Predictive capability of stratified proportional hazards models

Following on from the work of O'Quigley & Flandre (1994) and, more recently, O'Quigley & Xu (2000), we develop a measure, R2, of the predictive ability of a stratified proportional hazards regression model. The extension of this earlier work to the stratified case is relatively straightforward, both conceptually and in its practical implementation. The extension is nonetheless important in that the stratified model is making weaker assumptions than the full multivariate model. Formulae are given that can be readily incorporated into standard software routines, since the component parts of the calculations are routinely provided by most packages. We give examples on the predictability of survival in breast cancer data, modelled via proportional hazards and stratified proportional hazards models, the latter being necessary in view of the effects of a non-proportional hazards nature.