Estimating Non-homogeneous Intensity Matrices in Continuous Time Multi-state Markov Models

Multi-State-Markov (MSM) models can be used to characterize the behaviour of categorical outcomes measured repeatedly over time. Kalbfleisch and Lawless (1985) and Gentleman et al. (1994) examine the MSM model under the assumption of time-homogeneous transition intensities. In the context of non-homogeneous intensities, current methods use piecewise constant approximations which are less than ideal. We propose a local likelihood method, based on Tibshirani and Hastie (1987) and Loader (1996), to estimate the transition intensities as continuous functions of time. In particular the local EM algorithm suggested by Betensky et al. (1999) is employed to estimate the in-homogeneous intensities in the presence of missing data. A simulation comparing the piecewise constant method with the local EM method is examined using two different sets of underlying intensities. In addition, model assessment tools such as bandwidth selection, grid size selection, and bootstrapped percentile intervals are examined. Lastly, the method is applied to an HIV data set to examine the intensities with regard to depression scores. Although computationally intensive, it appears that this method is viable for estimating non-homogeneous intensities and outperforms existing methods.

Department dc:contributor.department

Dalla Lana School of Public Health

Year dc:date.issued

2011

Author dc:creator

• Lebovic, Gerald

Advisor dc:contributor.advisor

• Tomlinson, George

• Biostatistics
• Multi State Models
• Ordinal Data

Statement dc:rights

• Attribution 3.0 Unported

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/3.0/

Language dc:language.iso

en_ca

Handle dc:identifier.uri

http://hdl.handle.net/1807/29786

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/29786