Enfoque bayesiano para obtener las tasas de transición en un modelo de estados múltiples. Aplicación a datos sobre artritis reumatoide
Bayesian approach for obtaining the transition rates in a multi-state model. Application to Reumathoid Arthritis data
Abstract (en)
Multi-state models have shown to be useful to analize longitudinal data, especially those involving information about the progression of a disease through time. On the other hand, bayesian methods are useful in highly complex situations where Monte Carlo Marco Chain based techniques are used. In this work, a bayesian method for obtaining the transition rates that govern a three state model with first orden markovian structure is implemented. These transition rates are linked to the covariates by means of a Andersen-Gill type model. In this way, the optimal estimation of the covariates effects will improve the estimated values of the transition rates. This bayesian technique based on the Gibbs sampler is compared, using a simulation study, both with a technique proposed by Iral and Salazar and a method based on the discretization of the domain of the posterior distribution. Finallly, these techniques are ilustrated using real data about Rheumatoid Arthritis collected in Colombian patients.
Abstract (es)
Los modelos de estados múltiples han demostrado ser de utilidad para el análisis de datos longitudinales, particularmente aquellos que involucran información acerca de la progresión de una enfermedad a través del tiempo. Por otra parte, los métodos bayesianos son útiles en situaciones de alta complejidad cuando se usan técnicas como Monte Carlo Markov Chain. En este trabajo se implementa un método bayesiano basado en el muestreador de Gibbs con el fin de obtener las tasas de transición que gobiernan un modelo de tres estados con estructura markoviana de primer orden. Estas tasas de transición se vinculan con las covariables por medio de un modelo del tipo Andersen-Gill. De esta manera, la estimación óptima de los efectos de las covariables permitirá obtener mejores estimaciones de las tasas de transición. Esta técnica bayesiana se compara vía simulación con la técnica de estimación estudiada por Iral & Salazar (2007) y con un método basado en la discretización del soporte de la distribución posterior. Finalmente, estas técnicas de estimación se ilustran usando datos reales sobre pacientes colombianos con artritis reumatoide.
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