Flowgraph models for generalized phase type distributions having non-exponential waiting times

Aalen (1995) introduced phase type distributions based on Markov processes for modelling disease progression in survival analysis. For tractability an d to maintain the Markov property, these use exponential waiting times for transitions between states. This article extends the work of Aalen (1995) b y generalizing these models to semi-Markov professes with non-exponential w aiting times, The generalization allows more realistic modelling of the sta ges of a disease where the Markov property and exponential waiting times ma y not hold, Flowgraph models are introduced to provide a closed form for th e distributions in situations involving non-exponential waiting times. Flow graph models work where traditional methods of stochastic processes are int ractable. Saddlepoint approximations are used in the analysis. Together, ge neralized phase type distributions, flowgraphs, and saddlepoint approximati ons create exciting and innovative prospects for the analysis of survival d ata.