  Prediction performance of a risk scoring system needs to be carefully
assessed before its adoption in clinical practice. Clinical preventive care
often uses risk scores to screen asymptomatic population. The primary clinical
interest is to predict the risk of having an event by a pre-specified 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 cutoff threshold value that dichotomizes the risk scores. The need
for a cut-off value 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. We develop a nonparametric
estimator and provide an inference procedure for comparing this summary measure
between competing risk scores for censored time to event data. We conduct a
simulation study to examine the finite-sample performance of the proposed
estimation and inference procedures. Lastly, we illustrate the use of this
measure on a real data example, comparing two risk score systems for predicting
heart failure in childhood cancer survivors.
