Bayesian nonparametric mixtures of directed acyclic graphs for heterogeneous causal inference

Abstract

Quantifying causal effects of exposures on outcomes, such as a treatment and a disease respectively, is a crucial issue in medical science for the development and administration of effective therapies. Importantly, any related causal-inference analysis should account for all those variables, e.g. clinical features, that can affect both outcomes and exposures and in particular can act as risk factors involved in the occurrence of a disease. In addition, the selection of targeted strategies for therapy administration requires to quantify such treatment effects at personalized, i.e subject-specific, level rather than at population level. We address these issues by proposing a modelling framework based on categorical Directed Acyclic Graphs (DAGs) which provide an effective tool to learn and quantify causal relationships and causal effects between variables from the data. In addition, we account for population heterogeneity by considering a Dirichlet Process (DP) mixture of categorical DAGs, that allows to cluster individuals into homogeneous groups characterized by common causal structures, dependence parameters and in turn causal effects. We develop computational strategies for Bayesian posterior inference, from which a battery of causal effects at subject-specific level can be eventually recovered. Our methodology is evaluated through simulation studies and applied to a dataset of breast cancer patients to investigate side effects associated with the occurrence of cardiotoxicity and possibly implied by the administration of common anticancer therapies.