The Cox Proportional Hazards Model

Abstract

The proportional hazards (PH) or Cox model holds on E, if the hazard rate has the form

$$\begin{aligned} \lambda _{x(\cdot )}(t) = r\{x(t)\} \;\lambda _0(t), \quad x(\cdot ) \in E, \end{aligned}$$

where $\lambda _0(\cdot )$ is an unspecified baseline hazard rate function , and $r(\cdot )$ is a positive function on E. The function $r(\cdot )$ explains the summing effect of all $x_i(\cdot )$ on the distribution of T.