Question

A new screening test for West Nile Virus is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. 300 subjects are screened at a clinic during the first year the new test is implemented. (Assume the true prevalence of West Nile Virus among clinic attendees is 10%.), The predictive value of a positive test is:

Answer 1

The predictive value of a positive test is is 0.43.

------------------

This question is solved using the concepts of sensitivity and specificity.

• Sensitivity: It is the true negative rate, that is, the proportion of people without the disease that test negative.
• Specificity: It is the true positive rate, that is, the proportion of people with the disease that test positive.

------------------

• Sensitivity of 60% means that of the 100 - 10 = 90% of people without the disease, 60% test negative and 100 - 60 = 40% test positive.
• Specificity of 70% means that of the 10% with the disease, 70% test positive.

------------------

The predictive value of a positive test is:

Probability of a positive test, which is 40% of 90% plus 70% of 10%, so:

$p = 0.4\times0.9 + 0.7\times0.1 = 0.43$

The predictive value of a positive test is is 0.43.

A similar question is given at brainly.com/question/22373775