arXiv subjects

Dafne Zorzetto

Publications and source records attributed to Dafne Zorzetto.

9 recordsLinked to original sources

arXiv2026

Bayesian Nonparametrics for Principal Stratification with Continuous Post-Treatment Variables

Principal stratification provides a causal inference framework for investigating treatment effects in the presence of a post-treatment variable. Principal strata play a key role in characterizing the treatment effect by identifying groups of units with the same or similar values for the potential post-treatment variable at all treatment levels. The literature has focused mainly on binary post-treatment variables. Few papers considered continuous post-treatment variables. In the presence of a continuous post-treatment, a challenge is how to identify and characterize meaningful coarsening of the latent principal strata that lead to interpretable principal causal effects. This paper introduces the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with binary treatment and continuous post-treatment variables. CASBAH leverages Bayesian nonparametric priors with an innovative hierarchical structure for the potential post-treatment outcomes that overcomes some of the limitations of previous works. Specifically, the novel features of our method allow for (i) identifying coarsened principal strata through a data-adaptive approach and (ii) providing a comprehensive quantification of the uncertainty surrounding stratum membership. Through Monte Carlo simulations, we show that the proposed methodology performs better than existing methods in characterizing the principal strata and estimating principal effects of the treatment. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

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arXiv2026

Multivariate Causal Effects: a Bayesian Causal Regression Factor Model

The impact of wildfire smoke on air quality is a growing concern, contributing to air pollution through a complex mixture of chemical species with important implications for public health. While previous studies have primarily focused on its association with total particulate matter (PM2.5), the causal relationship between wildfire smoke and the chemical composition of PM2.5 remains largely unexplored. Exposure to these chemical mixtures plays a critical role in shaping public health, yet capturing their relationships requires advanced statistical methods capable of modeling the complex dependencies among chemical species. To fill this gap, we propose a Bayesian causal regression factor model that estimates the multivariate causal effects of wildfire smoke on the concentration of 27 chemical species in PM2.5 across the United States. Our approach introduces two key innovations: (i) a causal inference framework for multivariate potential outcomes, and (ii) a novel Bayesian factor model that employs a probit stick-breaking process as prior for treatment-specific factor scores. By focusing on factor scores, our method addresses the missing data challenge common in causal inference and enables a flexible, data-driven characterization of the latent factor structure, which is crucial to capture the complex correlation among multivariate outcomes. Through Monte Carlo simulations, we show the model's accuracy in estimating the causal effects in multivariate outcomes and characterizing the treatment-specific latent structure. Finally, we apply our method to US air quality data, estimating the causal effect of wildfire smoke on 27 chemical species in PM2.5, providing a deeper understanding of their interdependencies.

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arXiv2026

Bayesian Nonparametric Causal Inference for High-Dimensional Nutritional Data via Factor-Based Exposure Mapping

Diet plays a crucial role in health, and understanding the causal effects of dietary patterns is essential for informing public health policy and personalized nutrition strategies. However, causal inference in nutritional epidemiology faces several challenges: (i) high-dimensional and correlated food/nutrient intake data induce massive treatment levels; (ii) nutritional studies are interested in latent dietary patterns rather than single food items; and (iii) the goal is to estimate heterogeneous causal effects of these dietary patterns on health outcomes. We address these challenges by introducing a sophisticated exposure mapping framework that reduces the high-dimensional treatment space via factor analysis and enables the identification of dietary patterns. We also extend the Bayesian Causal Forest to accommodate three ordered levels of dietary exposure, better capturing the complex structure of nutritional data and enabling estimation of heterogeneous causal effects. We evaluate the proposed method through extensive simulations and apply it to a multi-center epidemiological study of Hispanic/Latino adults residing in the US. Using high-dimensional dietary data, we identify six dietary patterns and estimate their causal link with two key health risk factors: body mass index and fasting insulin levels. Our findings suggest that higher consumption of plant lipid-antioxidant, plant-based, animal protein, and dairy product patterns is associated with reduced risk.

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arXiv2025

Characterizing the Effects of Environmental Exposures on Social Mobility: Bayesian Semi-parametrics for Principal Stratification

Understanding the causal effects of air pollution exposures on social mobility is attracting increasing attention. At the same time, education is widely recognized as a key driver of social mobility. However, the causal pathways linking fine particulate matter (PM2.5) exposure, educational attainment, and social mobility remain largely unexplored. To address this, we adopt the principal stratification approach, which rigorously defines causal effects when a post-treatment variable--educational attainment--is affected by exposure--PM2.5--and may, in turn, affect the primary outcome--social mobility. To estimate the causal effects, we propose a Bayesian semi-parametric method leveraging infinite mixtures for modeling the primary outcome. The proposed method (i) allows flexible modeling of the distribution of the primary potential outcomes, (ii) improves the accuracy of counterfactual imputation--a fundamental problem in causal inference framework--, and (iii) enables the characterization of treatment effects across different values of the post-treatment variable. We evaluate the performance of the proposed methodology through a Monte Carlo simulation study, demonstrating its advantages over existing approaches. Finally, we apply our method to a national dataset of 3,009 counties in the United States to estimate the causal effect of PM2.5 on social mobility, taking into account educational attainment as a post-treatment variable. Our findings indicate that in counties where higher PM2.5 exposure significantly reduces educational attainment social mobility decreases by approximately 5% compared to counties with lower PM2.5 exposure. We also find that in counties where exposure to PM2.5 does not affect educational attainment, social mobility is reduced by approximately 2% hinting at the possibility of further, yet unexplored, pathways connecting air pollution and social mobility.

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arXiv2025

Zero-Inflated Bayesian Multi-Study Infinite Non-Negative Matrix Factorization

Understanding the association between dietary patterns and health outcomes, such as the cancer risk, is crucial to inform public health guidelines and shaping future dietary interventions. However, dietary intake data present several statistical challenges: they are high-dimensional, often sparse with excess zeros, and exhibit heterogeneity driven by individual-level covariates. Non-Negative Matrix Factorization (NMF), commonly used to estimate patterns in high-dimensional count data, typically relies on Poisson assumptions and lacks the flexibility to fully address these complexities. Additionally, integrating data across multiple studies, such as case-control studies on cancer risk, requires models that can share information across sources while preserving study-specific structure. In this paper, we introduce a novel Bayesian NMF model that (i) jointly models multi-study count data to enable cross-study information sharing, (ii) incorporate a mixture component to account for zero inflation, and (iii) leverage flexible Bayesian non-parametric priors for characterizing the heterogeneity in pattern scores induced by the individual covariates. This structure allows for clustering of individuals based on dietary profiles, enabling downstream association analyses with health outcomes. Through extensive simulation studies, we demonstrate that our model significantly improves estimation accuracy compared to existing Bayesian NMF methods. We further illustrate its utility through an application to multiple case-control studies on diet and upper aero-digestive tract cancers, identifying nutritionally meaningful dietary patterns. An R package implementing our approach is available at https://github.com/blhansen/ZIMultiStudyNMF.

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arXiv2025

Causal Inference for Latent Outcomes Learned with Factor Models

In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor models or representation learning. In this work, we investigate causal effects on $\textit{latent outcomes}$ derived from high-dimensional observed data using nonnegative matrix factorization. To the best of our knowledge, this is the first study to formally address causal inference in this setting. A central challenge is that estimating a latent factor model can cause an individual's learned latent outcome to depend on other individuals' treatments, thereby violating the standard causal inference assumption of no interference. We formalize this issue as $\textit{learning-induced interference}$ and distinguish it from interference present in a data-generating process. To address this, we propose a novel, intuitive, and theoretically grounded algorithm to estimate causal effects on latent outcomes while mitigating learning-induced interference and improving estimation efficiency. We establish theoretical guarantees for the consistency of our estimator and demonstrate its practical utility through simulation studies and an application to cancer mutational signature analysis. All baseline and proposed methods are available in our open-source R package, ${\tt causalLFO}$.

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arXiv2025

Sparse Bayesian Factor Models with Mass-Nonlocal Factor Scores

Bayesian factor models are widely used for dimensionality reduction and pattern discovery in high-dimensional datasets across diverse fields. These models typically focus on imposing priors on factor loading to induce sparsity and improve interpretability. However, factor scores, which play a critical role in individual-level associations with factors, have received less attention and are assumed to follow a standard normal distribution. This assumption oversimplifies the heterogeneity often observed in real-world applications. We propose the sparse Bayesian Factor model with MAss-Nonlocal factor scores (BFMAN), a novel framework that addresses these limitations by introducing a mass-nonlocal prior on factor scores. This prior allows for both exact zeros and flexible, nonlocal behavior, capturing individual-level sparsity and heterogeneity. The sparsity in the score matrix enables a robust and novel approach to determine the optimal number of factors. Model parameters are estimated via a fast and efficient Gibbs sampler. Extensive simulations demonstrate that BFMAN outperforms standard Bayesian factor models in factor recovery, sparsity detection, score estimation, and selection of the optimal number of factors. We apply BFMAN to the Hispanic Community Health Study/Study of Latinos, identifying meaningful dietary patterns and their associations with cardiovascular disease, showcasing the model's ability to uncover insights into complex nutritional data.

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arXiv2024

A Bayesian Nonparametric Method to Adjust for Unmeasured Confounding with Negative Controls

Unmeasured confounding bias threatens the validity of observational studies. While sensitivity analyses and study designs have been proposed to address this issue, they often overlook the growing availability of auxiliary data. Using negative controls from these data is a promising new approach to reduce unmeasured confounding bias. In this article, we develop a Bayesian nonparametric method to estimate a causal exposure-response function (CERF) leveraging information from negative controls to adjust for unmeasured confounding. We model the CERF as a mixture of linear models. This strategy captures the potential nonlinear shape of CERFs while maintaining computational efficiency, and it leverages closed-form results that hold under the linear model assumption. We assess the performance of our method through simulation studies. We found that the proposed method can recover the true shape of the CERF in the presence of unmeasured confounding under assumptions. To show the practical utility of our approach, we apply it to adjust for a possible unmeasured confounder when evaluating the relationship between long-term exposure to ambient $PM_{2.5}$ and cardiovascular hospitalization rates among the elderly in the continental US. We implement our estimation procedure in open-source software and have made the code publicly available to ensure reproducibility.

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arXiv2023

Confounder-Dependent Bayesian Mixture Model: Characterizing Heterogeneity of Causal Effects in Air Pollution Epidemiology

Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (PM2.5) increases mortality risk. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the Group Average Treatment Effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this work, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of PM2.5 on mortality are heterogeneous.

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