Khmaladze-type graphical evaluation of the proportional hazards assumption

Khmaladze-type goodness-of-fit tests are based on transforming an appropriate empirical process to one with a known large-sample distribution.Using Donskerʹs theorem, together with a theorem for proportional hazards generalising a theorem of Xu & OʹQuigley (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.