A vaccine is "95% effective." Does that mean 5 out of every 100 vaccinated people still get sick?
It sounds like it should. But "95% effective" doesn't describe the vaccinated group by itself. It compares two groups: how many people got sick with the vaccine versus without it.
Pfizer-BioNTech COVID-19 vaccine trial, 2020
COVID-19 cases per 10,000 people in each group
During the trial's first report, a median of about 2 months of follow-up
"95% effective" compares two groups; it isn't the share of vaccinated people who got sick. In this trial, the vaccinated group had 95% fewer cases than the placebo group. Only 8 of more than 18,000 vaccinated people got COVID-19 during the trial, not 5 in every 100.
The flip side matters too: 95% of what? The absolute numbers depend on how common the disease is and how long you watch. Over two months, most people in both groups stayed healthy. The same 95% cut means more cases prevented when a disease is spreading widely than when it's rare. The same gap works in reverse: a processed-meat habit that raises cancer risk "18%" adds about 1 case per 100 people. For any "percent effective" or "percent more or less risk" claim, from medicines to seat belts to smoke alarms, ask what the risk was to begin with.
What "percent risk" headline would you read differently if you knew the starting risk?
Three ways to describe the same trial result
| Way to say it | Number | What it tells you |
|---|---|---|
| Relative risk reduction | 95% | How much the vaccine cut the chance of getting sick, compared with no vaccine |
| Absolute risk, each group | 0.9% vs. 0.04% | How many people in each group actually got sick during the trial |
| Absolute risk reduction | 0.84 percentage points | The difference between the groups: about 84 fewer cases per 10,000 people over about 2 months |
All three are true descriptions of the same result. The relative number stays fairly steady from place to place; the absolute numbers grow the longer people are followed and the more the virus spreads. Protection against COVID-19 infection also changed later as the virus mutated and immunity faded, which is why later studies reported different effectiveness numbers.
Does a hot dog a day really raise your cancer risk by 18%?
Yes, but 18% of a small starting risk. The World Health Organization’s cancer agency found that eating 1.8 oz (50 g) of processed meat a day, about one hot dog, raises bowel cancer risk by 18%. That turns 56 lifetime cases in 1,000 people into 66: about 1 more person in every 100, not 18.
Processed meat and lifetime bowel cancer risk
What the headline sounds like vs. what actually changes
Each bar is 100 people, over a lifetime
| Way to say it | Number | What it compares |
|---|---|---|
| Relative risk increase | +18% | The risk for people who eat more processed meat, compared with those who eat less |
| Absolute risk, each group | 5.6% vs. 6.6% | The share of each group who get bowel cancer in their lifetime |
| Absolute risk increase | 1 percentage point | About 10 extra cases for every 1,000 people |
The 18% is for each 1.8 oz (50 g) of processed meat eaten daily. The 56 and 66 in 1,000 figures are Cancer Research UK's estimates for the UK's lowest and highest processed-meat eaters. Other factors, like age, family history, weight and exercise, also change a person's starting risk.
Related exhibits
Sources: F. P. Polack et al., "Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine," New England Journal of Medicine, December 31, 2020 (8 cases among 18,198 vaccine recipients and 162 among 18,325 placebo recipients, 7 or more days after the second dose; median follow-up about 2 months). Processed meat: International Agency for Research on Cancer (World Health Organization), press release 240, October 26, 2015; Cancer Research UK, "Processed meat and cancer – what you need to know," October 26, 2015; Harvard T.H. Chan School of Public Health, The Nutrition Source (50 g is about one hot dog).