Abstract
Multiple longitudinal outcomes are common in public health research and adequate methods are required when there is interest in the joint evolution of response variables over time. However, the main drawback of joint modeling procedures is the requirement to specify the joint density of all outcomes and their correlation structure, as well as numerical difficulties in statistical inference, when the dimension of these outcomes increases. To overcome such difficulty, we present two procedures to deal with multivariate longitudinal data. We first present an univariate approach, for which linear mixed-effects models are considered for each response variable separately. Then, a novel copula-based modeling is presented, in order to characterize relationships among the response variables. Both methodologies are applied to a real Brazilian data set on child growth.
Highlights
Longitudinal data or repeated measures data arise when multiple observations are made on the same subject or unit of analysis over time [33]
The main drawback of these joint modeling procedures is the requirement to specify the joint density of all outcomes or, at least, the correlation structure of the data, which can lead to parsimony and/or computation problems, as well as to numerical difficulties in statistical inference, when the dimension of these outcomes increases
Linear mixed-effects models, which contain a mixture of fixed effects and random effects, provide a way to deal with longitudinal responses within a subject
Summary
Longitudinal data or repeated measures data arise when multiple observations are made on the same subject or unit of analysis over time [33]. It is quite common in clinical trials and social science settings for multiple outcomes to be measured repeatedly within a set of study participants. Some examples are hearing thresholds measured on both ears of a set of participants, HIV studies with CD4 T-cell counts and viral RNA copy numbers are collected longitudinally on each participant, toxicological studies where doses of a toxic agent and some information on its deleterious effect are measured jointly (see [32]). Understanding relationships among multivariate outcomes is challenging due to the complex correlated nature of the problem, whilst providing a unique opportunity in studying the joint evolution of multiple response variables over time
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