A screening test to detect a certain disease has a sensitivity of 0.90 and a spe

Question

A screening test to detect a certain disease has a sensitivity of 0.90 and a specificity of 0.88.

a) Find the probability of a false negative test result. (+2)

b) Suppose that the prevalence of the disease in a certain population is 0.14. Find the predictive value of a positive test result. Carry out your calculations to 4 decimal places of accuracy. (+9)

c) Now we want to estimate the prevalence of the disease in another population using the test. Suppose that 1900 people were randomly selected from this second population and given the test. In the sample, 532 people tested positive. Estimate P(+ ) , the probability of a positive test. Then using the same sensitivity (0.90) and specificity (0.88) given above, estimate P (D), the prevalence of the disease in this second population, to 4 decimal places. (+9)

Explanation / Answer

a) probability of a false negative test result. =1-sensitivity =1-0.90=0.10

b)  predictive value of a positive test result =

true positive/(true positive+false positive)= 0.14*0.90/(0.14*0.9+0.86*0.12)=0.5497

c)

from above given data total tested postive =P(D)*sensitivity +(1-P(D))*(1-specificity)

(532/1900) =P(D)*0.90+(1-P(D))*(1-0.88)

0.28 =0.12+0.78*P(D)

0.78*P(D)=0.16

P(D)= 0.2051

please revert for any clarifcation required

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