13 Research methods, statistics, critical review and evidence-based practice13.5 Diagnostic studies
13.5.1 Prevalence, specificity and diagnostic odds
2 min read1 figure
Written by Resident Doctor Committee · Published
New in the 2027 syllabus
The College added this topic for exams from January 2027.
Keep the denominator in view
Prevalence is the proportion of a defined population who have the condition at a specified time or during a specified period.
Pre-test probability is your estimate of the chance of the condition before the test. The setting, the symptoms and what you already know can make it differ from prevalence in the general population.
Specificity is the proportion of people without the condition who test negative. The reference standard decides who has the condition.
Worked example
These counts are hypothetical. 1,000 people each had both the index test and the reference standard.
Index test | Condition present | Condition absent | Total |
|---|---|---|---|
Positive | 80 | 90 | 170 |
Negative | 20 | 810 | 830 |
Total | 100 | 900 | 1,000 |
Prevalence = 100 / 1,000 = 10%.
Specificity = 810 / 900 = 90%. Sensitivity = 80 / 100 = 80%.
Positive predictive value (the proportion of positive results that are true positives) = 80 / 170 = 47.1%. This differs from both specificity and sensitivity.
Converting probability to odds
Odds compare the chance of having the condition with the chance of not having it.
Odds = probability / (1 minus probability).
Probability = odds / (1 + odds). Odds can be greater than 1. Probabilities cannot.
Positive likelihood ratio = sensitivity / (1 minus specificity).
Negative likelihood ratio = (1 minus sensitivity) / specificity.
Using the same example:
Pre-test odds = 0.10 / 0.90 = 1/9.
Positive likelihood ratio = 0.80 / 0.10 = 8.
Post-test odds after a positive result = (1/9) x 8 = 8/9.
Post-test probability = (8/9) / (1 + 8/9) = 8/17 = 47.1%.
Interpreting results in context
Low prevalence: most people tested do not have the condition, so a test with fairly high specificity can still give many false positives.
Spectrum and threshold: the range of patients tested and the cut-off chosen can both change observed sensitivity and specificity. Check test performance in the setting where you intend to use it.
Case-control sampling: the numbers with and without the condition are fixed by design. The sample prevalence usually cannot give a clinical pre-test probability or predictive values directly.
Sequential testing: when tests are dependent, you need conditional likelihood ratios. Simply multiplying separately published ratios can overstate certainty.