The Hidden Complexity of Mental Health: Multi-Entropy Analysis of Response Patterns in Depression Severity Assessment

Abstract

This study proposes an entropy-based framework for depression severity assessment using PHQ-9 responses. Instead of relying only on total questionnaire scores, the system analyzes response patterns using information-theoretic measures such as Shannon entropy, sample entropy, permutation entropy, and multiscale entropy. Experimental results show that the proposed approach significantly improves classification performance, with Random Forest accuracy increasing from 81.2% to 99.2%. The findings also reveal a non-linear relationship between response entropy and depression severity, where entropy peaks at moderate depression and decreases in severe cases. ROC analysis further demonstrates that entropy can serve as a useful complementary digital marker for severe depression detection.