Robustness-Oriented Explainability Analysis of the PHQ-9 Depression Scale Using Ensemble Learning Under Response Perturbations

Reliable assessment of depression is essential for early identification of high-risk individuals, yet psychometric instruments such as the Patient Health Questionnaire-9 are vulnerable to response variability and uncertainty. This study aims to analyze the robustness, redundancy, and explainability of PHQ-9–based high-risk classification rather than propose a predictive diagnostic system. The objectives are to examine structural stability of the scale, evaluate effects of realistic Likert-scale perturbations on clinically relevant metrics, and assess resilience of high-risk detection under increasing uncertainty. An Extreme Gradient Boosting classifier was trained using clean PHQ-9 responses, with binary high-risk labels derived from established clinical thresholds. Robustness was evaluated by introducing bounded ±1 Likert-scale noise into symptom responses at multiple perturbation levels during testing. Results show that perfect performance under noise-free conditions reflects deterministic scale construction, while increasing perturbation produces gradual degradation in accuracy and sensitivity. Crucially, the ability to detect high-risk individuals remained above 97%, even when response variability increased, while the rate of missed cases rose only slightly. This trend suggests that the PHQ-9 survey possesses inherent internal consistency and structural stability, ensuring dependable risk categorization even when self-reported answers vary. The findings highlight the value of stress-testing assessments through response variation—a practical and clinically relevant way to verify the reliability of mental health tools. Ultimately, this approach advocates for the cautious interpretation and functional use of PHQ-9 screening in routine medical practice.