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).