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Flexible nonhomogeneous Markov models for panel observed data.

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Flexible nonhomogeneous Markov models for panel observed data. / Titman, Andrew C.
In: Biometrics, Vol. 67, No. 3, 09.2011, p. 780-787.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Titman AC. Flexible nonhomogeneous Markov models for panel observed data. Biometrics. 2011 Sept;67(3):780-787. doi: 10.1111/j.1541-0420.2010.01550.x

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Titman, Andrew C. / Flexible nonhomogeneous Markov models for panel observed data. In: Biometrics. 2011 ; Vol. 67, No. 3. pp. 780-787.

Bibtex

@article{6d5860b1979a41ae89f394586c3ca290,
title = "Flexible nonhomogeneous Markov models for panel observed data.",
abstract = "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 post-transplantation patients.",
keywords = "B-splines, Differential equations, Multi-state model, Nonhomogeneous Markov model, Panel observation",
author = "Titman, {Andrew C.}",
year = "2011",
month = sep,
doi = "10.1111/j.1541-0420.2010.01550.x",
language = "English",
volume = "67",
pages = "780--787",
journal = "Biometrics",
issn = "1541-0420",
publisher = "Wiley-Blackwell",
number = "3",

}

RIS

TY - JOUR

T1 - Flexible nonhomogeneous Markov models for panel observed data.

AU - Titman, Andrew C.

PY - 2011/9

Y1 - 2011/9

N2 - 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 post-transplantation patients.

AB - 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 post-transplantation patients.

KW - B-splines

KW - Differential equations

KW - Multi-state model

KW - Nonhomogeneous Markov model

KW - Panel observation

U2 - 10.1111/j.1541-0420.2010.01550.x

DO - 10.1111/j.1541-0420.2010.01550.x

M3 - Journal article

VL - 67

SP - 780

EP - 787

JO - Biometrics

JF - Biometrics

SN - 1541-0420

IS - 3

ER -