Semiparametric Analysis of Multivariate Panel Count Data with an Informative Observation Process

Abstract

Panel count data and recurrent event data often arise in event history studies. Unlike recurrent event data which are collected from studies that monitor subjects continuously, panel count data are encountered when subjects are observed only at discrete time points. In such case, the exact occurrence times of the events are unknown, but only the numbers of occurrences of the events between subsequent observation time points are recorded. Statistical analysis of panel count data have been studied based on two stochastic processes: an observation process and a response process that characterizes the occurrences of the events of interest.The first part of the dissertation will present a likelihood-based joint modeling procedure for the regression analysis of univariate panel count data with dependent observation equations and time processes. The inference procedure involves estimating equations and an EM algorithm for the estimation of all involved parameters. In the second part, we will extend the proposed methods to multivariate panel count data, which occurs when a recurrent event study involves several related types of recurrent events. In particular, we will present three types of multivariate modeling scenarios and the corresponding inference procedures. A model checking procedure is developed for the proposed univariate models and all three types of multivariate models. Simulation studies indicate that the proposed inference procedures have a good and consistent performance across various situations. The proposed methods are applied to a skin cancer study with bivariate panel count data on the occurrences of two types of related non-melanoma skin cancers.