# Clinical Biostatistics: The ESPRIT Trial, suggested answer 4

4. What is meant by hazard and hazard ratio and how can we interpret a hazard ratio = 0·80, 95% CI 0·66–0·98? What assumptions are made about the data for this calculation?

“Hazard” is used to mean the rate at which events happen at any given time. It varies over time. The probability that a random patient who has yet to experience an event will experience an event over a short time interval is the hazard at that time multiplied by the length of the interval. The hazard ratio is the ratio of the hazard in the aspirin with dipyridamole treated group to the hazard in the aspirin only group.

Hazard = 0.80 tells us that, at any given time, we estimate that patients in the aspirin with dipyridamole had a risk of an event which was 0.80 times the risk in the aspirin only group. The confidence interval does not include one, the value the hazard ratio would have if there were no difference between the treatments, so we have evidence that aspirin with dipyridamole reduces risk for such patients compared to aspirin alone. The reduction may be as large as one third (i.e. a factor = 0.66) or very small, as little as 2%, based on these data alone.

To estimate the hazard ratio, we must assume it is constant, i.e. that it is the same at all times over the period of follow-up. This is called the proportional hazards assumption. We must also assume that the survival times are the same for patients recruited at different times over the trial and that they re the same for patients who are followed up to the end of the trial and for those who have been lost for some reason.

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