π― Target Failure Rate
π Definition
The target failure rate (*pβ*) in cusum_analysis is a predefined acceptable rate of failure for a procedure. It acts as a baseline against which a traineeβs performance is compared. Deviations from this rate help determine learning progression or performance issues.
It must be set realistically based on clinical standards, published data, or institutional benchmarks.
π§ How to Choose a Target Failure Rate
Factors to consider:
- Literature-based complication rates
- Internal quality data from experienced clinicians
- Complexity of the procedure
- Training stage (novice vs expert-level target)
π Examples
| Procedure | Target Failure Rate (pβ) | Notes |
| ββββββββββββ- | ββββββββββ- | ββββ |
| lumbar_puncture | 10β20% | Includes traumatic taps or supervisor takeover |
| central_line_insertion | 5β10% | Includes failed placement, arterial puncture |
| intubation (1st pass) | 10β20% | Setting-dependent: OR vs ED vs ICU |
| ube_lumbar_discectomy | 10β15% | Includes incomplete decompression or conversions |
| laparoscopic_cholecystectomy | 5% | Conversion to open, bile leak, etc. |
π§ͺ In the CUSUM Formula
\[ S_i = S_{i-1} + (X_i - pβ) \] Where:
- Xα΅’ = 1 for failure, 0 for success
- pβ = target failure rate (e.g., 0.20 = 20%)
- Sα΅’ = cumulative sum at procedure *i*
β οΈ Pitfalls in Choosing pβ
- Setting *pβ* too low = premature labeling of underperformance
- Setting *pβ* too high = failure to detect real learning issues
- It should reflect a balance between ideal and realistic