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Title: A piecewise Weibull survival model for the analysis of breast cancer subject to endogenous and exogenous factors Authors:  Juan Eloy Ruiz-Castro - University of Granada (Spain)
Mariangela Zenga - Universita degli Studi di Milano-Bicocca -DISMEQ (Italy) [presenting]
Abstract: Markov processes are considered in the survival literature to model the evolution of illnesses by time. In this field, the homogeneity is a usual premise but sometimes it is a very strong constraint which can lead to an erroneous modeling. In this way the non-homogeneity arises in a natural way, since the transition probabilities between two any states are not constant by time generally. A general piecewise non-homogeneous Markov model is developed and it is considered to study the evolution of breast cancer. Multiple cutpoints are considered and discrete weibull distributions are included in the model. The model is built and interesting measures calculated. The effect of treatments, menopausal state and number of infected axillary glands are incorporated as time-depending covariates. Thus, we have a multi-state model with multidimensional covariates. The results are compared with the empirical and homogeneous cases for several risk groups. Implementations in Matlab and R are provided.