====== 📊 CUSUM Analysis ======

===== 📌 Definition =====
> **CUSUM (Cumulative Sum Control Chart) analysis** is a statistical technique used to monitor change detection over time. In medicine, it’s widely applied to analyze **learning curves**—especially in surgical procedures—to detect improvement or deterioration in performance.

Cumulative sum (CUSUM) of deviations from a target performance level. Tracks case-by-case trends and identifies when competence is achieved or errors increase.

It plots the cumulative sum of deviations from a predefined target or acceptable outcome rate, providing a **visual and quantitative assessment** of proficiency acquisition.

===== 🧠 In Surgical Training =====
<WRAP box>
CUSUM helps evaluate **how many procedures a surgeon needs** to achieve [[competency]] in a new technique, such as [[ube]], [[laparoscopy]], or [[microsurgery]].

**Key Uses:**
  * Detect performance trends over time
  * Identify the "turning point" where the surgeon achieves acceptable performance
  * Differentiate between **competence**, **proficiency**, and **mastery**
</WRAP>

===== 🧪 How It Works =====
Let:
  * **Xi** = outcome of case *i* (success = 0, failure = 1)
  * **p₀** = acceptable failure rate
  * **S₀** = 0 (initial sum)
  * **Si** = Si₋₁ + (Xi - p₀)

Then:
  * A steep upward trend suggests consistent **failures** (worsening performance)
  * A downward slope indicates **learning and improvement**
  * A flat line reflects **stable, competent performance**

===== 📈 Example in UBE =====
In a [[narrative_review]] on ube training, CUSUM analysis was used to assess:
  * Early technical errors (e.g., incomplete decompression, nerve root irritation)
  * Operative time benchmarks
  * Conversion to open surgery

This method revealed that **significant proficiency** in UBE lumbar decompression was typically achieved after **20–30 cases**, depending on prior endoscopic experience
((Espinoza XAS, Pérez EG, Choi DJ. The unilateral biportal endoscopy journey: proposing a 10-tier difficulty progression framework for unilateral biportal endoscopy. Asian Spine J. 2025 Apr 7. doi: 10.31616/asj.2025.0064. Epub ahead of print. PMID: 40195633.)).

===== ✅ Advantages =====
  * Objective tool for tracking learning curves
  * Provides early warning for declining performance
  * Can be adapted to binary (success/failure) or continuous variables (e.g., operative time)

===== ⚠️ Limitations =====
  * Requires consistent, well-defined outcome measures
  * Sensitive to data quality and completeness
  * May need combination with other metrics (e.g., risk-adjusted CUSUM, EWMA)

====== 📊 CUSUM Analysis for Lumbar Puncture ======

~~TOC~~

===== 📌 Objective =====
To evaluate the learning curve of medical trainees performing **[lumbar_puncture]**, using **[cusum_analysis]** to track the rate of successful procedures and determine the point at which competency is achieved.

===== 🧪 Method =====
**[[Target failure rate]] (p₀):** 20%  
**Success =** CSF obtained without requiring supervisor takeover  
**Failure =** CSF not obtained, traumatic puncture, or supervisor takeover

Let:  
  * **Xi =** 0 for success, 1 for failure  
  * **Si =** cumulative sum of (Xi - p₀)  

Initial value **S₀ = 0**

===== 📈 Example Case Series (First 20 LPs) =====
| Case # | Outcome | Xi | Si = Si-1 + (Xi - 0.2) |
|--------|---------|----|------------------------|
| 1      | Success | 0  | 0 - 0.2 = **-0.2**     |
| 2      | Success | 0  | -0.2 - 0.2 = **-0.4**  |
| 3      | Failure | 1  | -0.4 + 0.8 = **0.4**   |
| 4      | Success | 0  | 0.4 - 0.2 = **0.2**    |
| 5      | Success | 0  | 0.2 - 0.2 = **0.0**    |
| 6      | Success | 0  | 0.0 - 0.2 = **-0.2**   |
| 7      | Success | 0  | -0.2 - 0.2 = **-0.4**  |
| 8      | Failure | 1  | -0.4 + 0.8 = **0.4**   |
| 9      | Success | 0  | 0.4 - 0.2 = **0.2**    |
| 10     | Success | 0  | 0.2 - 0.2 = **0.0**    |
| 11     | Success | 0  | 0.0 - 0.2 = **-0.2**   |
| 12     | Success | 0  | -0.2 - 0.2 = **-0.4**  |
| 13     | Success | 0  | -0.4 - 0.2 = **-0.6**  |
| 14     | Success | 0  | -0.6 - 0.2 = **-0.8**  |
| 15     | Failure | 1  | -0.8 + 0.8 = **0.0**   |
| 16     | Success | 0  | 0.0 - 0.2 = **-0.2**   |
| 17     | Success | 0  | -0.2 - 0.2 = **-0.4**  |
| 18     | Success | 0  | -0.4 - 0.2 = **-0.6**  |
| 19     | Success | 0  | -0.6 - 0.2 = **-0.8**  |
| 20     | Success | 0  | -0.8 - 0.2 = **-1.0**  |

===== 🧠 Interpretation =====
The **CUSUM chart** would show an **initial learning phase** with small performance fluctuations. Around case **15–20**, the steady negative slope indicates consistent success below the target failure rate, suggesting **competency is achieved** after ~18–20 procedures.

===== ✅ Takeaways =====
  * CUSUM is a powerful tool to track **[learning_curve]** in procedural skills.
  * In this example, the trainee reached proficiency in LP after ~20 cases.
  * Regular monitoring helps detect early need for intervention or additional training.


===== CUSUM Analysis for Intracranial Pressure Monitor Placement =====
[[CUSUM Analysis for Intracranial Pressure Monitor Placement]]