An armed forces medical induction center is initiating a screening protocol for latent tuberculosis infection among incoming personnel. The protocol utilizes a highly standardized interferon-gamma release assay. Epidemiological surveillance indicates that the true prevalence of latent tuberculosis in this incoming cohort of recruits is exactly . The laboratory parameters for this specific assay demonstrate a sensitivity of and a specificity of .
If a recruit from this cohort receives a positive result on this assay, what is the probability that the individual actually has a latent tuberculosis infection? (Enter the value as a percentage rounded to the nearest whole number).
Answer: 65 %
Answer
65
The question asks for the probability that a patient with a positive test result actually has the disease, which is the definition of Positive Predictive Value (PPV). To calculate PPV, one must account for the prevalence of the disease in the specific cohort being tested. Using a 2x2 contingency table for the population of recruits, a prevalence of equates to individuals with latent tuberculosis and healthy individuals. Given a sensitivity of , the assay will correctly identify of the diseased individuals (True Positives). Given a specificity of , the false positive rate is ; therefore, the assay will incorrectly flag of the healthy individuals (False Positives). The total number of positive test results is the sum of True Positives and False Positives (). The PPV is the ratio of True Positives to Total Positives (), which equals . Converted to a percentage and rounded to the nearest whole number, the correct probability is .
Step-by-Step Solution
Key Concept
Positive Predictive Value (PPV) depends heavily on the disease prevalence in the tested population, in addition to the test's sensitivity and specificity.