The reference value (commonly denoted as k) in CUSUM analysis represents the target or expected failure rate for a procedure. It defines the benchmark against which actual outcomes are compared on a case-by-case basis.

k acts as a tolerance threshold:

• If a case has a worse outcome than k, the CUSUM score increases.
• If the outcome is better than k, the CUSUM score decreases or resets (depending on the method used).

The choice of k depends on:

• Published standards or meta-analyses
• Institutional audit data
• Expert consensus

For example:

• If the acceptable complication rate for ICP monitor placement is 10%, then k = 0.1.
• For a high-risk procedure with a 25% expected failure rate, k = 0.25.

• Success (0) vs. Reference (k = 0.1):

→ Cₙ = Cₙ₋₁ + (0 - 0.1) = Cₙ₋₁ - 0.1 → trend down

• Complication (1) vs. Reference (k = 0.1):

→ Cₙ = Cₙ₋₁ + (1 - 0.1) = Cₙ₋₁ + 0.9 → trend up

The reference value determines the sensitivity of the CUSUM chart. A lower k makes the chart more reactive to poor performance, while a higher k gives more leeway.

A well-chosen reference value ensures:

• Fair benchmarking across surgeons and institutions
• Meaningful interpretation of trends
• Appropriate threshold setting for alerting deviations