Regression Spline Applied In Panel Count Data

The purpose of this paper is to discuss the application of regression spline in panel count data.The first part is to discuss the nonparametric effect for the covariate and make statistical inference based on the estimator.The second part is to discuss the time-varying coefficient model in panel count data,and to discuss the theoretical properties for the estimatorsTo accommodate the potential non-linear covariate effect,we consider a nonpara-metric regression model for panel count data.The regression B-splines method is used to estimate the regression functions and the baseline mean function as well.The B-splines based estimation is shown to be consistent and the rate of convergence is obtained.More-over,the asymptotic normality for a class of smooth functionals of regression splines estimators is also established.Simulation studies are carried out to evaluate the finite sample properties.Finally,we apply the proposed method to analyze the non-linear effect of one of interleukin functions Interleukin 5 for the childhood wheezing studyOn the other hand,the covariate effect often depends on the time.How to fit a time-varying coefficient for panel count model is also our interesst.Especially for the risks of childhood wheezing.Therefore we describe a nonparametric time-varying coeffi-cient model for the analysis of panel count data.We extend the traditional panel count data models by incorporating B-spline estimates of the baseline hazard and time-varying coefficients.We show that the proposed model can be fitted using a nonparametric max-imum pseudo-likelihood method.We further examine the theoretical properties of the estimators of model parameters.The operational characteristics of the proposed method are evaluated through a carefully designed simulation study.For illustration,we ana-lyze data from a study of childhood wheezing,and describe the time-varying effect of an inflammatory marker on the risk of wheezing.