1. Positive predictive value of screening tests

2. PPV versus sensitivity: different denominators!
Disease +
Disease -
Total
Test + a b
a+b
Test - c d
c+d
a+c (total disease)
b+d (total healthy)
a+b+c+d
Sensitivity = those who screen positive/ total number
with disease [a/(a+c)]
PPV= those who are true positives/total positive screens [a/(a+b)]

3. How prevalence affects PPV
This is for the sceptics- the mathematical proof follows on the next few slides…
Start with a population of 1000 people
Assume that you have a screening test with sensitivity= 90% and specificity= 90%
How will PPV be affected if the disease prevalence is 10% in one case and 1% in another?

4. Disease prevalence 1% Disease + Disease - Total Test + 9 99 108 Test -
891
892 10
990
1000
Prevalence of 1% means 10 disease cases in a
population of 1000
Sensitivity of 90% means 9 cases are detected on screen
Specificity of 90% means that 891 out of 990 healthy people are correctly identified as true negatives
PPV= 9/108= 0.08= 8% or for every 100 people who screen positive, only 8 truly have the disease

5. Disease prevalence 10% Disease + Disease - Total Test + 90 180 Test -
810
820
100
900
1000
Prevalence of 10% means 100 disease cases in a
population of 1000
Sensitivity of 90% means 90 cases are detected on screen
Specificity of 90% means that 810 out of 900 healthy people are correctly identified as true negatives
PPV= 90/180= 0.5= 50% or for every 100 people who screen positive, 50 will actually have the disease

6. Ergo…
Given a fixed sensitivity and specificity for a screening test, the positive predictive value increases with increasing disease prevalence.
Q.E.D.