A Multiple-Absorbent Markov Process in Survival Studies: Application to Breast Cancer

A Markov process with several absorbent states is applied for analyzing a breast cancer dataset. The study examines the evolution of patients until death, and shows that two well-differentiated ways can be considered in the evolution of patients towards the death state: those who relapse and those who not. The risk groups we have considered are determined by the application of treatments radiotherapy and chemotherapy, which are introduced as covariates. Four states are distinguished: no relapse, relapse, death after metastasis, and death without metastasis, the last two absorbent. We apply a methodology that uses algorithmic procedures, avoiding differential equations. The transition probability functions and the likelihood function in the model are calculated. For the dataset, the survival functions and the mean times in states for the different group of risks are determined. We show that the metastasis is the main cause of death in this cohort, but the number of deaths by relapse is not negligible.