal framework represented by a Directed Acyclic Graph (DAG) model, whose vertices are the variables belonging to the TGF-beta pathway. A major obstacle in implementing the above program is represented by individual heterogeneity, implying that patients will respond differently to the same therapy. We address this issue through an infinite mixture of Gaussian DAG-models where both the graphical structure as well as the allied model parameters are regarded as uncertain. Our procedure determines a clustering structure of the units reflecting the underlying heterogeneity, and produces subject-specific causal effects through Bayesian model averaging across a variety of model features. When applied to the GBM dataset, it reveals that regulation of TGF-beta proteins produces heterogeneous effects, represented by clusters of patients potentially benefiting from selective interventions.