Evaluating Prediction Rules for<i>t</i>-Year Survivors With Censored Regression Models

Abstract

Suppose that we are interested in establishing simple but reliable rules for predicting future t-year survivors through censored regression models. In this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models, we derive consistent estimators for the above measures through substitution and cross-validation estimation procedures. Furthermore, we provide large-sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All of the proposals are illustrated with real examples, and their finite-sample properties are evaluated through a simulation study.