Multivariate Survival Analysis (II): An Overview of Multi-State Models in Biomedicine and Engineering Reliability

In this article, we review one of the two major models in multivariate survival analysis, the multi- state model (the other is the shared frailty model). Just like the whole multivariate survival analysis (MSA) subject, this category of models has been advanced mainly in biomedical research and is still in the development stage. Since similar models based on Markov chains have been widely used in engineering reliability, we try to put this review in the perspective of both biomedicine and engineering reliability, but with a focus on biomedicine applications. Although it is concise due to page limit, this overview covers the whole spectrum of multi-state modeling evolution, from progressive models, homogenous Markov process, general Markov process, Markov extensions (non-Markov) to the general multi-state modeling. There is a very encouraging notion that it is possible to estimate transition hazards and probabilities via non- or semi-parametric approaches, even if the model is formulated as non-Markov general multi-state models. In addition, we also briefly discuss the flow-graph model, which provides a powerful tool to analyze multi-state time-to-event data expressed with semi- Markov models.