STATISTICAL METHODS FOR MULTIVARIATE FAILURE-TIME DATA UNDER COMPETING RISKS

Traditional research on survival analysis often centered on univariate data where the observations are mutually independent. In many modern studies, however, data of interest are observed in clusters, so may be associated. Primary scientific interest often centers on the effect of a treatment on the individuals' outcomes in studies involving multivariate failure time data, but this thesis is mainly concerned with analyses in which the estimation of association between failure times is of interest. A considerable body of literature has addressed this topic, but they have been limited in many ways. They may depend on parametric assumptions that may easily be violated, they may not be flexbile enough, or their interpretations are not intuitive. The primary purpose of this thesis is to investigate the drawbacks of existing methods, and suggest an alternative measure of association that is flexible and interpretable, especially under the competing risks setting. This thesis consists of three main chapters. Chapter 2 discusses a nonparametric estimation of the local version of Kendall's $ \tau $. The performance of several smoothing methods are compared, and new methods to deal with censored data are also proposed and assessed. Chapter 3 studies the sensitivity of the Bandeen-Roche and Liang (2002) estimator of the CCSHR to the imposed statistical assumptions and investigate the source of a bias reported in its foundational work. In Chapter 4, novel parametric and nonparametric estimators for the association between failure causes are proposed. Various combinations of existing and new methods for the association between failure times and between failure causes are assessed