An R² -curve for evaluating the accuracy of dynamic predictions

In the context of chronic diseases, patient's health evolution is often evaluated through the study of longitudinal markers and major clinical events such as relapses or death. Dynamic predictions of such types of events may be useful to improve patients management all along their follow-up. Dynamic predictions consist of predictions that are based on information repeatedly collected over time, such as measurements of a biomarker, and that can be updated as soon as new information becomes available. Several techniques to derive dynamic predictions have already been suggested, and computation of dynamic predictions is becoming increasingly popular. In this work, we focus on assessing predictive accuracy of dynamic predictions and suggest that using an R² -curve may help. It facilitates the evaluation of the predictive accuracy gain obtained when accumulating information on a patient's health profile over time. A nonparametric inverse probability of censoring weighted estimator is suggested to deal with censoring. Large sample results are provided, and methods to compute confidence intervals and bands are derived. A simulation study assesses the finite sample size behavior of the inference procedures and illustrates the shape of some R² -curves which can be expected in common settings. A detailed application to kidney transplant data is also presented.