Sensitivity/Specificity — MCQs

Question 1: A pharmaceutical company develops a sequential testing protocol for a rare genetic disorder (prevalence 0.01%). Initial screening test has sensitivity 95% and specificity 90%. Positive results undergo confirmatory testing with sensitivity 99% and specificity 99.5%. The company claims this approach achieves PPV >80% for the final positive result. Evaluate this claim and the rationale for sequential testing in this context.

• A. The claim is true; sequential testing increases PPV by enriching the population tested in the second step (Correct Answer)
• B. The claim is false; sensitivity decreases with sequential testing, reducing PPV
• C. Sequential testing is unnecessary; the first test alone achieves adequate PPV
• D. The claim is false; sequential testing cannot achieve PPV >80% with such low prevalence
• E. The claim is true; the high specificity of the confirmatory test ensures high PPV regardless of prevalence

Explanation: ***The claim is true; sequential testing increases PPV by enriching the population tested in the second step*** - Sequential testing works by increasing the **pre-test probability** for the second test, as the cohort being tested has already screened positive once. - By applying a highly specific confirmatory test to this enriched group, the number of **false positives** is significantly reduced, which drastically improves the **Positive Predictive Value (PPV)**. *The claim is false; sequential testing cannot achieve PPV >80% with such low prevalence* - Even with a low **prevalence**, the multiplication of specificities in a sequential process can reduce the **False Positive** rate to a level where the PPV exceeds 80%. - This line of reasoning ignores that the **denominator** of the PPV calculation (True Positives + False Positives) decreases much faster than the numerator during the second stage. *The claim is true; the high specificity of the confirmatory test ensures high PPV regardless of prevalence* - While high **specificity** is crucial, PPV is always dependent on the **prevalence** (pre-test probability) of the condition in the group being tested. - The claim is true because sequential testing specifically raises that **pre-test probability**, not because prevalence is irrelevant to the calculation. *The claim is false; sensitivity decreases with sequential testing, reducing PPV* - It is true that **net sensitivity** decreases in sequential testing, but a decrease in sensitivity actually tends to have a negligible effect on PPV compared to specificity gains. - **PPV** is primarily driven by the **specificity** and the prevalence in the tested population, both of which are optimized in this two-step protocol. *Sequential testing is unnecessary; the first test alone achieves adequate PPV* - Given a prevalence of 0.01% and 90% specificity, the **first test** alone would yield a massive amount of false positives, resulting in a very low PPV (~0.09%). - A **confirmatory test** is clinically and ethically necessary to avoid wrongly diagnosing thousands of healthy individuals with a **rare genetic disorder**.