The Cox Proportional Hazards Model

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.