The Screening Programme
A national health service is considering a screening programme for a condition affecting 1 in 2,000 people. The test has a sensitivity of 95% and a specificity of 90%. Those who screen positive are offered a biopsy, which has a 1 in 200 risk of serious complication. The condition, if detected early, has a 5-year survival of 92%; if detected after symptoms appear, 5-year survival is 60%. A patient advocacy group argues that screening will save lives and that any delay costs lives. A group of clinicians argues that the harms of false positives outweigh the benefits. A health economist points out that the programme would cost $40 million per year and that the survival difference partly reflects lead-time bias.
1. Using the stated figures, estimate what a positive test means for a patient, and explain the significance of that estimate.
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Take 200,000 people. With a prevalence of 1 in 2,000, 100 have the condition and 199,900 do not.
- Of the 100 with the condition, 95 test positive (sensitivity 95%).
- Of the 199,900 without it, 10% test positive falsely: 19,990.
- Total positives: 95 + 19,990 = 20,085.
The probability that a positive result is a true positive is 95 / 20,085 ≈ 0.47%, or roughly 1 in 211.
This is the crucial number for the patient, and it is not obvious from the sensitivity and specificity alone. A patient told they have tested positive may reasonably assume the test is '95% accurate' and that they probably have the condition. In fact, more than 99% of positives are false.
The consequence is that the biopsy risk dominates. If all 20,085 positives are biopsied, at 1 in 200 serious complications that is about 100 serious complications - roughly equal to the number of true cases detected. The programme would harm about as many people seriously as it finds with the disease, before any benefit from early detection is counted. That does not settle the question, but it reframes it: the debate is not 'screening versus nothing' but 'which harms, to whom, and at what rate'.
2. The advocacy group claims screening 'saves lives'. Evaluate this claim in light of lead-time bias and the figures given.
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The claim needs separating into two parts: does screening detect earlier, and does earlier detection extend life?
The first is true by construction. Lead-time bias means that survival measured from diagnosis will improve simply because diagnosis happens earlier, even if death occurs on exactly the same date. A patient diagnosed five years earlier but dying at the same time appears to have survived five years longer. The 92% versus 60% five-year survival figures are therefore not by themselves evidence that screening extends life; they may be measuring the clock starting earlier.
To show a mortality benefit, the relevant endpoint is deaths from the condition in a screened population compared with an unscreened one, not survival after diagnosis. The setup gives no such figure, so the advocacy group's claim is unproven on the data available.
That does not make the claim false. Screening may genuinely reduce mortality, particularly if early treatment is more effective. But the burden of proof lies with the proponents, and the correct evidence is a mortality comparison. The advocacy group's rhetorical move - treating improved survival statistics as proof of lives saved - is exactly the error lead-time bias produces, and a careful reader should resist it while remaining open to genuine mortality data.