hazard ratio

Spruance and colleagues, writing in Antimicrobial Agents and Chemotherapy, define the hazard ratio as an estimate of the ratio of the hazard rate in the treated group versus the control group. The hazard rate is the chance of the event happening at a given instant among those it has not yet happened to. Dividing one by the other gives a single number for how the two groups compare: 0.5 means the event was occurring at half the rate, 2.0 at twice the rate. Because it works from instantaneous rates rather than a final tally, it uses the timing of events and not only their number.

It is not a statement about how much longer anyone lives. That is the paper's central warning. A hazard ratio of 2.0 does not mean the median survival time is halved, and the authors' own herpes treatment examples show how far apart the two can sit: two studies with the same hazard ratio of 1.9 had median ratios of 1.5 and 2.0, while a third, with a lower hazard ratio of 1.5, had the largest median ratio of the three at 3.1. How much time a given ratio buys depends on the shape of the underlying distribution of events, which the ratio itself does not carry, so for trials about duration the authors recommend reporting median times alongside it.

The figure also rests on an assumption. Proportional hazards regression, the method that usually produces it, assumes the hazard ratio is constant over time. Where a treatment works strongly at first and fades, or takes months to take hold, one summary ratio averages over that change and describes no particular moment well. The word adjusted in front of it means the model also accounted for listed differences between the groups, which addresses the confounders somebody measured and none of the ones they did not.