A screening test with 90% sensitivity and 95% specificity in a population with disease prevalence of 5% yields a positive predictive value closest to which percentage?

A screening test with 90% sensitivity and 95% specificity in a population with disease prevalence of 5% yields a positive predictive value closest to which percentage?

• A. 31%
• B. 70%
• C. 49%
• D. 85%

Answer: (C)

Positive predictive value reflects how likely it is that a person actually has the disease given a positive test. It depends not only on the test’s sensitivity and specificity, but crucially on how common the disease is in the tested population (the prevalence). When the disease is rare, false positives from the non-diseased group can make up a large share of the positive results, pulling the PPV down even if the test is pretty accurate. Think of 1,000 people. With a 5% prevalence, about 50 people actually have the disease and 950 do not. - True positives: 90% of 50 = 45 people test positive and truly have the disease. - False positives: 5% of 950 = 47.5 people test positive but do not have the disease. Total positives ≈ 45 + 47.5 = 92.5. The PPV is 45 / 92.5 ≈ 0.486, about 49%. So even with 90% sensitivity and 95% specificity, the positive predictive value in a population with 5% disease prevalence is around 49%. The other options (31%, 70%, 85%) would require different balances of true and false positives that don’t align with these numbers.

Positive predictive value reflects how likely it is that a person actually has the disease given a positive test. It depends not only on the test’s sensitivity and specificity, but crucially on how common the disease is in the tested population (the prevalence). When the disease is rare, false positives from the non-diseased group can make up a large share of the positive results, pulling the PPV down even if the test is pretty accurate.

Think of 1,000 people. With a 5% prevalence, about 50 people actually have the disease and 950 do not.

• True positives: 90% of 50 = 45 people test positive and truly have the disease.

• False positives: 5% of 950 = 47.5 people test positive but do not have the disease.

Total positives ≈ 45 + 47.5 = 92.5. The PPV is 45 / 92.5 ≈ 0.486, about 49%.

So even with 90% sensitivity and 95% specificity, the positive predictive value in a population with 5% disease prevalence is around 49%. The other options (31%, 70%, 85%) would require different balances of true and false positives that don’t align with these numbers.