Bayesian Network Modeling for Causal Inference: Cardiovascular Risk under Uncertainty
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Causal inference under uncertainty remains difficult in applied health research because real-world systems contain interacting variables, incomplete information, and probabilistic pathways that cannot always be tested through direct experimentation. This study develops and empirically evaluates a Bayesian network framework for causal-informed inference using the Framingham cardiovascular-risk dataset. The dataset includes 4,240 participants, 16 variables, and a binary ten-year coronary heart disease (CHD) outcome, with 644 positive cases (15.19% of the sample). The proposed approach combines an expert-guided directed acyclic graph with data-estimated conditional probability tables to represent relationships among demographic, behavioral, metabolic, cardiovascular, and disease-outcome variables. We handled missing values using mode and median imputation, discretized continuous variables into clinically meaningful states, and performed posterior inference through evidence propagation. We evaluated the Bayesian network using a stratified 70/30 train-test split and probability-based measures. The model achieved an area under the receiver operating characteristic curve (ROC-AUC) of 0.674, a Brier score of 0.123, a log-loss of 0.404, and an accuracy of 0.846, indicating useful probabilistic discrimination and strong average calibration for a transparent graphical model. Evidence-scenario analysis showed that posterior CHD probability increased from 2.04% in a low-risk profile to 39.13% in an older hypertensive profile and 75.00% in a combined high-risk profile. Sensitivity analysis identified age, systolic blood pressure, diabetes, hypertension, and glucose status as the most influential sources of posterior risk change. The study contributes a reproducible Bayesian network workflow for uncertainty-aware causal reasoning and demonstrates how directed probabilistic graphs can improve explainability in cardiovascular decision support while avoiding unsupported causal certainty from observational data.
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