Sensitivity, specificity and predictive values

7 DOH Abu Dhabi (HAAD) lab licensing practice questions on Sensitivity, specificity and predictive values, part of General Laboratory, Quality and Safety. The first 7 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. Question 1 · Hard

   A pre-employment health program screens 20,000 adults for hepatitis C antibody, with an expected prevalence of 0.5%. The screening immunoassay has a sensitivity of 99.0% and a specificity of 98.0%. Every reactive sample is then tested with a second, independent immunoassay that has a sensitivity of 98.0% and a specificity of 99.5%; assume that the two assays' errors are unrelated. Only samples reactive on both assays are reported as antibody positive. About what proportion of the people reported as antibody positive truly have the antibody?

   1. AAbout 20%
   2. BAbout 50%
   3. CAbout 99.5%
   4. DAbout 98%

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   Answer: D · About 98%

   Of 20,000 people, 100 have the antibody and 19,900 do not. The screen detects 99 of them (99%) and is falsely reactive in 398 (2% of 19,900), so on its own its PPV is only 99 / 497 ≈ 20%. The second assay is applied to this reactive group, where the prevalence is now about 20%: it confirms 97 true positives (98% of 99) and only 2 false positives (0.5% of 398). The PPV of the two-assay result is therefore 97 / 99 ≈ 98%. This is why, at low prevalence, reactive screening results are confirmed before they are reported.

   • A: About 20% is the PPV of the screening assay used alone.
   • B: About 50% is what the second assay would give if used alone on all 20,000 people.
   • C: 99.5% is the second assay's specificity, not a predictive value.

2. Question 2 · Hard

   In a screening program, 10,000 people are tested. Of 400 positive results, 100 are confirmed. Follow-up of the 9,600 people who tested negative finds 4 more with the disease. What is the test's specificity?

   1. A97.0%
   2. B25.0%
   3. C96.2%
   4. D99.96%

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   Answer: A · 97.0%

   Build the 2 × 2 table first: true positives 100, false positives 400 - 100 = 300, false negatives 4 and true negatives 9,600 - 4 = 9,596. Specificity = TN / (TN + FP) = 9,596 / 9,896 = 97.0%. Sensitivity is 100 / 104 = 96.2%, PPV only 100 / 400 = 25% and NPV 9,596 / 9,600 = 99.96%. The low PPV despite good specificity reflects the low prevalence of about 1%.

   • B: 25.0% is the positive predictive value, 100 / 400.
   • C: 96.2% is the sensitivity, 100 / 104.
   • D: 99.96% is the negative predictive value, 9,596 / 9,600.

3. Question 3 · Easy

   An evaluation of a rapid test shows that 97% of people with a negative result did not have the disease. This figure is the test's:

   1. ANegative predictive value
   2. BPositive predictive value
   3. CSpecificity
   4. DSensitivity

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   Answer: A · Negative predictive value

   Negative predictive value is the proportion of negative results that are true negatives: TN / (TN + FN). It starts from the test result, whereas specificity starts from disease status: the proportion of people without the disease who test negative, TN / (TN + FP). Predictive values answer the clinician's question of how likely disease is, given the result. Unlike sensitivity and specificity, they change with prevalence.

   • B: Positive predictive value is the share of positive results that are true positives.
   • C: Specificity is the share of people without the disease who test negative.
   • D: Sensitivity is the share of people with the disease who test positive.

4. Question 4 · Medium

   A laboratory lowers the positive cut-off of a screening immunoassay so that fewer infected patients are missed. What is the expected effect?

   1. ASensitivity and specificity both fall
   2. BSpecificity rises and sensitivity falls
   3. CSensitivity and specificity both rise
   4. DSensitivity rises and specificity falls

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   Answer: D · Sensitivity rises and specificity falls

   Results from infected and uninfected people overlap, so moving the cut-off trades one kind of error for the other. A lower cut-off calls more weak reactions positive: fewer false negatives (higher sensitivity) but more false positives (lower specificity). This suits screening tests, whose positives are then confirmed by a more specific test. A ROC curve shows this trade-off across all possible cut-offs.

   • A: Lowering the cut-off reduces false negatives, so sensitivity cannot fall.
   • B: Specificity rises only when the cut-off is raised.
   • C: With overlapping results, one measure can only improve at the expense of the other.

5. Question 5 · Medium

   A rapid malaria antigen test is compared with expert microscopy in 250 febrile travelers: 45 true positives, 5 false positives, 15 false negatives and 185 true negatives. What is its sensitivity?

   1. A90.0%
   2. B97.4%
   3. C92.5%
   4. D75.0%

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   Answer: D · 75.0%

   Sensitivity = TP / (TP + FN) = 45 / (45 + 15) = 75.0%, the share of infected travelers the test detects. One infection in four is missed, which is why microscopy remains the reference method for malaria. In the same table, specificity is 185 / 190 = 97.4%, PPV 45 / 50 = 90.0% and NPV 185 / 200 = 92.5%. The key is the denominator: sensitivity uses everyone who has the disease.

   • A: 90.0% is the positive predictive value, 45 / 50.
   • B: 97.4% is the specificity, 185 / 190.
   • C: 92.5% is the negative predictive value, 185 / 200.

6. Question 6 · Hard

   A test with 90% sensitivity and 95% specificity is used on a medical ward where 20% of patients have the disease, and on healthy blood donors, of whom 1% have it. What are its positive predictive values in the two groups?

   1. AAbout 90% in both groups
   2. BAbout 15% on the ward and 82% in donors
   3. CAbout 82% in both groups
   4. DAbout 82% on the ward and 15% in donors

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7. Question 7 · Hard

   A test has 80% sensitivity and 90% specificity. In a clinic where 10% of the patients tested have the infection, its negative predictive value is:

   1. A90.0%
   2. B2.4%
   3. C47.1%
   4. D97.6%

   Answer and explanation in LearnFree account