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:

The predictive value of a positive test is is 0.43.

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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.

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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.

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The predictive value of a positive test is:

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

The predictive value of a positive test is is 0.43.

A similar question is given at

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