Statistical inference for residual time quantiles in regression models for censored time-to-event data

Abstract

In this dissertation, we set out to develop new methods for the analysis of time-to-event data. In particular, we are concerned with residual time, or the time remaining to an event after a certain amount of time has passed since time zero. We develop methods to estimate quantiles of residual time under a few different settings: the Cox proportional hazards model (with fixed and with external time-varying covariates) and the additive hazards model. In each setting, we consider point estimation, asymptotic properties, variance estimation, confidence interval construction, and inference. We also perform simulations to demonstrate our estimators' performance and provide examples of their application to sample data sets. We finish by discussing the many opportunities for future work and expansion of our methods to address limitations or allow application in a wider array of settings.