Three state markov model: Comparing three parameterizations of the transition intensity rate. Application to rheumatoid arthritis data

Juan Carlos Salazar, René Iral Palomino, Enrique Calvo, Adriana Rojas, María Eugenia Hincapié, Juan Manuel Anaya, Francisco Javier Díaz

Resultado de la investigación: Contribución a RevistaArtículo

Resumen

We consider a three state model with an absorbing state assuming an underlying Markov process to explain the dependence among observations within subjects. We compare, using a simulation study, three different parameterizations of the transition intensity rate: the first one is based on the Andersen-Gill's multiplicative hazard model (Andersen et al. 1993), the second one is based on the logistic model, and the third one depends on the complementary log-log model. The method to estimate the effect of the parameters is based on the likelihood function which can be optimized using the exact solutions of a Kolmogorov forward differential equations system in conjunction with the Newton-Raphson algorithm (Abramowitz & Stegun 1972). We use the relative bias to select the best estimation estrategy. The methodology is ilustrated using longitudinal data about rheumatoid arthritis (RA) from the Corporación para Investigaciones Biológicas, CIB.
Idioma originalEnglish (US)
Páginas (desde-hasta)213-229
Número de páginas17
PublicaciónRevista Colombiana de Estadistica
EstadoPublished - dic 1 2007

Huella dactilar

Rheumatoid Arthritis
Parameterization
Markov Model
Newton-Raphson Algorithm
Multiplicative Model
Hazard Models
Logistic Model
Longitudinal Data
Likelihood Function
Absorbing
Markov Process
Exact Solution
Simulation Study
Differential equation
Methodology
Model
Estimate
Observation

Citar esto

Salazar, Juan Carlos ; Palomino, René Iral ; Calvo, Enrique ; Rojas, Adriana ; Hincapié, María Eugenia ; Anaya, Juan Manuel ; Díaz, Francisco Javier. / Three state markov model: Comparing three parameterizations of the transition intensity rate. Application to rheumatoid arthritis data. En: Revista Colombiana de Estadistica. 2007 ; pp. 213-229.
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abstract = "We consider a three state model with an absorbing state assuming an underlying Markov process to explain the dependence among observations within subjects. We compare, using a simulation study, three different parameterizations of the transition intensity rate: the first one is based on the Andersen-Gill's multiplicative hazard model (Andersen et al. 1993), the second one is based on the logistic model, and the third one depends on the complementary log-log model. The method to estimate the effect of the parameters is based on the likelihood function which can be optimized using the exact solutions of a Kolmogorov forward differential equations system in conjunction with the Newton-Raphson algorithm (Abramowitz & Stegun 1972). We use the relative bias to select the best estimation estrategy. The methodology is ilustrated using longitudinal data about rheumatoid arthritis (RA) from the Corporaci{\'o}n para Investigaciones Biol{\'o}gicas, CIB.",
author = "Salazar, {Juan Carlos} and Palomino, {Ren{\'e} Iral} and Enrique Calvo and Adriana Rojas and Hincapi{\'e}, {Mar{\'i}a Eugenia} and Anaya, {Juan Manuel} and D{\'i}az, {Francisco Javier}",
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Three state markov model: Comparing three parameterizations of the transition intensity rate. Application to rheumatoid arthritis data. / Salazar, Juan Carlos; Palomino, René Iral; Calvo, Enrique; Rojas, Adriana; Hincapié, María Eugenia; Anaya, Juan Manuel; Díaz, Francisco Javier.

En: Revista Colombiana de Estadistica, 01.12.2007, p. 213-229.

Resultado de la investigación: Contribución a RevistaArtículo

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AU - Hincapié, María Eugenia

AU - Anaya, Juan Manuel

AU - Díaz, Francisco Javier

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AB - We consider a three state model with an absorbing state assuming an underlying Markov process to explain the dependence among observations within subjects. We compare, using a simulation study, three different parameterizations of the transition intensity rate: the first one is based on the Andersen-Gill's multiplicative hazard model (Andersen et al. 1993), the second one is based on the logistic model, and the third one depends on the complementary log-log model. The method to estimate the effect of the parameters is based on the likelihood function which can be optimized using the exact solutions of a Kolmogorov forward differential equations system in conjunction with the Newton-Raphson algorithm (Abramowitz & Stegun 1972). We use the relative bias to select the best estimation estrategy. The methodology is ilustrated using longitudinal data about rheumatoid arthritis (RA) from the Corporación para Investigaciones Biológicas, CIB.

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JO - Revista Colombiana de Estadistica

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