Two infectious disease epidemiologists want to investigate a new laboratory test that identifies tuberculosis (TB) infections.Dr.Merritt uses the standard test,which has a sensitivity of 80% and a specificity of 90%.Dr.Foundry uses the new laboratory test,which is 90% sensitive and 99% specific.In City A,it is known that 100 of 1,000 people have TB infections.What is the positive predictive value of the standard test in City A?

A) 10%
B) 47%
C) 53%
D) 80%
E) 90%

Positive predictive value is the proportion of those who test positive who do have the disease or the probability that a person identified as diseased by the test will be a diseased person (case) in the population.Let us say there are 10,000 people in City A; 100 of 1,000 people actually have TB infection in City A which is 1,000 individuals.Therefore we have 1,000 cases and 9,000 noncases in City A (hypothetically).The number of people who identified as test positive from cases is 800.Among 1,000 people who actually have TB,80% of people will be identified as test positive (sensitivity).The number of people who identified as test positive from noncases is 900.Among 9,000 people who actually have TB,90% of people will be identified as test negative (specificity) and 10% of people will be identified as test positive.Among 1,700 people who identified as test positive,there are 800 people who actually have the disease.Therefore positive predictive value equals 800 divided by 1,700 (equals 0.47).