Marginalized transition random effect models for multivariate longitudinal binary data

Abstract

Key words and phrases: Bayesian hierarchical model; hybrid Monte Carlo.MSC 2000: Primary 62J12; secondary 60J22.Abstract: Generalized linear models with random effects and/or serial dependence are commonly used to analyze longitudinal data. However, the computation and interpretation of marginal covariate effects can be difficult. This led Heagerty (1999Heagerty ( , 2002 to propose models for longitudinal binary data in which a logistic regression is first used to explain the average marginal response. The model is then completed by introducing a conditional regression that allows for the longitudinal, within-subject, dependence, either via random effects or regressing on previous responses. In this paper, the authors extend the work of Heagerty to handle multivariate longitudinal binary response data using a triple of regression models that directly model the marginal mean response while taking into account dependence across time and across responses. Markov Chain Monte Carlo methods are used for inference. Data from the Iowa Youth and Families Project are used to illustrate the methods. Des modèlesà effets aléatoires età transition marginalisée pour des données longitudinales binaires multivariéesRésumé : On a souvent recoursà des modèles linéaires généralisés comportant des effets aléatoires et/ou une dépendance sérielle pour l'analyse de données longitudinales. Toutefois, le calcul et l'interprétation des effets marginaux des covariables est parfois ardu. Ceci a conduit Heagerty (1999Heagerty ( , 2002à proposer des modèles pour les données longitudinales binaires dans lesquels on commence par ajuster l'espérance marginale de la variable réponseà l'aide d'une régression logistique. La modélisation est ensuite complétée par une régression conditionnelle qui rend compte de la dépendance longitudinale intra-sujet au moyen d'effets aléatoires ou d'une régression sur les valeurs passées de la variable réponse. Dans cet article, les auteurś etendent les travaux de Heagerty au traitement de données longitudinales binaires multivariées grâceà trois régressions qui modélisent directement l'espérance marginale des variables réponses, en plus de décrire la dépendance entre elles et en fonction du temps. L'inférence s'appuie sur des méthodes de Monte-Carloà chaîne de Markov. Des données issues de l'étude sur la jeunesse et les familles de l'Iowa serventà illustrer le propos.

Bayesian semiparametric regression for longitudinal binary processes with missing data

“…Under ignorable missingness, an obvious choice would be to construct the DIC based on the observed data likelihood. This approach has been applied in the literature ([39, 40]), and can generally be implemented in WinBUGS. Nevertheless, for the first place we should keep in mind that given all the possible choices for model comparison techniques, we can only assess the fit of the full data model to the observed data.…”

The analysis of multivariate longitudinal data: A review

“…In a non-continuous context, Ilk and Daniels 84 used one latent variable for m binary outcomes, but the evolution over time was modeled using a Markov structure for the observed outcomes, whereas Oort 76 and Sivo 78 modeled the within-subject dependence over time on the latent level. Liu and Hedeker 85 introduced a model for multivariate longitudinal ordinal data in a psychometric context.…”

Joint Modeling of Transitional Patterns of Alzheimer's Disease

“…This approach allows modeling of covariate effects on marginal transition probabilities, as well as the association parameters. Ilk and Daniels [11] formulated marginalized random-effects models to accommodate multivariate longitudinal binary data, and Lee et al [12] later extended these models by using a new covariance matrix with a Kronecker decomposition. All of these methods are focused on the marginal transition patterns of multivariate binary data.…”

“…In addition, each univariate submodel in the proposed joint random-effects transition models can be flexible enough to accommodate various types of measurements (e.g., Gaussian, multi-categorical, count, etc.). Relative to the existing literature, the benefits of the joint random-effects transition models are multifold: (i) comparing with the modeling of single process in [5], [6], [7], they allow flexible correlation among multiple measurements for a disease; (ii) comparing with the marginal models in [8], [10], [11], they offer insights on patient-specific transitional patterns of disease measurements over time; (iii) comparing with the models for binary data in [10], [11], they offer flexible submodels for fitting the data with various types; and (iv) they can identify common and uncommon covariates that govern the transitional probabilities of each disease outcome. The joint random-effects transition models can help clinicians predict a patient's Alzheimer disease status over time, based on the patient's current status and other genetic or sociodemographic factors.…”