====== 🎯 Target Failure Rate ======

===== 📌 Definition =====
> The **target failure rate** (*p₀*) in [[cusum_analysis]] is a predefined acceptable rate of failure for a procedure. It acts as a baseline against which a trainee’s 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.

===== 🧠 How to Choose a Target Failure Rate =====
<WRAP box>
**Factors to consider:**
  * Literature-based complication rates
  * Internal quality data from experienced clinicians
  * Complexity of the procedure
  * Training stage (novice vs expert-level target)
</WRAP>

===== 📊 Examples =====
| **Procedure**                        | **Target Failure Rate (p₀)** | **Notes** |
|-------------------------------------|-------------------------------|-----------|
| [[lumbar_puncture]]                 | 10–20%                        | Includes traumatic taps or supervisor takeover |
| [[central_line_insertion]]          | 5–10%                         | Includes failed placement, arterial puncture |
| [[intubation]] (1st pass)           | 10–20%                        | Setting-dependent: OR vs ED vs ICU |
| [[ube_lumbar_discectomy]]           | 10–15%                        | Includes incomplete decompression or conversions |
| [[laparoscopic_cholecystectomy]]    | 5%                            | Conversion to open, bile leak, etc. |

===== 🧪 In the CUSUM Formula =====
\[
S_i = S_{i-1} + (X_i - p₀)
\]
Where:
  * **Xᵢ =** 1 for failure, 0 for success  
  * **p₀ =** target failure rate (e.g., 0.20 = 20%)  
  * **Sᵢ =** cumulative sum at procedure *i*

===== ⚠️ Pitfalls in Choosing p₀ =====
  * Setting *p₀* **too low** = premature labeling of underperformance
  * Setting *p₀* **too high** = failure to detect real learning issues
  * It should reflect a **balance between ideal and realistic**