A piecewise Markov process for analysing survival from breast cancer in different risk groups

A study of the relapse and survival times for 300 breast cancer patients submitted to post-surgical treatments is presented. After surgery, these patients were given three treatments: chemotherapy; radiotherapy; hormonal therapy and a combination of them. From the data set, a non-homogeneous Markov model is selected as suitable for the evolution of the disease. The model is applied considering two time periods during the observation of the cohort where the disease is well differentiated with respect to death and relapse. The effect of the treatments on the patients is introduced into the model via the transition intensity functions. A piecewise Markov process is applied, the likelihood function is built and the parameters are estimated, following a parametric methodological procedure. As a consequence, a survival table for different treatments is given, and survival functions for different treatments are plotted and compared with the corresponding empirical survival function. The fit of the different curves is good, and predictions can be made on the survival probabilities to post-surgical treatments for different risk groups.