Predictive accuracy and explained variation in Cox regression

We suggest a new measure of the proportion of the variation of possibly cen sored survival times explained by a given proportional hazards model. The p roposed measure, termed V, shares several favorable properties with an earl ier V-1 but also improves the handling of censoring. The statistic contrast s distance measures between individual 1/0 survival processes and fitted su rvival curves with and without covariate information. These distance measur es, D-x and D, respectively, are themselves informative as summaries of abs olute rather than relative predictive accuracy. We recommend graphical comp arisons of survival curves for prognostic index groups to improve the under standing of obtained values for V, D-x, and D. Their use and interpretation is exemplified for a Yorkshire lung cancer study on survival. From this an d an overview for several well-known clinical data sets, we show that the l ikely amount of relative or absolute predictive accuracy is often low even if there are highly significant and relatively strong prognostic factors.