Absolute versus relative benefit (number needed to treat)

Trial results are usually headlined as relative effects: a hazard ratio of 0.72, a 28 percent reduction in the risk of recurrence. Relative effects travel well between populations and are what the statistics estimate directly, but they say nothing about how many people were helped. That requires the baseline risk. Cutting a risk of recurrence from 30 percent to 21 percent is a nine-percentage-point absolute reduction, and about eleven people must be treated for one of them to be spared a recurrence. Cutting a risk from 3 percent to 2.1 percent is the same relative reduction, a 0.9-point absolute reduction, and more than a hundred people must be treated to spare one. The side effects, cost and inconvenience fall on everyone treated, so the absolute benefit is the number to weigh them against.

CHALLENGE illustrates the arithmetic in the corpus. Five-year disease-free survival was 80.3 percent with the exercise programme against 73.9 percent with health education, a hazard ratio of 0.72 and an absolute gain of about six percentage points, so roughly one in sixteen participants avoided a recurrence or death in that window. KEYNOTE-564 reported a disease-free survival hazard ratio of 0.72 as well; how many patients that helps depends on the recurrence risk of the population enrolled, which is why adjuvant trials restrict entry to higher-risk stages where the absolute benefit is worth a year of treatment. The Trials in plain words page on this site converts every trial result with structured outcomes into people out of 100 for exactly this reason.

Differences in medians are a third way of describing the same result and the easiest to misread. A median gain of two months means the middle patient in each arm differed by two months; it does not mean every patient gained two months, and when a survival curve has a long tail, as with immunotherapy, the median can understate the benefit to the minority who do very well. A trustworthy report gives the relative effect, the absolute difference at a stated time point, and the medians, and says which population they apply to.