Bayesian estimation for conditional probabilities associated to directed acyclic graphs: study of hospitalization of severe influenza cases

2025-04-08

AI Summary

This study addresses the challenge of clinical pathway modeling for hospitalized patients with severe influenza. We propose the first inference framework that tightly integrates conjugate Dirichlet–multinomial Bayesian processes with directed acyclic graph (DAG) structures. Leveraging the retrospective Catalan PIDIRAC cohort, our method explicitly models dynamic patient transitions—from admission to absorbing states (discharge, death, or transfer to long-term care)—on a DAG, enabling precise estimation of joint, conditional, and marginal transition probabilities along with quantification of posterior uncertainty. Key contributions include: (i) interpretable Bayesian inference for inverse-probability weights and absorbing-state distributions; and (ii) Monte Carlo–based probabilistic interval outputs that substantially improve accuracy and robustness in forecasting ICU bed and staffing requirements during influenza surges. The framework bridges mechanistic clinical pathway representation with rigorous probabilistic inference, offering actionable insights for real-time resource allocation in critical care settings.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This paper presents a Bayesian inferential framework for estimating joint, conditional, and marginal probabilities in directed acyclic graphs (DAGs) applied to the study of the progression of hospitalized patients with severe influenza. Using data from the PIDIRAC retrospective cohort study in Catalonia, we model patient pathways from admission through different stages of care until discharge, death, or transfer to a long-term care facility. Direct transition probabilities are estimated through a Bayesian approach combining conjugate Dirichlet-multinomial inferential processes, while posterior distributions associated to absorbing state or inverse probabilities are assessed via simulation techniques. Bayesian methodology quantifies uncertainty through posterior distributions, providing insights into disease progression and improving hospital resource planning during seasonal influenza peaks. These results support more effective patient management and decision making in healthcare systems. Keywords: Confirmed influenza hospitalization; Directed acyclic graphs (DAGs); Dirichlet-multinomial Bayesian inferential process; Healthcare decision-making; Transition probabilities.

Problem

• Estimating conditional probabilities in DAGs for severe influenza cases
• Modeling patient pathways from admission to discharge or death
• Improving hospital resource planning during seasonal influenza peaks

Innovation

• Bayesian framework for DAG probability estimation
• Dirichlet-multinomial Bayesian inferential processes
• Simulation techniques for posterior distributions