“Reduced the risk by 50%” tells you a relative change. It does not tell you the starting risk or how many people experienced the outcome. Both are needed to understand the size of the observed difference.
The numbers below are fictional arithmetic examples, not medical findings or predictions for any treatment.
Example one: 20 in 100 versus 10 in 100
Imagine two hypothetical groups of 100 people observed over the same fixed period. Twenty people in the comparison group experience an outcome, while ten in the intervention group do.
The comparison risk is 20%. The intervention risk is 10%. The absolute difference is 10 percentage points: 20% minus 10%. The relative reduction is 50%: the 10-point difference divided by the original 20% risk.
Both descriptions are mathematically correct. They answer different questions.
Example two: 2 in 100 versus 1 in 100
Now imagine the same group sizes and observation period, but only two people in the comparison group and one in the intervention group experience the outcome.
The relative reduction is again 50%. The absolute difference is now one percentage point rather than ten. The identical relative headline conceals a tenfold difference in the absolute change.
This does not mean relative measures are deceptive. It means the reader needs the baseline alongside them.
Keep the period and population attached
A risk measured over one month is not interchangeable with a risk measured over ten years. A result in a particular study population is not automatically a personal forecast for someone outside that population.
If an article gives only a relative percentage, ask for the underlying counts, denominators and follow-up. If the source does not provide them, label the missing information rather than manufacturing a table.
Do not subtract unlike outcomes
A numerical difference can look meaningful while comparing different events. “Any recurrence,” “severe recurrence” and “a particular laboratory change” are not the same endpoint merely because each can be expressed as a percentage.
Likewise, a relative risk reduction is not automatically the same as a hazard reduction. When a study reports a different statistical measure, preserve its name and explanation rather than replacing it with a familiar but inaccurate formula.
What this calculation does not establish
These examples do not include uncertainty estimates, design limitations or adverse effects. Arithmetic can clarify a reported result; it cannot supply evidence the study did not collect or determine whether a treatment is right for an individual.
Our preferred reporting sentence gives the measured event, both absolute figures, the relative measure when appropriate, the population and the time period. Harms receive the same discipline.
The cell-therapy evidence report is an example of preserving denominators and follow-up rather than using a free-floating success percentage. Good numerical reporting makes the result understandable without pretending that a number alone settles a medical decision.