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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.1 Bogotá Jan./June 2020 Epub June 05, 2020
https://doi.org/10.15446/rce.v43n1.77851
ARTÍCULOS ORIGINALES DE INVESTIGACIÓN
A Birnbaum-Saunders Model for Joint Survival and Longitudinal Analysis of Congestive Heart Failure Data
Un modelo Birnbaum-Saunders para el análisis conjunto de datos de supervivencia y longitudinales de insuficiencia cardíaca congestive
1 Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá D.C., Colombia. PhD. E-mail: dcfrancos@unal.edu.co
2 Departamento de Estatística, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil. PhD. E-mail: acarlos@ime.usp.br
3 Departamento de Estatística, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil. PhD. E-mail: jmsinger@ime.usp.br
We consider a parametric joint modelling of longitudinal measurements and survival times, motivated by a study conducted at the Heart Institute (Incor), São Paulo, Brazil, with the objective of evaluating the impact of B-type Natriuretic Peptide (BNP) collected at different instants on the survival of patients with Congestive Heart Failure (CHF). We employ a linear mixed model for the longitudinal response and a Birnbaum-Saunders model for the survival times, allowing the inclusion of subjects without longitudinal observations. We derive maximum likelihood estimators of the joint model parameters and conduct a simulation study to compare the true survival probabilities with dynamic predictions obtained from the fit of the proposed joint model and to evaluate the performance of the method for estimating the model parameters. The proposed joint model is applied to the cohort of 1609 patients with CHF, of which 1080 have no BNP measurements. The parameter estimates and their standard errors obtained via: i) the traditional approach, where only individuals with at least one measurement of the longitudinal response are included and ii) the proposed approach, which includes survival information from all individuals, are compared with those obtained via marginal (longitudinal and survival) models.
Key words: Linear mixed model; Parametric survival model; Repeated measures
Consideramos una modelación conjunta paramétrica de mediciones longitudinales y tiempos de supervivencia, motivados por un estudio realizado en el Instituto do Coração (Incor), São Paulo, Brasil, con el objetivo de evaluar el impacto del Péptido Natriurético tipo B (BNP) recolectado en diferentes instantes, sobre la supervivencia de pacientes con Insuficiencia Cardíaca Congestiva (ICC). Empleamos un modelo lineal de efectos mixtos para la respuesta longitudinal y un modelo Birnbaum-Saunders para los tiempos de supervivencia, permitiendo la inclusión de sujetos sin observaciones longitudinales. Obtenemos los estimadores de máxima verosimilitud de los parámetros del modelo conjunto y realizamos un estudio de simulación para comparar las probabilidades de supervivencia verdaderas con las predicciones dinámicas obtenidas al ajustar el modelo conjunto propuesto y para evaluar el desempeño del método para estimar los parámetros del modelo. El modelo conjunto propuesto se aplica a la cohorte de 1609 pacientes con ICC, de los cuales 1080 no tienen mediciones de BNP. Las estimaciones de los parámetros y sus errores estándar obtenidos por medio de: i) el enfoque tradicional, donde únicamente se incluyen individuos con al menos una medición de la respuesta longitudinal y ii) el enfoque propuesto, que incluye la información de supervivencia de todos los individuos; se comparan con los obtenidos por medio de los modelos marginales (longitudinal y de supervivencia).
Palabras clave: Medidas repetidas; Modelo de supervivencia paramétrico; Modelo lineal de efectos mixtos
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