A cohort of 300 women with breast cancer who were submitted for surgery is analysed by using a non-homogeneous Markov process. Three states are considered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non-homogeneous multistate process. The trends of the hazard rate functions of transitions between states increase and then decrease, showing that a changepoint can be considered. Piecewise Weibull distributions are introduced as transition intensity functions. Covariates corresponding to treatments are incorporated in the model multiplicatively via these functions. The likelihood function is built for a general model with k changepoints and applied to the data set, the parameters are estimated and life-table and transition probabilities for treatments in different periods of time are given. The survival probability functions for different treatments are plotted and compared with the corresponding function for the homogeneous model. The survival functions for the various cohorts submitted for treatment are ®tted to the empirical survival functions.

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An homogeneous Markov process in continuous time with three states (no relapse, relapse, and death) to model the influence of treatments in relapse and survival times to breast cancer is considered. Different treatments such as chemotherapy, radiotherapy, and hormonal therapy, and combinations of these were applied to a cohort of 300 patients after surgery. All patients were seen longitudinally every month. The treatments are introduced as covariates by means of transition intensity, thus providing three covariates. The likelihood function is built from the data and the parameters estimated. Original computational programmes are constructed using the MATHEMATICA and MATLAB programmes, by means of which we estimate the parameters, calculate the transition probability functions, plot the graphs of the survival curves, and fit the survival curves to treatments obtained from the model with the corresponding empirical functions.

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