Hazard ratios: what they measure and when the assumption breaks

A hazard ratio compares how fast an event, often death or disease progression, is happening in one group of a study compared with another, at any given moment during follow-up. A hazard ratio of 0.7 for death means that at each point in the trial, people in that group are dying at about 70 percent of the rate of the comparison group. It is one of the most printed numbers in a trial result, and one of the least understood, because a ratio of rates is not the same thing as a ratio of survival time.

The number comes from Cox proportional hazards regression, a method built on an assumption that gives it its name: the ratio between the two groups' event rates is assumed to hold steady across the whole study, from the first day of follow-up to the last. A single hazard ratio is meant to summarize the entire trial with one number, as if the relative difference between the groups never grew, shrank, or reversed. When that assumption does not hold, the printed number can flatten a far messier story into one tidy figure.

Two traps follow. First, a hazard ratio measures rate, not time, and gets misread as speed. Researchers reviewing antiviral drug trials found papers describing a hazard ratio of 2 as patients healing "twice as fast," when the actual reduction in days sick was often smaller or larger than that. Second, the constant-ratio assumption itself can fail. In the Women's Health Initiative hormone therapy trial, the risk of breast cancer barely differed between groups for the first four years and then rose, a trend the trial's own statisticians called significant, which meant one overall hazard ratio could not honestly describe the whole period.

So when a headline leans on a hazard ratio, remember it is a snapshot of relative rate, not a promise about how much sooner or later something happens, and it assumes that relative rate held steady throughout the study. Look at the actual survival or event curves if you can find them, not just the summary number, and notice whether they run roughly parallel or cross partway through. Pair the hazard ratio with the absolute risk and the number needed to treat, and a single ratio stops doing more work than it can bear.