Blood Test Probability

Question

Suppose the following of a blood test:

1. Positive 95% of the time when a patient does have the disease (true positive rate).
2. Positive 10% of the time when the patient does not have the disease (false positive rate).

Suppose the prevalence of the disease is 4%, and take this as your prior probability of disease. Answer the following:

1. Suppose the patient tests positive. What is the post-test probability the patient has the disease? This is also known as the "positive predictive value.
2. Suppose the patient tests negative. What is the post-test probability the patient does not have the disease? This is also known as the "negative predictive value

Answer 1

Pr(P/D) =.95

Pr(P/~D)=.10 Pr(~P/~D)=.9

Pr(D)=.04 Pr(~D) =.-96

Pr(D/P)=? = about 28%

Pr(D/~P)=? = about 0.2%

Pr(~D/~P) ? = about 99.8%

no guarantees on these answers

this might be revised soon or later

no other answers so far,

Use Bayes Theorem

Pr(P/D)Pr(D) = Pr(D/P)Pr(P)

.95(.04 = .038 = Pr(D/P)Pr(P)

Pr(P) = .95(.04 + .10(.96 = .132

Pr(D/P)= .95(.04)/.132 = about .234

Pr(D/~P= .05(.04)/.868 =about .0023

P(~D/~P) = about .998