Discrimination measures for discrete time-to-event predictions

Discrete time-to-event models have become a popular tool for the statistical analysis of longitudinal data. These models are useful when either time is intrinsically discrete or when continuous time-to-event outcomes are collected at pre-specified follow-up times, yielding interval-censored data. While there exists a variety of methods for discrete-time model building and estimation, measures for the evaluation of discrete time-to-event predictions are scarce. To address this issue, a set of measures that quantify the discriminatory power of prediction rules for discrete event times is proposed. More specifically, sensitivity rates, specificity rates, AUC, and also a time-independent summary index (“concordance index”) for discrete time-to-event outcomes are developed. Using inverse-probability-of-censoring weighting, it is shown how to consistently estimate the proposed measures from a set of censored data. To illustrate the proposed methodology, the duration of unemployment of US citizens is analyzed, and it is demonstrated how discrimination measures can be used for model comparison.