Assessment and comparison of prognostic classification schemes for survival data

Prognostic classification schemes have often been used in medical applications, but rarely subjected to a rigorous examination of their adequacy. For survival data, the statistical methodology to assess such schemes consists mainly of a range of ad hoc approaches, and there is an alarming lack of commonly accepted standards in this field. We review these methods and develop measures of inaccuracy which may be calculated in a validation study in order to assess the usefulness of estimated patient-specific survival probabilities associated with a prognostic classification scheme. These measures are meaningful even when the estimated probabilities are misspecified, and asymptotically they are not affected by random censorship. In addition, they can be used to derive R(2)-type measures of explained residual variation. A breast cancer study will serve for illustration throughout the paper.