Treatment Response Detection
Executive Summary
Patient 1: Treatment Response Analysis
| Metric | Pre-Acute (< 2026-02-09) | Post-Acute / Pre-Rux (2026-02-09 - 2026-03-16) | Post-Rux (≥ 2026-03-16) |
|---|---|---|---|
| HRV (RMSSD) | 7.6 (n=30) | 10.4 (n=34) | 12.1 (n=24) |
| Lowest Heart Rate | 79.6 (n=30) | 74.1 (n=34) | 72.2 (n=24) |
| Average Heart Rate | 88.7 (n=30) | 82.0 (n=34) | 80.6 (n=24) |
| Sleep Efficiency | 78.1 (n=30) | 79.1 (n=34) | 79.8 (n=24) |
| Deep Sleep | 1.2 (n=30) | 1.0 (n=34) | 1.2 (n=24) |
| Daily Steps | 2473.1 (n=32) | 2315.3 (n=35) | 3825.8 (n=28) |
Patient 2: Discovered Changepoints
| Date | Score | Confidence | Methods | Metrics |
|---|---|---|---|---|
| 2021-05-31 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2021-10-29 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2022-01-23 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2022-05-06 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2023-07-06 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2023-12-30 | 8 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, hrv_average, steps |
| 2022-08-08 | 7 | HIGH | cusum, rolling_window | deep_sleep_hours, efficiency, hr_average, hr_lowest, steps |
| 2024-06-03 | 6 | HIGH | cusum, rolling_window | hr_average, hr_lowest, hrv_average, steps |
| 2025-02-03 | 6 | HIGH | cusum, rolling_window | efficiency, hr_average, hr_lowest, hrv_average |
| 2024-01-22 | 5 | HIGH | cusum, rolling_window | hr_average, hr_lowest, hrv_average |
| 2025-02-11 | 5 | HIGH | cusum, rolling_window | efficiency, hr_average, hrv_average |
| 2025-03-25 | 5 | HIGH | cusum, rolling_window | efficiency, hr_average, hrv_average |
| 2021-02-20 | 2 | low | cusum | steps |
| 2025-12-02 | 2 | low | cusum | hrv_average |
Comparative Distributions
Multi-Metric Convergence
Patient 1: 4 days with 3+ metrics deviating beyond 1.5 SD (systemic shift events).
Patient 2: 28 days with 3+ metrics deviating beyond 1.5 SD (systemic shift events).
Patient 2: 2 days with 3+ metrics deviating beyond 1.5 SD (systemic shift events).
Methods Appendix
Changepoint Detection Methods
PELT (Penalized Exact Linear Time):
Uses the ruptures library with RBF kernel to detect optimal changepoints.
Signals are interpolated (for NaN) and standardized before fitting. Penalty is
derived from BIC: 2 * log(n) * variance.
CUSUM (Cumulative Sum): Computes the cumulative sum of deviations from the overall mean. Second-derivative sign changes identify inflection points. Filtered by magnitude threshold (0.5 SD).
BOCPD (Bayesian Online Change Point Detection): Implements Adams & MacKay (2007) with Normal-Gamma conjugate prior. Hazard rate set to 1/30 for Patient 1 (shorter observation window) and 1/50 for Patient 2 (longer data span). Changepoints where posterior probability exceeds 0.3.
Rolling Window Comparison: Adjacent 14-day windows compared via Welch's t-test and Cohen's d. Dates flagged where p < 0.01 AND |d| > 0.5, indicating both statistical significance and practical effect size.
Statistical Tests
Pre/Post Comparison: Mann-Whitney U test (non-parametric, two-sided) with Bonferroni correction for 6 simultaneous comparisons. Effect size: Cohen's d with pooled standard deviation. Confidence intervals: bootstrap with 1,000 iterations.
Consensus Scoring: For Patient 2, all (method x metric) detections are clustered within a 3-day tolerance window. The consensus score counts the number of unique methods and metrics detecting each cluster. High confidence = score >= 3.