Methods for describing the time-varying predictive performance of survival models

Abstract

In this dissertation we develop new methods for quantifying the predictive performance of a survival model at different times. We broadly categorize predictive performance into either calibration or discrimination, and propose new methods for measuring time-varying discrimination that complement existing methods such as time-varying AUC. Specifically, we introduce the hazard discrimination summary, HDS(t), a measure that characterizes the ability of a survival model to discriminate between incident events and survivors at each time point. We first motivate HDS(t) as an incident extension of the discrimination slope, and propose a semiparametric estimator along with a study of its asymptotic properties. Second, we show that HDS(t) is amenable to evaluating time-varying covariates, propose corresponding semiparametric estimators, and outline inferential procedures. Finally, we propose an alternative interpretation and nonparametric estimators for HDS(t), both of which illuminate connections between HDS(t) and fundamental information theoretic concepts.