The predictive value of a statistical model is conceptually different from the explained variation. In this paper we construct a measure of the predictive value of the Cox proportional hazards model, computed from the leave-one-out regression coefficients. These coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in R2-type measures of the proportion of explained variation. Our methods are illustrated by a study of chemotherapy for advanced ovarian cancer.