Multistate Models, Flowgraph Models, and Semi-Markov Processes
Abstract Semi-Markov models play an important role in the analysis of time to event data. However, in practice, data analysis for semi-Markov processes can be quite difficult and many simplifying assumptions are made. Markovian multistate models are popular for event history analysis and repeated events analysis for survival data. Semi-Markov processes provide a rich class of models applicable to this area. Flowgraph models provide a link between traditional multistate models and semi-Markov processes. Flowgraphs model semi-Markov processes and provide a data analytic method for estimating densities, survivor and reliability functions, and hazard functions for waiting times of interest in the presence of censored and incomplete data. While multistate models have been used primarily in medical research, flowgraph models are useful for time to event data arising from a variety of problems in many areas including engineering, medicine, operations research, and demography.