We consider a Semi-Markov Process (SMP) to model the evolution of bladder cancer, which takes different states over time. A multi-state model has been constructed and applied to data collected from 847 patients during a period of fifteen years. Biomedicine databases usually contain censored data and this study shows that, despite this, a good fit of the main survival measures is achieved by using our specific model. This paper aims to present estimators for the semi-Markov kernel, the survival function and the mean time to disease progression. The strong consistency properties of the estimators are proved.