Sensitivity and specificity

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Sensitivity and specificity are fundamental characteristics of diagnostic imaging tests.

The two characteristics derive from a 2x2 box of basic, mutually exclusive outcomes from a diagnostic test:

  • true positive (TP): an imaging test is positive and the patient has the disease/condition
  • false positive (FP): an imaging test is positive and the patient does not have the disease/condition
  • true negative (TN): an imaging test is negative and the patient does not have the disease/condition
  • false negative (FN): an imaging test is negative and the patient has the disease/condition

On a first pass, we don't assume some relationship between the test and the disease/condition, but we hope there will be some relationship between the test and the disease/condition, because otherwise the test would be worthless.

Sensitivity

For a given test and disease/condition, its sensitivity is how well it can be positive among all those with the condition. Therefore:

  • sensitivity = TP / (TP + FN)
    • true positives / (all those with the disease)
Specificity

For a given test and disease/condition, its specificity is how well it can distinguish those with disease from those without. The test must not just fail to pick up a segment of the population (that might be poor sensitivity), it must distinguish those without the disease... the true negatives (TNs). Therefore:

  • specificity = TN / (TN + FP)
    • true negatives / (all those without the disease)
SpPin and SnNout rule

SnNout: if a diagnostic test, characterized by high sensitivity (Sn), returns the negative value (N), then it excludes the diagnosis (out).

SpPin: if a diagnostic test, characterized by high specificity (Sp), returns the positive value (P), then it admits the diagnosis (in).

See also