Semiparametric regression analysis of longitudinal data with informative observation times

Abstract

Longitudinal data often occur in a long-term study where each individual is measured repeatedly at distinct time points rather than continuous times and also the observation times and censoring times may vary from subject to subject. Many researchers have considered the analysis of such longitudinal data under the assumption that observation process is independent of response process completely or conditional on covariates, which may not be true in practice. This thesis investigates semiparametric analysis of longitudinal data when the response process is correlated with the observation times. We develop a new class of semiparametric mean models for longitudinal data which allows for the interaction between the observation history and covariates, leaving patterns of the observation process to be arbitrary. Although panel count data is a special case of longitudinal data, it has particular features which can not be described by general longitudinal models. Thus, to analyze the panel count data, we propose a new class of flexible semiparametric regression models by incorporating the interaction between the observation history and some covariates to the mean model of the recurrent event process, without any formation restriction on the informative observation process. For inference on the regression parameters and the unknown baseline functions involved in both longtidunial data and panel count data models, spline-based least square estimation approachs are proposed, respectively, and asymptotic properties including the consistency, rate of convergence and asymptotic normality of the proposed estimators are established for both models. Simulation studies demonstrate that the proposed inference procedures perform well for both models. The analyses of a bladder tumor data are presented to illustrate the proposed methods. Furthermore, it would be desirable to develop estimation procedures for panel count data with informative observation times, and also with time-dependent covariates and informative censoring times. Thus we extend the joint frailty models proposed by Zhao and Tong (2011) to panel count data with the time-dependent covariates and informative observation and censoring times. A novel estimating equation approach that does not depend on the distribution of frailty variables and the link function is proposed for estimation of parameters, and the asymptotic properties of the proposed estimators are established. The performance of proposed inference procedure are demonstrated by some simulation studies and illustrated by the analysis of a bladder tumor data.