Bayesian nonparametric mixtures of categorical directed graphs for personalized causal inference

Quantifying the causal effect of a treatment on a disease is a crucial task in medical science for the administration of effective therapies. Typically, such causal effects are inferred from multivariate data that are collected on patients and recorded in the form of categorical variables, including risk factors involved in disease progression, treatment assignments, and disease status. This feature motivates an approach to causal inference based on categorical Directed Acyclic Graphs (DAGs), which provide an effective framework for causal reasoning in complex multivariate settings. In this context, traditional DAG-based methods assume population homogeneity and accordingly attribute a unique causal effect to all subjects. However, this assumption is often unrealistic in clinical contexts, since patients may exhibit heterogeneous characteristics, possibly linked to unmeasured features. To address this issue, we propose a Bayesian nonparametric methodology based on a Dirichlet Process mixture of categorical DAGs, which allows treatment effects to vary across individuals because of underlying clustering structures in the data. We develop a Markov chain Monte Carlo algorithm for Bayesian posterior inference and evaluate our methodology through simulation studies. We then analyze patients affected by HER2+ breast cancer undergoing therapies that may cause cardiotoxic side effects. Importantly, our findings show that approaches neglecting population heterogeneity may produce biased results, since they can over- or under-estimate the risk of cardiotoxicity across patients.