The dependence between two random variables is completely described by their bivariate distribution. Bivariate survival analysis arises in the time to events analysis of measurements that are paired. Although, there are several consistent estimators of the bivariate distribution function, an efficient and consistent estimation has proven to be a difficult problem. It is of interest to determine if it exists, the possible association between pairs of variables, both of which are subject to censoring with recurrence times of kidney infection as a case study. Copula models which is one of the existing methods of measuring the possible association between bivariate censored variables were reviewed. The overall average recurrence time and its standard deviation are 102 and 131, respectively though the recurrence time in the first kidney has average and standard deviation of 112 and 144.01, respectively while the average and standard deviation of recurrence time in the second kidney recurrence time is 92 and 117.20, respectively. The study also showed that the modal recurrence time in the 2 kidneys is 42. The correlation between infection recurrence in the pairs of kidneys was found to be 0.268 with 95% confidential interval of (-0.1854985, 0.7206918).