A screening report that confuses denominators
A fictional prevention program evaluates a screening questionnaire against a defined reference assessment. One hundred participants have the reference condition, and 80 of them test positive. Three hundred participants do not have the reference condition, and 270 of them test negative. A draft report calls the 80 percent figure the probability that any person with a positive result has the condition. The program also proposes transferring this value unchanged to a community with a different prevalence, without checking recruitment or test procedures. The reviewer has the counts needed for basic sensitivity and specificity calculations, but the report still needs correct interpretation and a clear description of the sampled population. This exercise is about the supplied data, not a claim about an actual disease test.
1. Calculate sensitivity and specificity.
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Sensitivity is 80 divided by 100, or 80 percent. Specificity is 270 divided by 300, or 90 percent. Thirty unaffected participants have false-positive results.
2. Explain the positive-result interpretation.
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Positive predictive value uses all positive results as its denominator: 80 divided by 110, approximately 72.7 percent here. It need not remain unchanged in a population with different prevalence or testing conditions.