Flowgraph Models for Generalized Phase Type Distributions Having Non‐Exponential Waiting Times

Aparna V. Huzurbazar

Scandinavian Journal of Statistics, 1999, vol. 26, issue 1, 145-157

Abstract: ABSTRACT. Aalen (1995) introduced phase type distributions based on Markov processes for modelling disease progression in survival analysis. For tractability and to maintain the Markov property, these use exponential waiting times for transitions between states. This article extends the work of Aalen (1995) by generalizing these models to semi‐Markov processes with non‐exponential waiting times. The generalization allows more realistic modelling of the stages of a disease where the Markov property and exponential waiting times may not hold. Flowgraph models are introduced to provide a closed form for the distributions in situations involving non‐exponential waiting times. Flowgraph models work where traditional methods of stochastic processes are intractable. Saddlepoint approximations are used in the analysis. Together, generalized phase type distributions, flowgraphs, and saddlepoint approximations create exciting and innovative prospects for the analysis of survival data.

Date: 1999
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