Glossary · Business Analytics

Cox Proportional Hazards Model

also: Cox PH · Cox regression

Definition

The Cox proportional hazards model is the semi-parametric workhorse of survival analysis: it estimates how covariates multiply the baseline hazard rate without requiring a parametric form for the baseline. It yields interpretable hazard ratios under the assumption that the ratio is constant over time.

Cox (1972) introduced partial likelihood estimation that removes the baseline hazard from the inference, leaving covariate effects as hazard ratios. The model assumes proportionality — each covariate multiplies the baseline hazard by a constant factor over time. When proportionality fails, extensions (stratified Cox, time-varying coefficients, deep survival nets) handle the complication at the cost of interpretability.

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