Abstract
Recurrent event data are frequently observed in many longitudinal and clinical studies. In the literature, various methods have been proposed to analyze covariate effects on the occurrence rate of a recurrent event, yet these methods usually require the assumption of independent censoring and accurately measured covariates. However, in many real data applications, informative censoring occurs when the recurrent event process is stopped by some terminal events that are related to the recurrent event (e.g. death). Additionally, the covariates could be measured with errors and need to be corrected. In this doctoral dissertation, we develop semi-parametric estimation to deal with informative censoring and measurement errors for recurrent event data. This dissertation contains two works. In the first work, we propose two approaches to estimate regression parameters for univariate recurrent event data in the presence of informative censoring and measurement errors. Explicitly, we impose a shared frailty model on the intensity function of a Poisson process to characterize the informative censoring and the dependence of the events within a subject without specifying the frailty distribution. To estimate the regression parameters, a regression calibration method and a moment corrected method are proposed for adjusting measurement errors. Both methods are referred to as the parametric correction because they assume that the underlying covariates and error terms are normally distributed. Moreover, the replicated data is needed to estimate the measurement error variance. In the second work, we extend the first work to accommodate informative censoring and measurement errors in multivariate recurrent event data, in which more than one type of events is of interest. Also, we consider a situation that a surrogate is available for all subjects but an instrumental variable is obtained only for a fraction of subjects. No replicated data or a validation set is available. To formulate the dependence of the informative censoring on the recurrent event processes, a shared frailty model is imposed on the rate function for each type of recurrent event, where the frailty distribution is unspecified. The shared frailty model also characterizes the association among different types of recurrent events. For regression parameter estimation, we first construct a simple correction approach, in which only subjects with an observed instrumental variable are involved in the estimation. To gain the efficiency of the simple correction estimator, we further develop a new correction approach to incorporate the information from the whole cohort. Distinct from the approaches in our first work, the approaches in the second work require neither the assumption of a Poisson process nor the distributional assumption of the underlying covariates and measurement errors. The asymptotic properties of the four proposed estimators are established. The performance of all proposed methods is investigated through simulation studies. We illustrate the proposed methods with the Nutritional Prevention of Cancer data, which aims to assess the effect of plasma selenium supplement on recurrences of squamous cell carcinoma and basal cell carcinoma.