Khmaladze‐type graphical evaluation of the proportional hazards assumption

Abstract

Khmaladze‐type goodness‐of‐fit tests are based on transforming an appropriate empirical process to one with a known large‐sample distribution. Using Donsker's theorem, together with a theorem for proportional hazards generalising a theorem of Xu & O'Quigley (1999), we indicate how to construct a Khmaladze‐type graphical test for evaluating the proportional hazards assumption. An illustration is given in which a partially proportional hazards model can be seen to provide a noticeably improved fit over a fully proportional hazards model.