Specialized Session 1: Causal Inference

This paper proposes a new statistical approach for assessing treatment effect using Bayesian Networks (BNs). The goal is to draw causal inferences from observational data with a binary outcome and discrete covariates. The BNs are here used to estimate the propensity score, which enables flexible modeling and ensures maximum likelihood properties, including asymptotic efficiency. When the propensity score is estimated by BNs, two point estimators are considered – Hájek and Horvitz-Thompson – based on inverse probability weighting, and their main distributional properties are derived for constructing confidence intervals and testing hypotheses about the absence of the treatment effect. Empirical evidence is presented to show the goodness of the proposed methodology on a simulation study mimicking the characteristics of a real dataset of prostate cancer patients from Milan San Raffaele Hospital.

Quantifying the causal effect of a treatment on a disease is crucial in medical science for the administration of effective therapies. Because patients may exhibit heterogeneous characteristics, the objective is to quantify treatment effects at personalized, rather than at population, level. To achieve this goal, we propose a methodology based on categorical Directed Acyclic Graphs (DAGs), which provide an effective tool for causal inference in multivariate settings. To address population heterogeneity, we develop a Dirichlet Process mixture of categorical DAGs, which clusters individuals into homogeneous groups characterized by common causal structures, dependence parameters and causal effects. Our methodology is applied to a dataset of patients affected by HER2+ breast cancer.

Assessing the short-term effects of air pollutants on health is crucial for public health. The Potential Outcome (PO) approach to causal inference has been applied in this field, but rarely to investigate the exposure-response function in the case of continuous environmental exposures. In this study, we use a matching method based on the Generalized Propensity Score to estimate the average exposure-response function describing the short-term effect of exposure to airborne particles with diameter less than 2.5 $\mu$m (PM$_{2.5}$) on mortality in the metropolitan area of Florence, for the years 2008-2019. We adopt a machine learning approach for GPS estimation and propose novel estimands to assess the impact of PM$_{2.5}$ in terms of attributable deaths, after defining different counterfactual scenarios. Our findings identify a positive causal relationship between air pollutant levels and mortality, with impacts that are not negligible, providing clear evidence of an effect of air pollution on population health in the study area.