Methods for the Analysis of Complex Time-to-Event Data
AbstractThis dissertation work is motivated by two time-to-event data examples, where current statistical methods are inadequate in addressing the nuances of data and the corresponding scientific question(s) of interest.
In Chapter 1, we address a current issue regarding the analysis of time-varying biomarkers of Alzheimer's disease. Relating time-varying biomarkers of Alzheimer's disease (AD) to time-to-event using a Cox model is complicated by the fact that AD biomarkers are sparsely collected, typically only at study entry; this is problematic since Cox regression with time-varying covariates requires observation of the covariate process at all failure times. The analysis might be simplified by using study entry as the time origin and treating the time-varying covariate measured at study entry as a fixed baseline covariate. We first derive conditions under which using an incorrect time origin of study entry results in consistent estimation of regression parameters when the time-varying covariate is continuous and fully observed. We then derive conditions under which treating the time-varying covariate as fixed at study entry results in consistent estimation. We provide methods for estimating the regression parameter when a functional form can be assumed for the time-varying biomarker, which is measured only at study entry. We demonstrate our analytical results in a simulation study and apply our methods to data from the Rush Religious Orders Study and Memory and Aging Project, and data from the Alzheimer’s Disease Neuroimaging Initiative.
In Chapter 2, we focus our attention on graft-versus-host disease (GVHD), a debilitating condition associated with significant morbidity, compromised quality of life and mortality, that is a frequent complication of hematopoietic cell transplantation (HCT). For the most part, researchers investigating risk factors for acute GVHD, a sub-category that is diagnosed within 100 days of transplantation, have used standard survival analysis methods or logistic regression. Doing so, however, ignores two important clinical issues. First, patients who undergo HCT are at significant risk of death in the short-term; in our motivating data, from the Center for International Blood and Bone Marrow Transplant Research (CIBMTR), 100-day mortality among 9,651 patients who underwent HCT between 1999-2011 was 15%. Naive treatment of death as a censoring mechanism (in either survival or logistic regression analyses), however, is problematic and can lead to erroneous conclusions. Second, acute GVHD is only diagnosed within 100 days of the transplant; beyond 100 days, a patient may be diagnosed with chronic GVHD for which treatment options/strategies generally differ. As such, in contrast to the typical assumption that the support for the event of interest is the positive part of the real line, patients who have undergone HCT are only eligible to experience the event of interest within a finite time interval. In this paper, building on the cure fraction and semi-competing risks literature, we propose a novel multi-state model that simultaneously: (i) accounts for mortality through joint modeling of acute GVHD and death, and (ii) explicitly acknowledges the finite time scale in which the event of interest can take place. The joint observed data likelihood is derived, with estimation and inference performed via maximum likelihood. The proposed framework is compared via comprehensive simulations to a number of alternative approaches that each acknowledge some but not all clinical aspects of acute GVHD. Finally, the methods are illustrated with an analysis of stem cell transplantation registry data from the CIBMTR.
In Chapter 3, we then consider risk prediction of both acute GVHD and death simultaneously. More generally, this work concerns joint risk prediction in the semi-competing risks setting. We propose to consider prediction through the calculation and evaluation of patient-specific absolute risk profiles for the acute GVHD and death. In particular, we note that at any given point in time after transplantation, a patient will: (1) have experienced both events; (2) be alive with a diagnosis of acute GVHD; (3) have died without acute GVHD; or (4) be alive without acute GVHD. Thus, in contrast to much of the prediction literature, we consider the task of prediction as being one where we seek to classify patients at any given point in time into one of four categories based on a vector of probabilities that add to 1.0. We develop this framework utilizing the proposed model in Chapter 2. We then propose a framework for evaluation of predictive performance for risk profiles based on the hypervolume under the manifold (HUM) statistic, an extension of the well-known area-under-the-curve (AUC) statistic for univariate binary outcomes. As part of this, we propose a method for estimating the HUM statistic in the presence of potential verification bias which arises when the true outcome category is unknown. Throughout, we illustrate the proposed methods using data from the CIBMTR.
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