Non-homogeneous Markov models in the analysis of survival after breast cancer

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 consid ered: no relapse, relapse and death. As relapse times change over time. we have extended previous approaches for a time homogeneous model to a non-hom ogeneous multistate process. The trends of the hazard rate functions of tra nsitions between states increase and then decrease. showing that a changepo int can be considered. Piecewise Weibull distributions are introduced as tr ansition intensity functions. Covariates corresponding to treatments are in corporated in the model multiplicatively via these functions. The likelihoo d 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 pr obabilities for treatments in different periods of time are given. The surv ival probability functions for different treatments are plotted and compare d with the corresponding function for the homogeneous model. The survival f unctions for the various cohorts submitted for treatment are fitted to the empirical survival functions.