Measures to assess the prognostic ability of the stratified Cox proportional hazards model

Many measures have been proposed to summarize the prognostic ability of the Cox proportional hazards (CPH) survival model, although none is universally accepted for general use. By contrast, little work has been done to summarize the prognostic ability of the stratified CPH model; such measures would be useful in analyses of individual participant data from multiple studies, data from multi-centre studies, and in single study analysis where stratification is used to avoid making assumptions of proportional hazards. We have chosen three measures developed for the unstratified CPH model (Schemper and Henderson's V , Harrell's C-index and Royston and Sauerbrei's D), adapted them for use with the stratified CPH model and demonstrated how their values can be represented over time. Although each of these measures is promising in principle, we found the measure of explained variation V very difficult to apply when data are combined from several studies with differing durations of participant follow-up. The two other measures considered, D and the C-index, were more applicable under such circumstances. We illustrate the methods using individual participant data from several prospective epidemiological studies of chronic disease outcomes.