Bayesian Shannon Entropy for Assessing Patient’s Data Interrelation in Medical Applications

This research explores the application of a proposed interrelation index for analyzing patient data in medical contexts. The patient data is represented as either quantitative time series or qualitative sequences. Conditional Bayesian inference rules were developed for both types of data. Shannon entropy was employed for the initial dataset, while Bayesian rules were applied to the randomized dataset. The interrelation index, calculated as the ratio between Bayesian Shannon entropy of the randomized dataset and Shannon entropy of the initial dataset, serves as an indicator of data coherence in time series or sequences. The medical applications of this interrelation index were demonstrated through the analysis of Heart Rate Variability (HRV) in patients with various cardiac diseases and the DNA sequences of a chronic lymphocytic leukemia (CLL) patient with different mutation statuses of the immunoglobulin heavy chain (IGHV) gene. Comparative analyses with normal cases were provided for both medical applications. In essence, the study highlights the utility of Bayesian inference in enhancing the sensitivity and accuracy of entropy-based analysis for quantitative time series and sequences of qualitative (nominal) variables.