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Consider a finite-state, time-continuous, homogeneous Markov chain with an absorbing state. The time to absorption in such a state is said to have a phase-type distribution. Markov models are useful because they may incorporate an understanding of how a phenomenon, for example, a disease, moves through different stages. However, for tractability and to maintain the Markov property, the stages are modeled with exponential waiting times. Aalen[1] introduced such phase-type distributions based on Markov processes for modeling disease progression in survival analysis. Huzurbazar[2] extended this work by generalizing these models to semi-Markov processes with nonexponential waiting times, called generalized phase-type distributions. The generalization allows more realistic modeling of the stages of the disease where the Markov property and exponential waiting times may not hold. Flowgraph models are used to provide a closed-form solution for the distributions in situations where involving nonexponential waiting times. Flowgraph models are a tool that aid in the analysis of semi-Markov processes. Densities and hazard rates of phase-type distributions can be calculated from standard Markov chain theory. Keywords: survival analysis; flowgraph model; hazard rate; Markov chain; quasi-stationarity; multistate model |
