===== Reference Value =====

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.

==== Purpose ====

''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).

==== Choosing the Right Reference Value ====

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''.

==== Example ====

  * 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

==== Why It Matters ====

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