A Mathematical Statistical Modeling Framework for Quantitative Analysis of Traditional Chinese Medicine Diagnosis and Treatment Patterns

Abstract

Traditional Chinese Medicine has accumulated a wealth of clinical experience over thousands of years, but its qualitative descriptions of symptoms, syndromes, and herbal prescriptions limit objective scientific analysis. To bridge the gap between traditional empirical knowledge and modern quantitative science, this work proposes a mathematical statistical modeling framework for the quantitative analysis of TCM diagnosis and treatment patterns. The framework integrates association rule mining based on the Apriori algorithm for discovering strong herbal combinations, hierarchical clustering analysis based on Jaccard distance and Ward linkage for identifying core herbal clusters, complex network analysis for characterizing the topology of herbal co occurrence, and logistic regression coupled with Bayesian inference for predicting syndrome categories from quantified symptom features. A real world TCM clinical dataset containing 312 distinct prescriptions and 1287 patient records covering ten standardized syndrome categories is employed as the experimental benchmark. Experimental results show that the proposed framework extracts 27 strong herbal association rules under suitable thresholds, recovers four interpretable herb clusters consistent with established TCM theory, and reaches a syndrome classification accuracy of 0.873, a macro average F1 score of 0.851, and a macro average area under the receiver operating characteristic curve of 0.940. The proposed framework provides a reproducible quantitative pathway for analyzing TCM clinical data and offers methodological support for the modernization and standardization of TCM.