Title: General discrete non-homogeneous Markov models with multiple absorbing states: Application to breast cancer
Authors: Juan Eloy Ruiz-Castro - University of Granada (Spain) [presenting]
Mariangela Zenga - Universita degli Studi di Milano-Bicocca -DISMEQ (Italy)
Abstract: A general multi-state non-homogeneous Markov models have been built to analyze the behavior of an illness with several absorbing states. The evolution of a disease occurs in continuous time, but it is observed in discrete time from scheduled revisions or emergency situations. Thus, this analysis has been focused on discrete time. The model is built, covariates depending on time are introduced, the likelihood function for different cases and relevant measures, such as survival function, transition probabilities, mean total times and the conditional probability of state change are determined for different risk groups. Several non-homogeneous Markov models are estimated for analyzing the behavior of breast cancer from a cohort of mastectomized patients. Several discrete probability distributions, such as log-logistic and Weibull, are considered. Cut-points are introduced and they are estimated jointly with the parameters by maximum likelihood. The results are obtained in a matrix algebraic form and they were implemented computationally with MATLAB and R.