Question

4. For a diagnostic test of a certain disease, let T1 denote the probability that the diagnosis is positive given that a subject has the disease, and let T2 denote the probability that the diagnosis is positive given that a subject does not have it. Let p denote the probability that a subject has the disease.
(a) More relevant to a patient who has received a positive diagnosis is the probability that they truly have the disease. Given that a diagnosis is positive, show that the probability that a subject has the disease (called the positive predictive value) is: πιρ (b) Suppose that a diagnostic test for HIV+ status has both sensitivity and specificity equal to 0.95, and that ρ-: 0.005. Find the probability that a sub- ject is truly HIV+, given that the diagnostic test is positive. (c) Discuss how the answer in (b) depends on the preva- lence ρ. Find the positive predictive value for ρ 0.005, 0.05, 0.10 and demonstrate the dependence.
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Answer #1

Answer:

Given that:

Let pi 1 denotes X and pi 2 denotes Y.

pi 1= P(Y=1 / X=1)

pi 2= P(Y=1 / X=2)(e)more relevant - a paterst uro hax ee Ti P e,Bes heorem The ply)i giver ve dliag Yedule KnoD thal poritfve 규、te pove prerclive 0005 O 08t2 0.5 0 6786 0.05 O IO P 5 Postfie Values.

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