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.
Essays on this concept
- Business Analytics
Survival Analysis for Subscription Businesses: Cox Proportional Hazards vs. Deep Recurrent Models
Binary churn models answer the wrong question. 'Will this user churn?' matters less than 'When will this user churn?' Survival analysis models the timing — and the when determines whether intervention is profitable.
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