TIBCO Statistica® Cox Proportional Hazards Models
The main characteristic of survival analysis that differentiates itself from other analytic methods is the ability to handle censored data. A data point is considered censored if the end point of interest is not observed for a particular individual. For this type of data, many modeling techniques are inappropriate, e.g., normal regression models. This makes it useful for:
- analysis of survival data from patients in medical studies
- consumer credit risk
- customer churn analysis
- modeling and failure of mechanical parts (reliability)
The British statistician David Cox introduced the proportional hazards model in the 1972 paper, "Regression Models and Life Tables," Journal of the Royal Statistical Society Series B 34 (2): 187–220. This statistical model, the Cox proportional hazards model, does not impose any specific form of the survivor function, allowing censored data to be modeled flexibly. Specifically, Cox’s proportional hazards model is a distribution-free model in which predictors are related to lifetime multiplicatively.
The form of the Cox proportional hazards model is as follows:
where h0(t) is the baseline hazard and is the vector of regression coefficients. This model does not impose any distributional assumption on the baseline hazard. It is referred to as proportional because the ratio of hazard rates of two individuals is constant and not dependent on time.