📊 CUSUM Analysis

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.

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

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

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 ¹⁾.

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)

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

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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.

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

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

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.

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

¹⁾

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.