Statistics you can move.
The diagnostic-test lab below is the real thing and free to use: change sensitivity, specificity and prevalence and watch the 2×2 table, PPV, NPV and likelihood ratios follow. Treatment effects, confidence intervals and power come with the CAP course.
Diagnostic tests
The same test behaves differently in different rooms. Move prevalence and watch the positive predictive value fall while sensitivity and specificity stay exactly where they are.
| Disease + | Disease − | |
|---|---|---|
| Test + | TP 43 | FP 95 |
| Test − | FN 7 | TN 855 |
Of the 138 people who test positive, 43 have the condition: a positive result is right 31% of the time.
The formulas
Why PPV changes and sensitivity does not
Sensitivity and specificity belong to the test. Positive predictive value belongs to the test in a particular population, because it depends on how many people in the room actually have the condition. A screening test with 85% sensitivity and 90% specificity is right about a positive result less than a third of the time at 5% prevalence, and more than 80% of the time at 40%. That is the single most examined idea in the diagnostic-test section of the CAP, and it is far easier to see than to memorise.
Likelihood ratios in one line
Post-test odds equal pre-test odds multiplied by the likelihood ratio. An LR+ above 10 rules a diagnosis in convincingly; an LR− below 0.1 rules it out. Values near 1 barely move you.