The cumulative sum at case (CUSUM value) represents the running total of deviations from the expected performance level up to a specific case number.

In a binary outcome model (e.g., success = 0, complication = 1), the CUSUM at each case is calculated using the formula:

Cₙ = max(0, Cₙ₋₁ + (Xₙ - k))

Where:

• Cₙ = cumulative sum at case n
• Cₙ₋₁ = cumulative sum at the previous case
• Xₙ = actual outcome of the current case (0 or 1)
• k = target complication rate (e.g., 0.1 for 10%)

• A CUSUM of 0 means performance is matching or better than expected.
• A rising CUSUM indicates more complications than expected.
• A declining or flat CUSUM suggests improving or consistent performance.

If the target complication rate k is 0.1 and the outcome sequence is:

• Case 1: success → C₁ = max(0, 0 + (0 - 0.1)) = 0
• Case 2: complication → C₂ = max(0, 0 + (1 - 0.1)) = 0.9
• Case 3: success → C₃ = max(0, 0.9 + (0 - 0.1)) = 0.8

The curve visually builds a story of performance across cases, and the CUSUM value at each case becomes a snapshot of deviation from target performance.

Tracking the cumulative sum at each case:

• Enables real-time feedback
• Helps detect early deviations from the expected outcome rate
• Facilitates monitoring during training and protocol changes
• Supports objective decision-making in quality assurance