A novel approach to breast cancer detection using modified logistic regression with optimized feature selection

Abstract

The World Health Organization (WHO) reports 2.3 million new cases and 670,000 fatalities annually, and breast cancer remains one of the most prevalent and life-threatening diseases on a global scale. These poor outcomes highlight the critical need for new diagnostic techniques that can identify breast cancer in its early stages, allowing for early detection and increasing survival rates. Traditional screening methods, such as mammography, are frequently restricted by their high false-positive rates, despite the fact that early and precise diagnosis is essential for enhancing survival rates. To enhance diagnostic accuracy, we recommend a Modified Logistic Regression (MLR) model that employs different activation functions (sigmoid and modified $$\tanh$$ ). In addition, we employed feature selection techniques to reduce redundancy and eradicate highly correlated features in the Wisconsin Diagnostic Breast Cancer (WDBC) dataset and Wisconsin breast cancer (WBC) dataset. The proposed MLR model was compared using standard machine learning algorithms, including Logistic Regression (LR), Support Vector Machine (SVM), Random Forest (RF), Decision Tree (DT), K-Nearest Neighbors (KNN), XGBoost, LightGBM, CatBoost and these models are integrated into a soft voting classifier (SVC) technique to enhance predictive accuracy. All machine learning models in this study were implemented using the scikit-learn library, except for the modified logistic regression model, which was manually coded without using the LogisticRegression class from sklearn. Each model’s performance is individually evaluated and then compared against MLR. The proposed MLR attains an accuracy that is competitive with the strongest baselines (98.25% on WDBC and 97.81% on WBC); a paired McNemar’s test confirms that this accuracy is statistically on par with standard logistic regression rather than significantly superior. The distinctive benefits of MLR lie elsewhere: it produces better-calibrated probability estimates (consistently lower Brier scores than logistic regression and far below the no-skill prevalence baseline), a lower false-negative rate, and more compact feature attributions with consistent ranking, within a flexible architecture that admits any differentiable activation. We further show analytically that the modified $$\tanh$$ used by MLR is equivalent to a logistic sigmoid evaluated at twice the logit, $$\tfrac{1+\tanh (z)}{2}=\sigma (2z)$$ , so the training objective remains convex in the effective logits and the learnable bias weight introduces no spurious minima. These results position MLR as a reliable, well-calibrated instrument for supporting early breast cancer diagnosis.