Methods for Flexible Survival Analysis and Prediction of Semi-Competing Risks

Abstract

Methods for the analysis of time-to-event outcomes enable two vital tasks in health research: development of risk prediction tools to aid clinical decisionmaking, and associational modeling to assess relationships between such outcomes and possible risk factors. Risk prediction has unique potential in the setting of semi-competing risks, in which the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event.

Chapters 1 and 3 of this dissertation address this task directly with novel methods for modeling and prediction of semi-competing risks, motivated by application to the outcomes of preeclampsia and delivery. In Chapter 1 we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels, for which we develop efficient computational tools and establish theoretical statistical error rate results. In Chapter 3 we address the potential for `immediate' terminal events occurring after the non-terminal event, such as induction of delivery immediately upon preeclampsia diagnosis. We propose an augmented illness-death multi-state model incorporating a logistic regression submodel to capture the probability of such events, with Bayesian estimation via a custom Markov Chain Monte Carlo sampling algorithm. We further establish novel formulae for risk prediction that distinguish the probabilities of immediate and non-immediate terminal event occurrence following the non-terminal event.

Finally, we also considered the task of associational modeling motivated by the study of Alzheimer's disease in older adults, and based on the accelerated failure time model for time-to-event outcomes. This model structures covariate effects as constant multiplicative shifts on survival quantiles of the outcomes, and in Chapter 2 we propose a flexible extension to this model allowing covariates to have quantile-varying multiplicative effects on the survival quantiles. We also extend this framework to admit time-varying covariates, and introduce an array of graphical tools for visualizing these effects. We perform estimation in the Bayesian paradigm using a Hamiltonian Monte Carlo sampler implemented using the Stan language, enabling both parametric and non-parametric specifications for the baseline survival distribution.