Semiparametric marginal mean models for multivariate counting processes

Data of multiple-type recurrent events are routinely collected in longitudinal medical studies. Examples include multiple-type infections among patients after stem cell transplantation and recurrent wheezing and cough among patients with bronchial asthma. In this dissertation, we studied (1) nonparametric mean model for one-type recurrent events; (2) semiparametric regression models for marginal means of one-type recurrent events; (3) semiparametric regression models for marginal means of two-type recurrent events.; One-type recurrent events can be simply modeled as univariate counting process. The estimation methods for both non- and semi-parametric models for the means of recurrent events are derived from a simple nonhomogeneous Poisson process assumption. The large sample properties are established under a general probability assumption for the counting process.; The idea is extended to two-type recurrent events which can be modeled as bivariate counting processes. The two-type recurrent events may be correlated over time. A relatively simple estimation procedure for semiparametric marginal mean models is proposed. To derive this estimation procedure, we model explicitly the dependence between the two types of recurrent events via an analytically tractable Gamma frailty bivariate Poisson process. To allow robust inference, large sample properties are investigated under a general underlying probability distribution for the bivariate point process which may be beyond the assumed model. This complicates the technical matters: the usual martingale methods for counting process are no longer valid. We apply the general theory of modern empirical process to establish the consistency and weak convergence properties. Small sample properties are studied using Monte-Carlo simulations. We show that our estimators are relatively efficient compared to the method that analyzes the two types of recurrent events independently. We illustrate our method with the recurrent wheeze and cough data collected in a clinical trial for bronchial asthmatic patients and data for multiple-type infections after bone marrow stem cell transplantation.