===== Statistical Method =====

CUSUM (Cumulative Sum Control Chart) is a sequential analysis technique used to monitor change detection in binary outcomes. It is particularly effective for identifying small but consistent shifts in performance over time.

In this study, we used a **standard one-sided CUSUM chart** to track deviations from an acceptable complication rate. The core formula applied was:

''Cₙ = max(0, Cₙ₋₁ + (Xₙ - k))''

Where:  
  * ''Cₙ'' = CUSUM value at case ''n''  
  * ''Xₙ'' = binary outcome (1 for complication, 0 for success)  
  * ''k'' = reference value or allowable failure rate (set to 0.1)

This one-sided version resets to zero when performance improves (i.e., when the sum drops below zero), allowing early detection of deterioration.

An optional alert threshold (decision interval) was set at **2.5** to visually flag possible deviation requiring investigation.

For more complex scenarios involving heterogeneous patient risk, a **risk-adjusted CUSUM** is recommended, incorporating expected probabilities per case based on logistic regression models or clinical scoring systems (e.g., ASA, GCS, tumor location/size).