Lanterna Rally

Author: Yu-Ru Su

Publisher:

Published: 2011

Total Pages:

ISBN-13: 9781267029829

There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right censored survival data. In the first part of my dissertation, we consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open however for the important case where longitudinal covariates are present in survival models. A joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right censored data, but this approach faces substantial additional challenges in the presence of left truncation. Here we thus propose an alternative likelihood to overcome these difficulties and show that the regression coefficient in the survival component can be estimated unbiasedly and efficiently. Issues about the bias for the longitudinal component are discussed. The new approach is illustrated numerically through simulations and data from a multi-center AIDS cohort study. In the second part, we investigate frailty models for clustered survival data which are subject to both left- and right-censoring. The classical proportional hazards model encounters difficulties when the independent assumption among subjects is violated, e.g. when familial data are observed. Under a frailty model, a frailty variable is often included to account for the associations of event-times within a cluster. The majority of the literature are devoted to clustered survival data subject to right-censoring. Here we consider a more complicated scenario with the presence of double censoring as defined in Turnbull (1974). We developed the estimating procedure through the likelihood approach and the associate large sample theory for both the parametric and nonparametric estimates. The parametric estimates are shown to be semi-parametrically efficient as well. A modified EM algorithm is proposed to resolve the challenges in the EM-algorithm and shown numerically to perform satisfactorily. The new procedure is applied to a study of Hepatitis B virus infection.