Abstract

Multi-state models are widely used in event history analysis. Often the state of the process is only known at a set of discrete, potentially unequally spaced and subject specific, examination times leading to panel data. Most analyses for panel data assume a Markov model, but we may instead wish to allow the transition intensities to depend on the time spent in the current state leading to a semi-Markov model. The likelihood for general semi-Markov models is somewhat intractable. This talk focuses on semi-Markov models with phase-type sojourn distributions which allow an aggregated (or hidden) Markov representation making computation simpler. Two main approaches can be considered. Firstly, the states in the model can be assumed to have phase-type distributions directly [1]. Alternatively, phase-type distributions approximations to parametric distributions can be used to build an approximate likelihood for Weibull or Gamma semi-Markov models [2]. In either case, the addition of misclassification of the disease states can be incorporated relatively easily. The methods are illustrated on chronic disease data from post-lung-transplantation patients.

[1] Titman A.C., Sharples L.D. Semi-Markov models with phase-type sojourn distributions. Biometrics. 2010. 66 (3): 742-752. [2] Titman A.C. Estimating parametric semi-Markov models from panel data using phase-type approximations. Statistics and Computing. 2012. Online First.