Questions: Screening Programs and Diagnostic Test Performance

Question 1

A diagnostic test has 99% sensitivity and 95% specificity. It is applied to a population where 1 in 1,000 people have the disease. Which result best approximates the positive predictive value (PPV)?

• A. Approximately 99%, because the sensitivity is 99%
• B. Approximately 95%, because the specificity is 95%
• C. Approximately 2%, because false positives vastly outnumber true positives at low prevalence
• D. Approximately 50%, because sensitivity and specificity are nearly equal

Answer: (C)

In 100,000 screened people: ~100 have the disease and ~99 test positive (99% sensitivity). Of the ~99,900 healthy people, ~4,995 test positive (5% false positive rate). PPV = 99 / (99 + 4,995) ≈ 2%. This illustrates Bayes' theorem in action: even a near-perfect test produces mostly false positives in a low-prevalence population. Options A and B confuse test properties with predictive value — sensitivity and specificity describe the test's performance; PPV describes what a positive result actually means for the patient.

Question 2

A screening program reports that 5-year survival for screen-detected cancer is 80%, compared to 40% for symptom-diagnosed cancer. Which conclusion is best supported?

• A. Screening is clearly beneficial because survival doubled
• B. This difference may reflect lead-time and length-time bias rather than genuine mortality benefit
• C. Screening is harmful because it identifies so many more cases
• D. The test's sensitivity is approximately 80%

Answer: (B)

Improved 5-year survival is a notoriously unreliable measure of screening benefit. Lead-time bias means detection earlier in the natural history inflates survival time without changing when the patient dies. Length-time bias means screening preferentially catches slow-growing, less dangerous tumors, making screened cases appear less aggressive. Only a randomized controlled trial with cause-specific mortality as the endpoint can determine whether screening actually prevents deaths — improved survival statistics alone cannot.

Question 3

The positive predictive value of a diagnostic test is a fixed property of the test itself, determined by its sensitivity and specificity alone.

• T. True
• F. False

Answer: False

PPV is not fixed — it depends on disease prevalence in the tested population. The formula PPV = (sensitivity × prevalence) / [(sensitivity × prevalence) + (1 − specificity)(1 − prevalence)] shows that prevalence is a direct input. The same test with the same sensitivity and specificity will have a very high PPV in a high-risk clinic (high prevalence) and a very low PPV in a general population (low prevalence). This is Bayes' theorem: the pre-test probability (prevalence) fundamentally shapes the meaning of a positive result.

Question 4

A highly sensitive screening test is the most important property for a population-level screening program because it minimizes missed cases.

• T. True
• F. False

Answer: False

While sensitivity matters, a highly sensitive test with low specificity generates large numbers of false positives. Each false positive triggers follow-up tests, patient anxiety, and sometimes invasive procedures — all in people without the disease. The population-level harm from false positives can exceed the benefit from early detection. A viable screening program requires that the test perform well on both dimensions, that the disease has a detectable preclinical phase, that early treatment improves outcomes, and that prevalence is high enough for PPV to be clinically useful.

Question 5

Why can improved 5-year survival in a screened population not by itself demonstrate that a screening program reduces cancer mortality?

Model answer: Improved 5-year survival in screened populations is inflated by two biases. Lead-time bias: screening detects disease earlier in its natural history, so survival is measured from an earlier starting point — but if the patient still dies at the same biological time, the death date hasn't changed, only the detection date. Length-time bias: screening preferentially detects slow-growing, indolent tumors that spend more time in the detectable preclinical window; rapidly fatal cancers progress too quickly to be caught. Screen-detected cases therefore appear less deadly, but this reflects which cancers get caught, not whether screening prevented deaths. Only randomized trials tracking cause-specific mortality can establish genuine benefit.

These biases explain why many screening programs with impressive survival statistics failed to demonstrate mortality benefit in randomized trials. Survival from detection is the wrong endpoint; what matters is whether people assigned to screening die of the target disease at lower rates than controls.