Assessing performance and clinical usefulness in prediction models with survival outcomes: practical guidance for Cox proportional hazards models

Risk prediction models need thorough validation to assess their performance. Validation of models for survival outcomes poses challenges due to the censoring of observations and the varying time horizon at which predictions can be made. We aim to give a description of measures to evaluate predictions and the potential improvement in decision making from survival models based on Cox proportional hazards regression. As a motivating case study, we consider the prediction of the composite outcome of recurrence and death (the ‘event’) in breast cancer patients following surgery. We develop a Cox regression model with three predictors as in the Nottingham Prognostic Index in 2982 women (1275 events within 5 years of follow-up) and externally validate this model in 686 women (285 events within 5 years). The improvement in performance was assessed following the addition of circulating progesterone as a prognostic biomarker. The model predictions can be evaluated across the full range of observed follow up times or for the event occurring by a fixed time horizon of interest. We first discuss recommended statistical measures that evaluate model performance in terms of discrimination, calibration, or overall performance. Further, we evaluate the potential clinical utility of the model to support clinical decision making. SAS and R code is provided to illustrate apparent, internal, and external validation, both for the three predictor model and when adding progesterone. We recommend the proposed set of performance measures for transparent reporting of the validity of predictions from survival models.