Explained variation

Some suggestions on possible measures of explained variation which have appeared in the literature are considered. Following this an outline of the recommended approach is given. Leaning upon the theory of explained variation detailed in Chapter 2 and in particular 3.9 we show how a solid theory of explained variation for proportional and non-proportional hazards regression can be established. This contrasts with a substantial body of literature on this topic, almost entirely constructed around intuitive improvisations and ad-hoc modifications to sample based quantities gleaned from classical linear regression. The main reference here is the paper by O'Quigley and Flandre (1994) which showed how the Schoenfeld residuals provide the required ingredients for the task in hand. The properties of population quantities and sample based estimates have been studied thoroughly (O'Quigley and Xu 2001) and these provide the user with the necessary confidence for their practical use.