Hazard ratio

A hazard ratio compares how fast an event is happening in two groups: 1.0 means no difference, and 0.8 means it is happening 20 percent less often in the treated group. It is the figure most often quoted when a study reports that something reduced deaths, and it is routinely misread.

Two misreadings are common. The first treats it as an absolute quantity, when it says nothing at all about how many people were affected: 20 percent less of a rare event is still a rare event. The second treats it as steady over time. A single hazard ratio compresses the whole follow-up into one number, and the usual method for producing it assumes the gap between the groups held roughly constant throughout.

That assumption is not always safe, and the statistical test built on it decides which findings count as findings. A 2024 reanalysis of two decades of mouse data from the NIA Interventions Testing Program showed this plainly. The log-rank test, which assumes a uniformly reduced risk across the lifespan, is insensitive to a compound whose effect is not uniform. Re-running the same data through the Gehan test, which is more sensitive to differences earlier in life, identified five further compounds, among them metformin and enalapril.

Nothing about the mice changed between the two analyses. What changed was the question the statistics were asked. That is worth holding on to whenever a headline states that a compound does or does not work.