Abstract
Recurrent event data occurs in many disciplines such as actuarial science, biomedical studies, sociology, and environment to name a few. It is therefore important to develop models that describe the dynamic evolution of the event occurrences. One major problem of interest to researchers with these types of data is models for the distribution function of the time between events occurrences, especially in the presence of covariates that play a major role in having a better understanding of time to events. This work pertains to statistical inference of the regression parameter and the baseline hazard function in a Cox-type model for recurrent events that accounts for the effective age and time varying covariates. Estimators of the regression parameters as well as baseline hazard function are obtained using the counting processes and martingales machinery techniques. Asymptotic properties of the proposed estimators and how they can be used to construct confidence intervals are investigated. The results of the simulation studies assessing the performance of the estimators and an application to a biomedical dataset illustrating the models are presented. The impact of unit effective age is also assessed. To check the validity of the models used, many decision rules are developed for checking the validity of the various components of Cox-type model. Specifically, using martingales residuals, we proposed test statistics for checking the link function and the covariates functional form. Asymptotic properties of test statistics and simulation studies are presented as well