Universal Cancer Screening in a Low-Prevalence County
A county health department proposes universal screening for a rare cancer using a new blood test. The test has 90% sensitivity (detects 90% of true cases) and 95% specificity (correctly clears 95% of people without cancer). The cancer affects 1 in 1,000 residents. The department estimates that screening all 500,000 adults will find 'most' cases early and thereby reduce cancer deaths by 30%. No randomized trial has tested whether early treatment from screening improves survival; the only evidence is that patients whose cancer was found early live longer after diagnosis than patients diagnosed after symptoms. Advocacy groups support the plan, and a vendor offers a discounted price. A legislator notes that the county's treatment capacity is already strained and that false positives require biopsy. The test costs $40 per person, and the 1-in-1,000 estimate comes from a 1990 study of a different region. The department has not set a protocol for repeat testing. The council must decide whether to fund screening.
1. Among 500,000 screened adults, estimate the number of true positives and false positives, and explain what the result implies about the department's 'most cases early' claim.
Read the worked answer
With prevalence 1 in 1,000, 500,000 adults contain about 500 true cases. Sensitivity 90% yields about 450 true positives. The remaining 499,500 people do not have cancer; with 95% specificity, 5%-about 24,975-will falsely test positive. Total positives are about 25,425, so the positive predictive value is 450/25,425 ≈ 1.8%. The department's phrase 'most cases early' is technically true for true cases (90% detected), but it is misleading as a policy claim: almost 98% of positive results are false, each triggering biopsy and anxiety. Moreover, detecting a case earlier is not the same as reducing death; survival after diagnosis can lengthen merely because the diagnosis was advanced (lead-time bias). The calculation shows that the screening's benefits and harms cannot be inferred from sensitivity and specificity alone.
2. Identify the key unstated assumption behind the 30% mortality-reduction estimate, and explain why the early-survival evidence does not establish it.
Read the worked answer
The department must assume that treatment begun after screen detection reduces mortality more than treatment begun after symptoms-not merely that patients live longer after diagnosis. The early-survival evidence is compatible with lead-time bias: if screening moves diagnosis three years earlier without changing the date of death, survival time increases by three years. It is also compatible with length bias: screening disproportionately detects slow-growing tumors that have better prognosis anyway. To support a 30% mortality reduction, the department needs trial evidence that screening plus early treatment lowers death rates, plus assumptions about follow-up, treatment uptake, and whether false-positive harms offset benefits. The 1990 prevalence estimate from another region is a further weak link.
3. What is the strongest argument against funding the program based on the provided details?
Read the worked answer
The strongest argument against funding is that the program imposes certain, large harms for an unproven mortality benefit. About 24,975 false positives would require biopsies in a county whose treatment capacity is already strained; some will have complications. The test costs $40 per person, or $20 million for 500,000 adults, before follow-up costs. The only survival evidence is vulnerable to lead-time and length bias, and no randomized trial shows fewer deaths. The prevalence estimate is old and from another region, so the false-positive burden could be even higher if prevalence is lower. This does not prove screening is worthless, but it shows the department has not met the burden for a universal mandate.