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Modeling nonhomogeneous Markov processes via time transformation.
Biometrics 2008; 64(3):843-50B

Abstract

Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.

Authors+Show Affiliations

Department of Biostatistics, University of Washington, Box 357232, Seattle, Washington 98195, USA. rhubb@u.washington.eduNo affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't

Language

eng

PubMed ID

18047532

Citation

Hubbard, R A., et al. "Modeling Nonhomogeneous Markov Processes Via Time Transformation." Biometrics, vol. 64, no. 3, 2008, pp. 843-50.
Hubbard RA, Inoue LY, Fann JR. Modeling nonhomogeneous Markov processes via time transformation. Biometrics. 2008;64(3):843-50.
Hubbard, R. A., Inoue, L. Y., & Fann, J. R. (2008). Modeling nonhomogeneous Markov processes via time transformation. Biometrics, 64(3), pp. 843-50.
Hubbard RA, Inoue LY, Fann JR. Modeling Nonhomogeneous Markov Processes Via Time Transformation. Biometrics. 2008;64(3):843-50. PubMed PMID: 18047532.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Modeling nonhomogeneous Markov processes via time transformation. AU - Hubbard,R A, AU - Inoue,L Y T, AU - Fann,J R, Y1 - 2007/11/19/ PY - 2007/12/1/pubmed PY - 2009/1/29/medline PY - 2007/12/1/entrez SP - 843 EP - 50 JF - Biometrics JO - Biometrics VL - 64 IS - 3 N2 - Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery. SN - 1541-0420 UR - https://www.unboundmedicine.com/medline/citation/18047532/Modeling_nonhomogeneous_Markov_processes_via_time_transformation_ L2 - https://doi.org/10.1111/j.1541-0420.2007.00932.x DB - PRIME DP - Unbound Medicine ER -