Nonparametric and semiparametric models for multivariate panel count data

Multivariate panel count data arise when multiple types of recurrent events are under investigation and each study subject is examined only at discrete random time points. The data consist only of event counts that have occurred prior to the observation times, while the exact event times are unknown. This type of data is often seen in clinical, health expenditure, reliability, and demographic studies. In this thesis, we introduce frailty variables to account for the subject heterogeneity and the correlation between processes. We propose nonparametric and semiparametric frailty models of mean functions of the counting processes for bivariate panel count data.;In the nonparametric models, given a frailty variable gamma, the underlying bivariate counting process is assumed to consist of two independent nonhomogeneous Poisson processes with the conditional mean functions given by E[ Np(t)|Z,gamma] = gammaLambda p0(t), p ∈ {1, 2}. We propose estimators of the baseline mean functions based on the isotonic regression estimators and a statistic in order to test the equality of the mean functions between different groups.;In addition, with the presence of the vector of baseline covariate Z, the underlying bivariate counting process is assumed to consist of two independent nonhomogeneous Poisson processes with the conditional mean functions given by E[Np(t)| Z, gamma] = gammaLambdap0 (t) exp(beta'p0 Z), p ∈ {1, 2}. The semiparametric methods provide both model-based inference of the covariates and the nonparametric inference of baseline mean functions for the bivariate counting process.;The methods are illustrated via a analysis of data from a cancer chemoprevention trial conducted by the University of Wisconsin Comprehensive Cancer Center in Madison, Wisconsin, on the effectiveness of difluoromethylornithine in preventing non-melanoma skin cancer in the population with previous skin cancer.;Both nonparametric and semiparametric models with consideration of frailty are useful tools to describe the natural history of multiple disease processes via the mean functions and enable us to evaluate efficiently the effects of explanatory factors. The methods can be applied to clinical and epidemiological studies of patients with different type of metastatic lesions, AIDS patients with multiple repeated medical conditions, recurrent medical conditions of the right/left eye or the right/left kidney and patients with multiple types of recurrent superficial bladder cancer.