A fictional screening table
A hypothetical test is applied to ten thousand people. For the supplied model, one hundred have the specified condition and nine thousand nine hundred do not. Sensitivity is ninety percent and specificity is ninety-five percent. These characteristics are assumed fixed for this calculation, and all disease-status assignments are treated as correct. The programme director expects almost every positive result to represent disease because the test’s sensitivity sounds high. No treatment decision is authorized by the scenario. The analyst must construct the table, explain why prevalence matters and describe why a positive screen still needs the appropriate next step. The exercise concerns the model rather than a recommended screening programme for any actual disease.
1. Calculate true and false positive counts and predictive value.
Read the worked answer
There are ninety true positives and 495 false positives. Positive predictive value is 90/(90+495), approximately 15.38 percent under the supplied assumptions.
2. Explain the low predictive value without calling sensitivity poor.
Read the worked answer
The low-prevalence population contains many more people without the condition. Even a five-percent false-positive proportion among that large group produces more false than true positives.