In this dissertation, we aim to develop a brand new method with a two-stage procedure to investigate the association between multivariate recurrent event processes. First, under the assumption of independent censoring, we model each recurrent event process marginally through a mean rate model. There are two popular mean rate assumptions - multiplicative or additive to an unspecified baseline rate function. The robust semi-parametric approaches can be applied to estimate the covariate effects as well as the baseline rate function.Second, inspired by Kendall\textsc{\char13}s tau, we propose the rate ratio as an association measurement, which is the quotient of two conditional rates - the mean rate of two joint events over the marginal rates, both conditional on the covariates. Utilizing the information from the first stage, an unbiased and consistent estimator of the rate ratio is developed under the Generalized Estimation Equation method. The asymptotic properties of the rate ratio estimators are derived theoretically. Without modeling the joint events directly, the rate ratio can measure the association between two recurrent processes over time.Since the rate ratio we proposed can be parametric, time and covariate dependent, it has good interpretability. We developed a formal hypothesis testing procedure to validate the parametric assumption of the rate ratio. Simulation studies show it is quite powerful under moderate to a strong association. The proposed method is applied to the hemodialysis (HEMO) Study. Patients enrolled in HEMO study depend on blood dialysis or transplant surgery to continue their lives and experienced prevalent comorbidities such as diabetes, cardiovascular diseases, and infections. To increase the expected lifespan of patients, it is vital for us to understand the associations among these comorbidities. Our study finds that the dependence between cardiac and infectious hospitalization recurrences for patients in the HEMO study was not constant over time and was significantly positively related to the difference of recurring times. We also find a strong association between past-current cardiac hospitalizations: patients who have experienced cardiac hospitalizations have increased risk of cardiac hospitalizations than those who have not.