Two identical numbers that mean different things
Consider two fictional information sheets. One says 5 in 100 people experience an event within a year. The other says 5 in 100 experience it within ten years. The percentages match, but the second sheet spreads the same cumulative probability across a much longer period.
Neither tells you exactly when an event might occur. Nor does either mean that precisely five people will experience it in every group of 100. A probability describes uncertainty, not a scheduled allocation of outcomes.
Why multiplying by years can go wrong
If an event can happen only once, a constant 5% annual risk among those still event-free would imply a ten-year cumulative risk of about 40%, calculated as 1 minus 0.95 to the tenth power. It would not imply 50%.
That is a mathematical illustration with demanding assumptions: the annual conditional probability stays constant, and competing events are ignored. Real risks may change with age, exposure, treatment, and other circumstances. Multiplying an annual number by ten can therefore fail for more than one reason.
Three details to recover from the source
- What event counts? A first diagnosis differs from a repeat episode or a positive screening test.
- Who is included? People already living with a condition may not belong in the population at risk of first developing it.
- When does follow-up start and end? Ten years after enrollment differs from risk by a particular birthday.
The CDC's measures-of-risk material distinguishes risks from rates, which can use person-time in their denominator. A rate of five events per 100 person-years is not automatically a five-year probability of 25%.
If a graphic gives a risk without a period, the missing detail is consequential. Finding it can change the comparison before any debate about whether the number is large or small.
