The Cox model is used to estimate the relationship between the rate at which an event occurs (such as death or failure of a mechanical system) and a set of covariates, such as age, sex, or treatment group. The model assumes that the hazard rate (i.e., the instantaneous probability of the event occurring at a given time, given that the individual has survived up to that time) is proportional across different levels of the covariates.

The key assumption of the Cox model is that the hazard ratio (HR) remains constant over time. This means that the ratio of the hazard rate of two individuals with different covariate values remains constant over time. The Cox model estimates the HR for each covariate, which provides a measure of the effect of that covariate on the hazard rate.

The Cox model is a popular tool in medical research, where it is used to analyze the survival times of patients with different diseases or conditions, and to evaluate the effectiveness of different treatments. It is also used in other fields such as engineering, finance, and social sciences to analyze time-to-event data.