A Logistic Regression Approach for Cardiovascular Disease Prediction

English

Overview

This study proposes an enhanced logistic regression framework for predicting cardiovascular disease (CVD). The approach integrates Recursive Feature Elimination with Cross-Validation (RFECV) and custom weight initialization to improve interpretability and accuracy. Cardiovascular disease remains one of the most critical global health concerns, highlighting the need for data-driven and interpretable predictive models.

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Mathematical Formulation

Logistic Regression Model

The model predicts the probability \( P(y = 1 \mid \mathbf{x}) \) that a patient has cardiovascular disease given features \( \mathbf{x} = (x_1, x_2, \ldots, x_n) \).

\[z = \omega_1 x_1 + \omega_2 x_2 + \cdots + \omega_n x_n + b\] \[P(y = 1 \mid \mathbf{x}) = \sigma(z) = \frac{1}{1 + e^{-z}}\]

where:
\( \omega_i \): weight of each feature
\( b \): bias term
\( \sigma(z) \): sigmoid (logistic) activation function

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Cost Function and Optimization

The cost function is defined by binary cross-entropy:

\[J(\omega, b) = -\frac{1}{m} \sum_{i=1}^{m} \Big[ y^{(i)} \log(\hat{y}^{(i)}) + (1 - y^{(i)}) \log(1 - \hat{y}^{(i)}) \Big]\]

Model parameters are updated via gradient descent:

\[\omega_j := \omega_j - \alpha \frac{\partial J}{\partial \omega_j}, \quad b := b - \alpha \frac{\partial J}{\partial b}\]

where \( \alpha \) is the learning rate.

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RFECV-Based Weight Initialization

RFECV ranks each feature’s predictive power. The initial weights are set inversely proportional to the ranking:

\[\omega_j^{(0)} = \frac{1}{\text{RFECVrank}(x_j)}\]

This ensures that the most critical clinical features (e.g., age, blood pressure, cholesterol) receive higher importance during early training, accelerating convergence.

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Dataset and Experiment

• Dataset: UCI Heart Disease Dataset (303 samples, 13 features)
• Cross-Validation: 5-Fold
• Optimization: Gradient Descent (\( \alpha = 0.01 \))
• Evaluation Metrics: Accuracy, F1-Score

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Results

Model	Accuracy	F1-Score
Logistic Regression (baseline)	79.0%	74.8%
RFECV-only Logistic Regression	84.2%	84.6%
Proposed (RFECV + Weight Init.)	87.5%	87.4%

The proposed approach outperformed both baseline and RFECV-only models, demonstrating a strong balance between precision and generalization.

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Awards

🏅 KSEF 2025 Junior BIO – Domestic Gold Medal
🥈 KSEF 2025 Junior BIO – Inter Silver Medal

These achievements recognize the project’s contribution to biomedical AI research and its educational significance in applying interpretable machine learning to real-world health prediction.

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Contribution

This study demonstrates how interpretable machine learning can advance biomedical prediction models, making logistic regression not only explainable but also clinically useful. Its structure provides a reproducible example for AI-driven medical research education.

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한국어

연구 개요

본 연구는 심혈관 질환(CVD) 예측을 위한 로지스틱 회귀(Logistic Regression) 모델을 개선한 방식으로 제안합니다. 기존의 단순한 회귀 모델에 교차검증 기반 재귀적 특성 제거(RFECV)와 가중치 초기화(Weight Initialization) 기법을 결합하여, 의료 데이터 분석에서 해석 가능성과 정확도를 동시에 향상시켰습니다.

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수학적 정의

\[z = \omega_1 x_1 + \omega_2 x_2 + \cdots + \omega_n x_n + b\] \[P(y = 1 \mid \mathbf{x}) = \frac{1}{1 + e^{-z}}\]

\( \omega_i \): 각 특성(feature)의 가중치
\( b \): 편향(bias)
\( P(y=1 \mid \mathbf{x}) \): 질병이 존재할 확률

모델 학습은 이진 교차 엔트로피 손실함수(Binary Cross-Entropy Loss)를 최소화하는 방향으로 진행됩니다.

\[J(\omega, b) = -\frac{1}{m} \sum_{i=1}^{m} [ y^{(i)} \log(\hat{y}^{(i)}) + (1 - y^{(i)}) \log(1 - \hat{y}^{(i)}) ]\]

경사하강법(Gradient Descent)을 통해 매개변수는 다음과 같이 업데이트됩니다.

\[\omega_j := \omega_j - \alpha \frac{\partial J}{\partial \omega_j}, \quad b := b - \alpha \frac{\partial J}{\partial b}\]

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RFECV 기반 가중치 초기화

\[\omega_j^{(0)} = \frac{1}{\text{RFECVrank}(x_j)}\]

RFECV로 도출된 변수 중요도에 따라 초기 가중치를 설정하여, 중요한 특성(나이, 혈압, 콜레스테롤 등)에 더 빠르게 수렴하도록 유도합니다.

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실험 결과

모델	정확도	F1 점수
기본 로지스틱 회귀	79.0%	74.8%
RFECV 적용	84.2%	84.6%
제안된 모델 (RFECV + 초기화)	87.5%	87.4%

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수상 내역

🏅 2025년 KSEF Senior BIO 국내 부문 금상
🥈 2025년 KSEF Senior BIO 국제 부문 은상

본 연구는 바이오메디컬 인공지능 응용의 가능성을 인정받아 교육적 및 연구적 우수성을 동시에 입증하였습니다.

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연구 의의

이 연구는 단순한 회귀 분석이 아닌, 특성 선택(Feature Selection)과 가중치 최적화를 결합한 해석 가능한 머신러닝 모델로, 실제 의료 환경에서도 적용 가능한 의사결정 지원형 AI 모델의 가능성을 보여줍니다.