Interpreting a Vaccine Trial Table
A public-health team reports results from a two-group trial of a new flu vaccine. In the vaccinated group, 8,000 people were followed and 40 developed the flu. In the unvaccinated control group, 8,000 people were followed and 160 developed the flu. A journalist writes: "The vaccine prevented 120 cases of flu." A second journalist writes: "The vaccine is 75% effective." A third claims: "Vaccinated people are 4 times less likely to get the flu, so the vaccine eliminates most risk." The team must decide which statements are defensible from the table alone and which overreach.
1. Calculate the flu rate in each group and evaluate the claim that the vaccine is 75% effective.
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Vaccinated rate: 40 ÷ 8,000 = 0.005 = 0.5%. Unvaccinated rate: 160 ÷ 8,000 = 0.02 = 2.0%.
Relative risk reduction: (2.0% − 0.5%) ÷ 2.0% = 1.5 ÷ 2.0 = 0.75 = 75%.
So the "75% effective" statement is defensible as a relative reduction in this trial. It does not mean 75% of vaccinated people are protected - it means their risk dropped by 75% relative to the control rate.
2. Evaluate the claim "the vaccine prevented 120 cases." What assumption does it require?
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Raw difference: 160 − 40 = 120 fewer cases among 8,000 vaccinated people.
This is an accurate count within this trial, but calling them "prevented" assumes the vaccinated group would have had the same 2.0% rate as the control group absent the vaccine. That requires the groups to be comparable (similar age, exposure, health). If the vaccinated group was healthier or less exposed, the 120 figure overstates the effect. The number is defensible as an observed difference, not as a proven causal count without that assumption.
3. Assess the third claim about "eliminating most risk."
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The relative risk (2.0% ÷ 0.5%) is 4, so vaccinated people were about 4 times less likely to get the flu - that part is correct. But "eliminates most risk" confuses relative and absolute risk. The absolute risk only fell from 2.0% to 0.5%, a drop of 1.5 percentage points. About 99.5% of vaccinated people would not have gotten the flu anyway in this window. The claim overstates the practical benefit; the defensible statement is a 1.5-point absolute reduction.