The Studies On Robust Estimation Of Panel Count Data

Panel count data are generated from studies that concern recurrent events or event history studies in which the subjects are observed only at specific points in time.This type data occur in various fields including medical research,insurance studies,reliability and tumorigenicity experiences.Recently,research on panel count data has drawn considerable attention.However,these methods are sensitive to outliers and literature on robust estimation of panel count data has so far been quite limited.The purpose of this thesis is to discuss some robust estimation of panel count data.The content of this thesis is as follows(1)A robust variable selection approach based on the quantile regression function in a joint frailty model is proposed to analyze panel count data.A three-step estimation method is introduced to estimate the coefficients and unknown functions.In the first step,the observation process is estimated by a nonparametric estimation for the baseline function and penalized estimation for the covariates.In the second step,an EM algorithm and penalized estimation are used for the follow-up process.In the third step,a robust variable selection method based on the quantile regression function is developed for the recurrent event process.As panel count data are discrete,a smoothing technique is used to get the continization of the data.Then a spline basis expansion is applied to approximate the unknown baseline function.Finally,a penalized estimation based on quantile regression is proposed to estimate the parameters of interest.Consistency and Oracle properties are established under some mild regularity conditions.Simulations are used to assess the proposed estimation method.Bladder cancer data are also re-analyzed as an illustration(2)A semiparametric partially linear varying coefficient model of the panel count data with informative observation times is developed to accommodate the nonlinear interact effects between covariates.For statistical inference of the unknown parameters,quantile regression approaches are proposed,in which the baseline function and the varying coefficients are approximated by B-spline basis functions.Moreover,asymptotic properties for the estimators are established.Some numerical studies are performed to confirm and evaluate the finite-sample behaviors of the proposed method.Finally,the proposed model and method are applied to the bladder cancer data as an application(3)By incorporating the correlation within subjects,we applied the tool of quantile regression for the time-varying coefficient panel count data model on the basis of quadratic inference functions.The proposed procedure can easily take into account the correlation within subjects and yield a more efficient estimator even when the working correlation is misspecified.An efficient nonparametric hypothesis testing is also proposed to test whether coefficient functions are time varying or time invariant.Asymptotic results of the estimators are established under some regularity conditions.Some simulation studies are carried out to confirm and evaluate the finite-sample behaviors of the proposed method and to compare the estimation efficiency.Finally,a real dataset from a bladder cancer study is re-analyzed by the proposed method(4)The observation process may be correlated with the panel count data.A more general panel count data model with dependent observation process is proposed.Penalized composite quantile regression(CQR)is developed for the proposed panel count data model.Consistency and Oracle properties are established under some mild regularity conditions.Some numerical simulations are carried out to confirm and assess the performance of the proposed model and approach,and an example from the blander cancer study is also providedThe innovations of the achievements in this thesis are described as following.Firstly,we develop a robust variable selection approach based on the quantile regression function in a joint frailty panel count data model,which further enrich the robust estimation for panel count data.Secondly,we consider the quantile estimation of a semiparametric partially linear varying coefficient panel count data model with informative observation times and the proposed method has good robustness and not sensitive to outliers.Thirdly,we take into account the correlation within subjects for the time-varying coefficient panel count data model and yield a more efficient estimator by quantile regression on the basis of quadratic inference functions.Fourthly,a more general panel count data model with dependent observation process is proposed and a penalized composite quantile regression is developed to get efficient estimation.