Positive predictive value of screening tests

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)]

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?

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

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

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