—Dr Mauro has pointed out a very interesting aspect of the algebra of calculating positive predictive values or PV +.
PV+ is the probability that this subject has the disease tested for (D +) given that the test for the disease is positive (T +). PV+ can be written as prob(D + T +) = the probability of the disease given a positive test.
This is a classic Bayes' formula issue and a subtle one that I have not seen discussed anywhere in my reading. For the record, I will go through the algebra in case someone challenges Dr Mauro's assertions.
If you flip a coin instead of performing a test, you will get pr(T + D +) of.50; that is, the probability of a positive test T+ is the probability of, say, "heads."
Also, the probability of a positive test among subjects without the disease, pr(T + D-), will also be