11.13 Proportional Hazards

The proportional hazards assumption states that (ISLR2 11.14):

\[ h(t|x_i)= h_0(t) \exp\left(\sum_{j=1}^{p}x_{ij}\beta_k\right) \]

Assumes separate time dependence (baseline hazard \(h_0\)) from feature dependence.

• Important to check proportional assumption!

  • Qualitative feature: plot the log hazard function for each level of the feature

  • Quantitative feature: stratify (cut) the feature and do the above.

Source ISLR Fig 11.4