Non-homogeneous Markov processes for biomedical data analysis

Some time ago, the Markov processes were introduced in biomedical sciences in order to study disease history events. Homogeneous and Non-homogeneous Markov processes are an important field of research into stochastic processes, especially when exact transition times are unknown and interval-censored observations are present in the analysis. Non-homogeneous Markov process should be used when the homogeneous assumption is too strong. However these sorts of models increase the complexity of the analysis and standard software is limited. In this paper, some methods for fitting non-homogeneous Markov models are reviewed and an algorithm is proposed for biomedical data analysis. The method has been applied to analyse breast cancer data. Specific software for this purpose has been implemented.