Modeling bladder cancer using a Markov process with multiple absorbing states

The aim of this study is to analyze survival until extirpation in bladder carcinoma. For this it is necessary to study the different stages of this chronic disease: multiple recurrences and progression. The sum of two random independent variables is considered, each of them being associated with a homogeneous time-continuous Markovian process of multiple absorbing states. The distribution function of the variable sum is modeled by means of a new associated Markov process. In order to maintain manageable problem dimension we have applied the Fréchet derivate and the Kronecker matrix representation.