Statistical Modeling And Analysis Of Clustered Recurrent Event Data

In this thesis, we mainly deal with statistical analysis of the clustered recurrent event data.Firstly, recurrent event data often arise in biomedical studies, and individuals within a cluster might not be independent. We propose a scmiparamctric additive rates model for clustered recurrent event data, wherein the covariatcs arc assumed to add to the unspecified baseline rate. For the inference on the model parame-ters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established. We asses the finite sample properties of the proposed estimators through simulation studies. The simulation results perform well for the proposed estimation procedures.Secondly, we propose a class of semiparamctric additive-multiplicative rates mod-els for clustered recurrent event data, which allows some covariate effects to be ad-ditive while others to be multiplicative. For the inference on the model parameters, estimating equation approaches are developed. Based on modern empirical process theory, the consistency and asymptotic normality of the proposed estimators arc established.Thirdly, scmiparamctric marginal transformation models are a class of scmi-paramctric models, which include the scmiparamctric additive model and the scmi-paramctric multiplicative rates models. A class of scmiparametric marginal trans-formation models of clustered recurrent event data is proposed. For the inference on the unknown model parameter and nonparamctric function, generalized estimat-ing equation methods are developed. Based on modern empirical process theory, the consistency and asymptotic normality properties of the proposed estimators arc proved.Fourthly, we present a natural extension of accelerated failure time model for survival data to formulate the effects of eovariates on the mean function of the count-ing process for clustered recurrent event data. In the proposed model, the covariatc is to accelerate or decelerate the time to each recurrence. For the inference on the unknown model parameter, generalized estimating equation methods arc developed. Based on modern empirical process theory, the consistency and asymptotic normality properties of the proposed estimators arc proved.