In the previous section, we introduced the idea that Cox proportional hazards is used to estimate hazard rates for individuals using recorded time-to-event data, values for each predictor variable included in the model, and some undefined baseline hazard function. In this section, we will explore how the hazard rate can be related to the survival function, and how each of these can be linked back to the original time-to-event data. Note that this section will be somewhat heavy on the underlying mathematics behind survival analysis. While this information is quite useful in understanding how these analyses work, it is not required to understand the math in this section in order to perform and interpret a survival analysis.

The mathematical details of Cox regression are presented on the following pages:

•Mathematics of the survival function

•Mathematics of the hazard function

•Mathematics of the cumulative hazard function

•Mathematics of model coefficients and the concept of tied data

If you don’t want to get into the specific mathematical details, check out these other sections instead:

•How to: Kaplan-Meier survival analysis

•Results of Kaplan-Meier survival analysis

•How to: Cox proportional hazards regression

•Results of Cox proportional hazards regression