Measures of prediction error for survival data with longitudinal covariates

Prediction of future events using longitudinally collected patient measurements is increasingly popular as technical and methodological advances allow the construction of more and more complex prognostic models. We aim to give an overview of existing approaches to measure the prediction error of such dynamic predictions and link these to a measure proposed in a preceding paper (Schoop et al.), the conditional prediction error. We present theoretical results of the conditional prediction error, especially regarding the comparison of different prediction rules and its behavior in the presence of misspecification of the link between longitudinal covariates and survival time. A simulation study investigating the performance of its estimator in finite sample sizes rounds off this paper.