Topics in Survival Analysis

This dissertation, "Topics in Survival Analysis" by Kwok-fai, Lam, 林國輝, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "TOPICS IN SURVIVAL ANALYSIS" Submitted by Kwok-fai LAM For the Degree of Doctor of Philosophy at The University of Hong Kong in June 1994 This thesis deals with the modelling and analysis of failure time data and is divided into four main topics in survival analysis. In modelling proportion of immunes or surviving fraction in a population, it is common to assume a mixture model which combines a logistic regression model and a positive distribution. In some applications, the model may not be appropriate especially in the presence of heterogeneity among individuals in subpopulations. It is shown that frailty or random effects model can also be used in such situations provided that the frailty distribution has a discrete mass at zero, and the mixture model mentioned is only a special case of the frailty model representations when the frailty term has a logistic regression model. Examples of some frailty distributions and their relative merits are discussed in the first topic. It is well known that frailty models can also be used to generate dependent multivariate survival distributions. A large number of estimation methods have been proposed in the literature, most of them depend on specific dis- tributional assumptions for the frailties. The second topic advocates the marginal likelihood approach as a unified approach to parameter estimation in frailty models for multivariate survival data analysis. As it is impossible to evaluate the marginal likelihood function analytically, two Monte Carlo approximations are proposed, and the frailty prediction by Monte Carlo em- pirical Bayes approach is also considered. Two classes of multivariate non-parametric tests are proposed for testing the equality of failure rates in a competing risks setup, which turns out to be of equivalent form. Optimal weight functions which yield optimal local asymptotic power for certain alternative hypotheses are considered for the two classes, and a more empirical way of choosing weight function in application to a data set is illustrated with an example in the third topic. The last topic deals with a special type of multivariate survival data which can be represented by a compartmental model or the so-called illness and death model. A non-parametric inference procedure in estimating the cumulative rate of morbidity of a certain disease is proposed with the time to onset of the disease being unobservable, which is generally true in real life. General difficulties for such models are also discussed. ii DOI: 10.5353/th_b3040899 Subjects: Survival analysis (Biometry) Failure time data analysis