A Threshold-free Prospective Prediction Accuracy Measure for Censored Time to Event Data

Prediction performance of a risk scoring system needs to be carefully assessed before its adoption in clinical practice. The choice of an appropriate performance metric is important. In risk prediction, the primary interest is to predict the risk of having an event by a pre-specified \textit{future} time $t_0$. Prospective accuracy measures such as positive predictive values have been recommended for evaluating the predictive performance. However, for commonly used continuous or ordinal risk score systems, these measures require a subjective cut-off threshold value that dichotomizes the risk scores. The need for a cut-off value has created barriers for practitioners and researchers. In this paper, we propose a threshold-free summary index of positive predictive values that accommodates time-dependent event status. For censored event times, we develop a non-parametric estimator for the proposed metric. We conduct a simulation study to examine the finite sample performance of our nonparametric estimator. Lastly, we illustrate this metric on a real data example, comparing two risk score systems for predicting heart failure in childhood cancer survivors.