This research was motivated by a clinical trial with bladder cancer patients who went through a surgery and were followed up for cancer recurrence. One of the main objectives of the trial was to evaluate the time to cancer recurrence in patients in control and experimental groups. At the time of recurrence, the disease stage was also evaluated. Because the stage of cancer at recurrence significantly impacts future treatment and patient prognosis of survival, analyzing the time to cancer recurrence and the stage at recurrence jointly provides more clinically relevant information than analyzing the time to recurrence alone. In this paper, we propose a stochastic model for the joint distribution of time to recurrence and cancer stage that (1) accounts for the recurrence caused by cancer cells surviving a treatment or a surgery and for the recurrence caused by spontaneous carcinogenesis, and (2) incorporates parameters that have biological meaning. To estimate the parameters, we use the maximum-likelihood method combined with the EM algorithm. To demonstrate the performance of our modeling, we evaluate the data from a clinical trial in patients with bladder cancer. We also use simulations to assess the sensitivity of the method.