Clinic Positivity: A Rising Rate That Isn't
A district clinic reports on its HIV counselling-and-testing programme. In 2023 it tested 1 200 people and recorded 96 positive results. In 2024 it tested 1 500 people and recorded 150 positive results. In January 2024 the clinic began actively recruiting clients from two high-risk groups - long-distance drivers and sex workers - who had not previously been targeted. Of the 150 positive results in 2024, 60 were repeat tests of clients already known to be HIV-positive and already on treatment. The district manager writes in her quarterly report: "Positivity has risen from 8% to 10%. Testing efforts are therefore reaching more infected people, but the programme's prevention message is clearly failing."
1. Check the two percentages the manager quotes, then calculate a positivity figure for 2024 that is more comparable to 2023. State what each figure is measuring.
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Checking the quoted figures
- 2023: 96 ÷ 1 200 = 0,08 → 8% ✓
- 2024: 150 ÷ 1 500 = 0,10 → 10% ✓
A more comparable measure Remove the 60 repeat tests from the numerator, since those clients were already known positive and cannot represent newly detected infection:
- New positives 2024 = 150 − 60 = 90
- New-client positivity = 90 ÷ 1 500 = 0,06 → 6%
What each figure measures
- The 8% and 10% are test-yield rates: positives per test performed, mixing first-time and repeat testers.
- The 6% is a new-case detection rate.
On the comparable measure positivity fell from 8% to 6%, the opposite of the manager's headline. Even this comparison is imperfect, because the 2024 denominator was deliberately enriched with high-risk clients, which should if anything have pushed detection up - making the fall more striking, not less.
2. The manager concludes that the prevention message is failing. Identify the reasoning errors in that inference and list the additional data you would need before accepting or rejecting it.
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Error 1 - treating a ratio as if only the numerator moved. Positivity has a numerator (positives) and a denominator (tests). Both changed in 2024, and the denominator changed by design: recruiting high-risk clients mechanically raises yield with no change whatsoever in transmission.
Error 2 - contaminated numerator. Sixty of the 150 positives are repeat tests of people already in treatment. Counting them as "more infected people reached" double-counts clients the programme already knew about.
Error 3 - wrong indicator for the claim being made. "Prevention is failing" is a statement about new infections in a population. Test yield measures who walked through the door, not what is happening in the district. A falling yield can coexist with rising incidence (if low-risk people are tested more) and a rising yield with falling incidence (if testing is well targeted).
Data needed before judging
- Number of first-time testers per year, and their risk profile.
- Repeat-test policy and the size of the known-positive cohort.
- District population denominators (tests per 1 000 population).
- A direct incidence measure: new diagnoses in a defined cohort, or antenatal sentinel prevalence.
- Treatment coverage, which affects infectivity and therefore future incidence.
3. Rewrite the manager's conclusion as a single sentence that the evidence would actually support.
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Defensible rewrite
"Testing volume rose 25% (1 200 → 1 500) and was deliberately redirected towards higher-risk groups, yet positivity among newly tested clients fell from 8% to 6%; this is consistent with prevention having some effect, but without incidence data it cannot be attributed to the prevention campaign."
Why this wording works
- 1 500 ÷ 1 200 = 1,25, i.e. a 25% increase in volume - stated so the reader sees the denominator shift.
- The 6% figure is used, not the inflated 10%.
- "Consistent with … but cannot be attributed" marks the difference between a pattern and a causal claim.
- The confounder (targeted recruitment) is named in the same sentence rather than buried.