Posters · Glossary
What is a hazard ratio?
A hazard ratio compares the rate at which an event, such as death, relapse or recovery, happens in one group with the rate in another group at any moment during follow up. A value of 1 means no difference, below 1 means the event happens more slowly in the first group, and above 1 means it happens faster.
Hazard ratios come out of survival analysis, usually a Cox model, and they are the headline number on most trial and cohort posters with time to event outcomes. They are also one of the most misread numbers in a results panel, because a ratio of rates is not a ratio of times.
Indunil Asanka · Co-founder
5 min read · Published
| Hazard ratio | Event rate in group A against group B | Chance a person in A has the event before a person in B |
|---|---|---|
| 0.5 | Half the rate at any point in follow up | 33% |
| 0.75 | A quarter lower | 43% |
| 1.0 | The same rate | 50% |
| 1.5 | Half as high again | 60% |
| 2.0 | Twice the rate | 67% |
| 3.0 | Three times the rate | 75% |
Hazard, rate and ratio
The hazard is the instantaneous rate of the event among people who have not had it yet: of everyone still event free at a given moment, how likely is the event in the next very short interval. A hazard ratio divides the hazard in one group by the hazard in the other. Cox proportional hazards regression estimates it while adjusting for other variables such as age, sex or baseline severity, which is why most posters report an adjusted hazard ratio beside a crude one. Spruance and colleagues point out a useful translation: the hazard ratio equals the odds that a person in the higher hazard group reaches the event first, so a ratio of 2 means a two in three chance of being first, as the table shows.
Why HR 2 does not mean twice as fast
The commonest misreading is to treat a hazard ratio as a ratio of times. A ratio of 2 does not halve the median time to the event. How much time is gained or lost depends on the shape of the survival curves, which depends on the disease and the follow up. Spruance and colleagues show curves with a hazard ratio of 3 where median survival moves by only 10 percent, and curves with a ratio of 1.5 where it moves by 50 percent. When the benefit in time matters to the reader, report the median time in each group, or the difference in restricted mean survival time, beside the hazard ratio.
The proportional hazards assumption
A single hazard ratio assumes the ratio stays roughly constant over the whole follow up. When survival curves cross, or when a treatment helps early and fades later, one number averages effects that point in different directions. Check the assumption with log minus log plots or Schoenfeld residuals, and if it fails, report hazard ratios for separate periods or a different summary. On a poster the Kaplan-Meier curve beside the ratio lets a reader see at a glance whether the gap between groups is steady.
Common mistakes in a results panel
Reporting a hazard ratio with no confidence interval, which hides how precise it is. Writing that a ratio of 0.7 means 70 percent fewer events, when it means a 30 percent lower rate. Mixing hazard ratios with odds ratios or risk ratios in one forest plot without saying which is which. Leaving out what the model adjusted for, so a reader cannot compare the crude and adjusted values. And quoting a p value alone, when the interval says the same thing with the size of the effect attached.
Showing it on a poster board
A hazard ratio usually earns a key number block, with the interval and the adjustment set written in the line below it. Stat blocks appear on 26 of the 40 poster layouts, and every board has a figure block, a section slot and a reference block, so the ratio, the curve and the source of the method all have a place. The cohort study example reports a crude hazard ratio of 1.9 that fell to 1.5 after adjustment, with the cumulative incidence in each group beside it, which is the pattern worth copying. The generator fills numbers only from the brief, so include the ratio, the interval, the follow up time and the variables in the model when you describe the study.
Questions people ask
Is a hazard ratio the same as relative risk?
No. Relative risk compares the proportion of people who had the event by the end of a fixed period. A hazard ratio compares the rate of events at each moment, using everyone still at risk, and it uses the timing of events and censored follow up. The two are close when events are rare and follow up is short, and drift apart when many people have the event.
What does a confidence interval that crosses 1 mean for a hazard ratio?
It means the data are consistent with no difference in the event rate between the groups, at the chosen confidence level. An interval of 0.85 to 1.20, for example, allows a 15 percent lower rate, a 20 percent higher rate or none at all. Report it as an uncertain result rather than as proof that the groups are the same.
Can a hazard ratio be calculated from a Kaplan-Meier curve?
Not exactly by eye. A log rank test compares the curves and an observed over expected calculation gives an approximate ratio, but the usual method is a Cox model on the individual data. Meta analysts sometimes reconstruct approximate data from published curves when the paper omits the ratio, which is why reporting it directly helps later reviews.
Should I report the crude or the adjusted hazard ratio?
Report both when space allows, with the adjusted one as the headline if confounding is likely, as in most observational studies. Name the variables in the model in one line. In a randomised trial the unadjusted ratio is usually the primary result, with any adjusted analysis labelled as prespecified or exploratory.
Why do some posters show a hazard ratio below 1 as good and others as bad?
It depends on the event and which group is on top of the ratio. If the event is death and the treatment group is the numerator, a ratio below 1 is benefit. If the event is recovery, a ratio above 1 is benefit. State the event, the reference group and the direction in words next to the number.
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Create a poster with OneCraftRelated questions
- What is a Kaplan-Meier curve?A Kaplan-Meier curve plots the share of people still event free over time. How to read its steps, censoring ticks, median and the numbers at risk table.
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- What is thematic analysis?Thematic analysis finds patterns of meaning across interviews or open text. Braun and Clarke's six phases, codes against themes, and themes on a poster.
- What is an odds ratio?What is an odds ratio: the odds of an outcome in one group divided by the odds in another. A worked 2x2 example, how to read it, and why it is not a risk ratio.
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