(alternate title: What’s a hazard ratio?)
Today I was faced with the not-entirely-straightforward task of explaining what a hazard ratio is. It’s a measure that pops up quite a lot in epidemiological statistics, when you’re conducting a study into survival times. It’s not immediately obvious, however, what it is, and when faced with the inevitable “so, what’s this hazard ratio all about then?” question, I struggled to find a good answer.
Wikipedia’s explanation is, frankly, rubbish (paraphrasing: “a hazard ratio is the ratio of the hazards”). Other attempts to explain it that I found online were similarly confusing. I found a very nice explanation online in the Pharmaceutical Statistics journal, which sadly falls down on two counts:
- it’s still too long for “30-second elevator speech” purposes, and
- it’s paywalled, so it’s useless to non-subscribers.
So, armed with this paper, I came up with the following even shorter explanation, which I now share with t’interwebz. I wrote it in the context of a “time-to-death” analysis, though survival analysis can be used to analyse times to almost any event you choose, not just mortality.
First of all, it would probably help to begin by explaining what a hazard is.
The hazard can be thought of as the instantaneous risk of dying at a given time point. This may vary over time, though how the hazard rises and falls over time is usually of secondary interest.
A survival analysis compares hazards between different groups of subjects in the study. One of the assumptions I made in this analysis is proportional hazards (you might encounter the phrase “assuming proportional hazards” in the epidemiological literature quite a bit). This means that we assume that although hazards may be different in different groups, and might for all we care rise/fall willy-nilly over time, when the hazard from one group changes over time, the hazard in all the other groups change by the same proportion.
In other words, the ratio between the hazards remains constant over the course of the entire study, even though the hazards themselves change over time. It’s this ratio that is the hazard ratio, and it summarizes mortality differences along the whole length of time being analysed.
I think that gives you the gist of it anyway. Feel free to rehearse it, tweak it, and drop it into your talks and lectures.