Applied case · Public health · about 60 minutes
Evaluating a screening programme
Build the 2×2 table, estimate sensitivity and specificity with intervals, and show why predictive values depend on base rates — then decide who the programme should target.
The brief
A regional health authority piloted a community screening programme for a silent condition using a rapid test. 5,000 adults were screened, and every participant also received the slower definitive reference test, so we know who truly has the condition.
The programme board must decide whether to extend the rapid test to all adults or target older age groups. Every positive rapid test triggers a specialist follow-up appointment costing about SAR 650 (a scenario assumption, not a real tariff), and the board has heard complaints from people who were frightened by a positive result that turned out to be false.
Your tasks:
- tabulate the results and check the design;
- estimate how accurate the test is — and how precisely we know that;
- explain what a positive result means for a person, overall and by age group;
- recommend who should be screened.
The data. screening has one row per participant: age group, sex, true condition status (reference test) and the rapid-test result. The programme, the condition and the data are fictional and synthetic; nothing here describes a real test or disease.
Stakeholders. The programme board (budget and policy), clinicians running follow-up clinics, and the public (who need honest information about what a positive result means).
Dataset
Population screening test
5,000 rows · one row = one screened person · synthetic data
| Person | Age group | Sex | Has condition | Test positive |
|---|---|---|---|---|
| S0001 | 18-39 | Male | false | false |
| S0002 | 18-39 | Female | false | false |
| S0003 | 60+ | Female | false | false |
| S0004 | 18-39 | Male | false | false |
| S0005 | 18-39 | Male | false | false |
| S0006 | 18-39 | Male | false | false |
Included with a Formula Quest membership
This case has 4 stages and 9 graded tasks, ending with a written report.
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