Adaptive Mean–Regression Modeling for Medical Diagnosis: A Hybrid Statistical Learning Framework with Interpretable and Adaptive Properties

This paper proposes a new statistical machine learning algorithm for medical diagnosis, called the Adaptive Mean-Regression Model (AMRM). The approach combines class-wise mean estimation with a basic linear regression correction mechanism to enhance diagnostic quality as precisely as possible, while retaining the entire interpretation. Compared with complex deep learning or probabilistic models, AMRM uses only simple statistical functions, such as calculating the mean, computing Euclidean distance, and performing linear regression. An adaptive update rule modifies the influence weights within classes based on observed diagnostic errors, allowing the model to learn from misclassifications without gradient-based optimization. Compared with more traditional machine learning models such as logistic regression, support vector machines, and random forests, the proposed AMRM achieves similar predictive accuracy while being much more interpretable and having lower computational complexity. This makes the model particularly applicable in clinical settings where transparency is crucial. The accuracy, precision, sensitivity, and specificity of the UCI Heart Disease dataset are 81.3%, 80.5%, 78.6%, and 83.7%, respectively. The proposed AMRM, in contrast to conventional regression-based classifiers, offers a hybrid statistical framework that combines the class-wise mean representation with regression-based correction and adaptive feature weighting. This combination improves interpretability while preserving competitive predictive performance. The findings indicate that AMRM can provide a good balance between statistical transparency and diagnostic accuracy.