cheat sheet on terminology of medical diagnostic testing

              \  the true situation
               \
                \    +       -
                 +-------+-------+---
                 |       |       |
               + |   a   |   b   |  a+b
what the         |       |       |
diagnostic       +-------+-------+---
test returns     |       |       |
               - |   c   |   d   |  c+d
                 |       |       |
                 +-------+-------+---
                 |       |       |
                 |  a+c  |  b+d  |   t

true positives

a = positive testers who have disease

true negatives

d = negative testers who are without disease

false positives

b = positive testers who are without disease

false negatives

c = negative testers who have disease

prevalence

(a+c)/t = fraction of population that has disease

sensitivity

a/(a+c) = what fraction of those with disease test positive

specificity

d/(b+d) = what fraction of those without disease test negative

predictive value positive

a/(a+b) = what fraction of positive tests have disease

predictive value negative

d/(c+d) = what fraction of negative tests are without disease

accuracy

(a+d)/t = what fraction of tests are correct; depends on prevalence

diagnostic odds ratio

(a/b)/(c/d) = ad/bc = usefulness of test; independent of prevalence

Information retrieval people know sensitivity as "recall" and predictive value positive as "precision."

Screening with a cheap test with high sensitivity then an expensive test with high specificity is often the best (most cost effective) strategy.

And, finally, from above where prevalence is the fraction of the population that has disease, we also define incidence as the rate per unit time at which new cases appear and duration as average length of the disease period in a given case of infection. The three measures are mutually redundant: Duration=(Prevalence/Incidence)