Question 1 · Medium
A new rapid test for syphilis is evaluated in 1,000 adults at an STI clinic, of whom 100 have syphilis by the reference test. The rapid test is positive in 90 of the people with syphilis and in 90 of those without it. What is the positive predictive value of the rapid test?
- A98.8%
- B50%
- C10%
- D90%
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Answer: B · 50%
The 2x2 table is: true positives 90, false negatives 10, false positives 90 and true negatives 810. PPV = true positives / all positives = 90/(90 + 90) = 50%, so half of the people who test positive actually have syphilis. Sensitivity (90/100) and specificity (810/900) are both 90%, and NPV is 810/820 = 98.8%. With the same test, PPV falls further as prevalence falls, which is why positive screening tests in low-prevalence groups need confirmation.
- A: 98.8% is the negative predictive value.
- C: 10% is the prevalence in this group.
- D: 90% is the sensitivity (and the specificity), not the PPV.