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Help for this question please and have details For the combined ELSIA-Western blot blood test
for HIV positive status, the sensitivity is about 0.999 and the specificity is about 0.9999.Consider
a high risk group has a positive lest result. Find the positive predictive value of the test.
Solution
Let
D = has disease
T = test positive
Here, note that
P(true positive) = P(D) P(T|D) / P(T)
As
P(T) = P(D) P(T|D) + P(D') P(T|D') = 0.10*0.999 + (1-0.10)*(1-0.9999) = 0.09999
P(true positive) = 0.10*0.999 / 0.09999 = 0.99909991 [ANSWER]

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Help for this question please and have details For the combined ELSI.pdf

  • 1. Help for this question please and have details For the combined ELSIA-Western blot blood test for HIV positive status, the sensitivity is about 0.999 and the specificity is about 0.9999.Consider a high risk group has a positive lest result. Find the positive predictive value of the test. Solution Let D = has disease T = test positive Here, note that P(true positive) = P(D) P(T|D) / P(T) As P(T) = P(D) P(T|D) + P(D') P(T|D') = 0.10*0.999 + (1-0.10)*(1-0.9999) = 0.09999 P(true positive) = 0.10*0.999 / 0.09999 = 0.99909991 [ANSWER]