Statistical and Mathematical Modelling for Diabetes Risk Prediction: A Comparative Analysis of Predictive Factors and Classification Methods

Abstract

Diabetes mellitus is a complex chronic disease that results from the interaction of demographic, clinical, metabolic, and hereditary factors. This study proposes an integrated statistical and mathematical modelling framework for predicting diabetes risk using secondary health data. The publicly accessible Pima Indians Diabetes Dataset is selected as the primary source of data. The proposed approach includes data preprocessing, exploratory statistical analysis, assessment of predictor variables, mathematical model development, model validation, and comparative evaluation of predictive performance. Four classification techniques—Logistic Regression, Decision Tree, Random Forest, and Support Vector Machine—are examined as alternative mathematical approaches for representing the association between the selected predictor variables and diabetes status. The study specifically considers the treatment of missing values and physiologically unrealistic observations, feature scaling, class distribution, feature selection, and model stability. Model performance is evaluated using several measures, including accuracy, precision, sensitivity, specificity, F1-score, receiver operating characteristic area under the curve (ROC-AUC), and precision-recall analysis. The findings suggest that diabetes risk is influenced by multiple factors, with glucose level, body mass index, and age providing considerable predictive information, while other clinical and hereditary characteristics offer additional predictive value. The study further demonstrates that predictive performance is influenced by data preprocessing procedures, feature selection, parameter optimization, and the adopted validation strategy. Overall, the proposed framework combines statistical interpretation with computational prediction and establishes a foundation for developing interpretable and population-specific diabetes-risk prediction models based on secondary health data.