Bayesian Decision Network for Heart Disease Diagnosis

A Python implementation of a Bayesian Decision Network (BDN) applied to the clinical problem of whether to recommend diagnostic testing for heart disease, given observed patient characteristics.

Background and Attribution

The factor algebra at the core of this project — factor product, marginalization, evidence observation, and Expected Utility Factor calculation — is adapted from programming assignments in the course Probabilistic Graphical Models (Daphne Koller, Stanford University / Coursera). The original assignments were written in MATLAB; this project re-implements those algorithms from scratch in Python/NumPy.

Beyond the algorithmic foundation, the following components are original contributions applied to a real-world clinical dataset:

• Empirical CPT estimation from a real-world dataset (Heart Disease UCI, n = 1,025)
• Feature discretization pipeline with clinically motivated bin boundaries
• A custom utility table encoding realistic asymmetric costs of clinical decisions
• DAG visualization using NetworkX
• Patient-specific conditional MEU queries based on observed evidence
• Expected Value of Perfect Information (EVPI) calculation
• Posterior probability heatmaps across joint risk factor combinations

Problem Statement

A clinician observes patient characteristics (age, cholesterol level, maximum heart rate, exercise-induced angina) and must decide whether to order further diagnostic testing. The decision carries asymmetric consequences: missing a diseased patient is far more costly than unnecessarily testing a healthy one. The goal is to identify the decision that maximises expected utility under uncertainty about the true disease state.

Network Structure

The influence diagram encodes the following causal assumptions:

Age (A) ──► Chol (C) ──►
Age (A) ──► HR (H)   ──► Disease (D) ──► Utility (U)
Age (A) ──► Exang (E)──►                      ▲
                              Decision (S) ────┘

Node	Type	States
Age (A)	Random	3 bins: <40, 40–55, >55
Cholesterol (C)	Random	3 bins: <200, 200–240, >240 mg/dL
Max Heart Rate (H)	Random	3 bins: <120, 120–160, >160 bpm
Exercise-induced Angina (E)	Random	Binary: No / Yes
Disease (D)	Random	Binary: No / Yes
Decision (S)	Decision	Binary: No Test / Test
Utility (U)	Utility	Defined by table below

Utility Table

Disease	Decision	Utility
No disease	No test	+10
No disease	Test	−20
Disease	No test	−100
Disease	Test	+80

Results

Quantity	Value
MEU — unconditional (population prior)	30.35
Optimal decision — unconditional	Test
MEU — high-risk evidence profile	0.04
Optimal decision — conditional	No Test
Expected Value of Perfect Information (EVPI)	14.90

The unconditional analysis recommends testing as the default policy. However, specific patient evidence can reverse this recommendation — demonstrating that the optimal action is not fixed but evidence-dependent. The EVPI of 14.9 sets an upper bound on the utility gain from acquiring perfect diagnostic information before deciding.

Dataset

Heart Disease UCI via Kaggle (ketangangal/heart-disease-dataset-uci) 1,025 patient records with features: age, sex, chest pain type, resting blood pressure, cholesterol, fasting blood sugar, resting ECG, maximum heart rate, exercise-induced angina, ST depression (oldpeak), slope, vessels colored by fluoroscopy, thalassemia, and binary disease target.

Repository Structure

.
├── Decision_Making.ipynb    # Main notebook
└── README.md

Dependencies

numpy
pandas
matplotlib
networkx
kagglehub

Usage

Open Decision_Making.ipynb in Jupyter or Google Colab and run cells sequentially. The notebook fetches the dataset automatically via kagglehub.

Reference

Koller, D. & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.

Koller, D. (2012). Probabilistic Graphical Models (Course). Stanford University / Coursera.