Statistical Analysis Of Panel Count Data Based On Several Classes Of Conditional Models

In recent years,with the development of biology,medical sciences and economics,the study of recurrent event process has made great progress,but we still need further studies in panel count data arising from recurrent event processes.This thesis mainly considers the influence of covariates,individual unobservable heterogeneity and dependent observation process to the recurrent event process,we propose the general rate model,mixed effects model and the semi-parametric model with propensity score weighting,which make it more reasonable to explain the recurrence event process.The main contributions of this thesis are as follows:1.According to the structural features of panel count data,under the assumption of nonhomogeneous poisson distribution,we present the general rate model suitable for panel count data,and the maximum likelihood estimation method is developed for the parameters.Through the asymptotic properties of the estimation,numerical simulation and a real bladder cancer data analysis show a conclusion that taking thiotepa can reduce the recurrence rate of bladder cancer effectively.2.Under the assumption of the parameter model,we consider the frailty which can reflect the individual heterogeneity,and establish the mixed effects model with random effect term and parametric components,and the maximum likelihood estimation method is developed for the parameters.The maximum likelihood estimates obtained under the mixed effects model are more stable than the model under ideal conditions by specific numerical simulation,and reduces the standard error of parameter estimation.3.We consider not only the influence of covariates on the recurrence event process and observation process,the influence of the dependent observation process on the recurrent event process,but also the influence of dependence between observation process and recurrence event process on the error of parameter estimation.Therefore,we use propensity score to reduce or even eliminate the confounding bias arising from the dependence of observation process on recurrent event process,and establish the semiparametric model with propensity score weighting to analyze the panel count data.Compared with the model without propensity score weighting,this model improves the efficiency of parameter estimation.We establish the inverse probability weighting estimating equation procedures to estimate the unknown parameters in this model and prove the large sample properties of the estimates.Under different assumptions,numerical simulations are conducted by MATLAB software to illustrate the finite sample performance and the rationality of these estimates.