Assessing Predictive Abilities of Hazard-Based Regression Models for Survival Data: a Tutorial for Prognosis Modelling

Abstract Predicting the occurrence of an event over time for a newly diagnosed individual is a common aim in medical statistics. For time-to-event outcomes, this prediction is typically based on a regression model. The Cox proportional hazard (PH) model represents one of the most popular regression models for analysing time-to-event data. However, several flexible models that go beyond the assumption of proportionality of hazards have been recently developed. These include flexible hazard-based models using splines or models based on more general hazard structures. In these 2 types of models, non-linear associations and time-varying regression coefficient(s) can be easily included. Assessing the predictive ability of a hazard-based regression model is necessary to validate a predictive model but it might prove difficult for models other than the Cox PH model. We present a tutorial which explains how the predictive ability of hazard-based regression models can be assessed, focusing on the 3 commonly used performance measures. We report (i) the overall prediction ability using prediction error curve and the Brier score, (ii) the discriminative ability using the cumulative/dynamic area under the receiving operator characteristic curve, and (iii) the calibration ability, i.e., the agreement between observed and predicted probabilities, using calibration plots and graphical comparison between predicted and observed survival. We provide an implementation of these methods in R together with an illustrative example using a publicly available data set.