Semiparametric analysis of time-to-event data and longitudinal data
No Thumbnail Available
Authors
Meeting name
Sponsors
Date
Journal Title
Format
Thesis
Subject
Abstract
Interval-censored failure time data are commonly observed in demographical, epidemiological, financial, medical, and sociological studies. It is well-known that the proportional hazards model is one of the most used regression models for the analysis of failure time data, and significant literature has been established for fitting it to interval-censored data. Many authors have discussed the problem when complete information on the covariates is available, or the missing is completely at random. Nevertheless, an established method for the situation where the missing is at random does not seem to exist. The first part of this dissertation discusses fitting the proportional hazards model to interval-censored failure time data when there may exist missing on covariates. A sieve maximum likelihood estimation approach is proposed with the use of I-splines to approximate the unknown cumulative baseline hazard function. For the implementation of the method, we develop an EM algorithm based on two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. Many authors have discussed the joint analysis of longitudinal data and time-to-event data, but most of the existing methods are the hazard-based approach for the failure time of interest. It is well-known that sometimes the mean residual life (MRL) model, which measures the remaining life expectancy, may be of more interest. To address this issue, the second and third parts of this dissertation consider an MRL-based method for the joint analysis, which gives a meaningful and informative alternative to the hazard-based approach. In the second part, we propose to utilize the proportional mean residual life (PMRL) function with latent random effect to jointly access the observed baseline prognostic factors and continuous longitudinal risk factor on the MRL function. The proposed method extends the conventional proportional mean residual model to accommodate a latent random effect that links the time to event with longitudinal measurement. For the parameter estimation, we propose an extended estimating equation approach. The simulation study shows that the performance of the proposed method is satisfactory. We then apply the proposed method to the ADNI study that reveals insights into critical factors that influence the progression time from MCI status to AD conversion. To further accommodate binary longitudinal outcome, in the third part, the proportional mean residual model and the generalized linear mixed model are employed to model the failure time of interest and the longitudinal variable, respectively. For estimation, a quasi-likelihood approach is developed with the use of Laplace approximation. A simulation study is conducted, and the proposed method is applied to a set of real data.
Table of Contents
PubMed ID
Degree
Ph. D.