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

The Patient Health Questionnaire-9 (PHQ-9) is generally used to determine the level of depression, and clinical decisions are usually made based on the overall score. Nevertheless, there can be significant variation in the response pattern of individuals who have the same score, indicating that there are variations in the organization of symptoms. To overcome this drawback, this paper presents an entropy-based computation system that describes PHQ-9 responses in a way that is not limited by a score measure. Responses to individual items are fused with information-theoretic quantities, such as Shannon entropy, Sample entropy, Permutation entropy, and Multiscale entropy, to form a more detailed feature space to classify depression severity. The proposed framework significantly increased the accuracy of the sum-score baseline in fivefold stratified cross-validation of the existing data, with the Random Forest adding 18.0 percentage points to the accuracy of 81.2 percent, reaching 99.2 percent. Statistical analysis also shows that the relationship between response entropy and the severity of depression is not linear, where entropy is at its highest when depression is moderate and reduced with severe depression. A potentially useful screening signal in this data set was observed to be an entropy threshold (0.439). These results suggest the complexity of the response patterns as a concomitant measure of digital depression.