Publication record · 18.cifr/1972.cox.proportional-hazards
18.cifr/1972.cox.proportional-hazardsThe analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
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Cox outlined extensions to time-varying covariates, competing risks, and stratified models. Formal theoretical justification of partial likelihood as a valid likelihood object was later resolved by others. Extensions to frailty models and machine-learning hazard estimation remain active research areas.