The Cox model (proportional hazards model, Cox proportional hazards) is a statistical method of survival analysis that links the time to an event (for example, death) with one or more factors. It was proposed in 1972 by Sir David Cox.
It is a workhorse of the epidemiology of aging: it is precisely with its help that mortality risk is estimated on data from large cohorts such as UK Biobank.
What kind of method it is
The model describes the hazard — the instantaneous probability of an event at a given moment, provided it has not yet occurred. Cox's key insight: if the proportionality assumption holds, the effect of the factors can be estimated without specifying the full form of the baseline hazard function. That is why the method is called semiparametric.
The hazard ratio and how to read it
The main result of the model is the hazard ratio (HR), equal to exp(β). It shows how many times higher or lower the risk of an event is when a factor changes. The HR shows relative, not absolute, risk, and should always be accompanied by a confidence interval.
Where it is used
The Cox model is the standard in medicine and epidemiology for analyzing mortality and disease progression with adjustment for many factors. On it rests the testing of how well a given biomarker of aging predicts outcomes, as well as most cardiovascular-risk estimates. An important condition for validity is the proportional-hazards assumption (a constant ratio of hazards over time).
Reference ranges
How to interpret the hazard ratio (HR):
| HR = 1 | the risk of the event is the same in the groups |
| HR > 1 (for example, 1.5) | the risk is higher — by 50% |
| HR < 1 (for example, 0.7) | the risk is lower — by 30% |
Calculate using this marker
Calculators where Cox regression is used directly:
Frequently asked questions
What does a hazard ratio of 1.3 mean?
The risk of the event in the group studied is about 30% higher than in the comparison group. How reliable this is is shown by the confidence interval.
How does the hazard ratio differ from ordinary risk?
The HR is a relative rate at which the event occurs over time, not an absolute probability. HR<1 means a protective effect, HR>1 an increased risk.