A Multivariate Model to Measure the Effect of Treatments in Survival to Breast Cancer

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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