Low-Prevalence Glaucoma Screening and the Meaning of a Positive Test
A community health program proposes screening adults aged 55-80 years for primary open-angle glaucoma using optic disc photographs read by a single trained grader. In the target population, the prevalence of definite glaucoma is estimated at 2%. In a pilot study using a reference standard of comprehensive examination, the photographs had a sensitivity of 85% and a specificity of 92%. The program director is encouraged because the test is right most of the time and wants to know how many positive screens will be false positives. The program has limited capacity for confirmatory examinations and is considering raising the threshold for referral. There is no current data on treatment harm in screen-detected cases. The grader will work without a second reader or automated quality check.
1. Calculate the positive predictive value and interpret it in plain language.
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Assume 10,000 screened people. With 2% prevalence, 200 have glaucoma. Sensitivity 85% means 170 are true positives and 30 are false negatives. Of 9,800 without glaucoma, specificity 92% means an 8% false-positive rate, or 784 false positives. Total positives are 170 plus 784, or 954. The positive predictive value is 170 divided by 954, which equals 17.8%, about 18%. In plain language, fewer than 1 in 5 positive screens actually has glaucoma; more than 4 in 5 positives are false alarms. This is not because the test is useless but because disease prevalence is low. The calculation shows why a test with reasonably high sensitivity and specificity can still generate mostly false positives in a community screening program.
2. Explain what would happen to PPV and to sensitivity and specificity if the referral threshold were raised, and why prevalence matters.
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Raising the referral threshold generally increases specificity and lowers sensitivity: fewer false positives but more missed cases. PPV would rise because the false-positive fraction falls, but the number of false negatives would increase. Sensitivity and specificity are properties of the test at a chosen cutoff, but PPV depends on prevalence. In a higher-prevalence clinic population, PPV would be higher for the same sensitivity and specificity. Conversely, in a lower-prevalence community, even a good test yields many false positives. The program cannot interpret PPV without the local prevalence and the referral threshold. The trade-off is not free: reducing false positives by raising the threshold necessarily increases missed disease.
3. Recommend how the program should use these results before implementation.
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Before implementation, the program should plan a confirmatory examination pathway, estimate the number of false positives and the cost and harm of labeling, and decide whether the goal is case finding or population screening. It should also consider whether treatment of screen-detected glaucoma improves outcomes and whether follow-up capacity exists. A pilot should measure real-world sensitivity and specificity, not just the single grader's performance, and track missed cases. If confirmatory capacity is limited, raising the threshold may be reasonable only if the program accepts more false negatives and has safety-netting. The judgment is that a mostly right test can still produce mostly false positives when prevalence is low, so policy must be based on predictive values and downstream capacity, not accuracy alone.