Flexible Nonhomogeneous Markov Models for Panel Observed Data
Article first published online: 9 FEB 2011
© 2011, The International Biometric Society
Volume 67, Issue 3, pages 780–787, September 2011
How to Cite
Titman, A. C. (2011), Flexible Nonhomogeneous Markov Models for Panel Observed Data. Biometrics, 67: 780–787. doi: 10.1111/j.1541-0420.2010.01550.x
- Issue published online: 14 SEP 2011
- Article first published online: 9 FEB 2011
- Received April 2010. Revised November 2010. Accepted November 2010.
- Differential equations;
- Multi-state model;
- Nonhomogeneous Markov model;
- Panel observation
Summary Methods for fitting nonhomogeneous Markov models to panel-observed data using direct numerical solution to the Kolmogorov Forward equations are developed. Nonhomogeneous Markov models occur most commonly when baseline transition intensities depend on calendar time, but may also occur with deterministic time-dependent covariates such as age. We propose transition intensities based on B-splines as a smooth alternative to piecewise constant intensities and also as a generalization of time transformation models. An expansion of the system of differential equations allows first derivatives of the likelihood to be obtained, which can be used in a Fisher scoring algorithm for maximum likelihood estimation. The method is evaluated through a small simulation study and demonstrated on data relating to the development of cardiac allograft vasculopathy in posttransplantation patients.