Predictive values answer the clinician's question but depend on prevalence
Mnemonic
SnNout and SpPin for the test’s own properties:
- SnNout - a highly Sensitive test, when Negative, rules the diagnosis out
- SpPin - a highly Specific test, when Positive, rules it in
Sensitivity and specificity belong to the test; predictive values belong to the population. That single distinction is the whole of the topic.
Positive predictive value falls as prevalence falls. A test that is 99 per cent sensitive and 99 per cent specific has a PPV of about 92 per cent at 10 per cent prevalence, but only about 9 per cent at 0.1 per cent prevalence: the same test, wrong ten times out of eleven.
Likelihood ratios avoid the problem: a positive ratio above 10 or a negative ratio below 0.1 shifts probability decisively, while values between 0.5 and 2 change almost nothing.
Expansion
- Positive predictive value = a / (a + b): of those who test positive, the proportion who have the disease
- Negative predictive value = d / (c + d): of those who test negative, the proportion who are truly disease free
These are what the patient and clinician actually want to know, and unlike sensitivity and specificity they depend heavily on prevalence.
A worked illustration: a test with 99 per cent sensitivity and 99 per cent specificity.
- In a population with 10 per cent prevalence, of 10,000 people: 990 true positives and 90 false positives, giving a PPV of about 92 per cent
- In a population with 0.1 per cent prevalence: about 10 true positives and 100 false positives, giving a PPV of about 9 per cent
The same test, unchanged, is now wrong about a positive result ten times out of eleven. This is the mathematical reason that screening asymptomatic populations generates so many false alarms, and why pre-test probability must always be considered before ordering a test.
Likelihood ratios avoid the prevalence problem and are the most useful bedside form:
- Positive likelihood ratio = sensitivity / (1 - specificity)
- Negative likelihood ratio = (1 - sensitivity) / specificity
A positive ratio above 10 or a negative ratio below 0.1 produces a large and often conclusive shift in probability; values between 0.5 and 2 barely change anything.
The practical lesson: a test ordered without a clinical question, in a patient with a low pre-test probability, is more likely to mislead than to inform. This is the basis of overdiagnosis, and of the incidental finding cascade.