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A joint marginal-conditional model for multivariate longitudinal data.

ABSTRACT: Multivariate longitudinal data frequently arise in biomedical applications; however, their analyses are often performed one outcome at a time, or jointly using existing software in an ad hoc fashion. A main challenge in the proper analysis of such data is the fact that the different outcomes are measured on different unknown scales. Methodology for handling the scale problem has been previously proposed for cross-sectional data, and here we extend it to the longitudinal setting. We consider modeling the longitudinal data using random effects, while leaving the joint distribution of the multiple outcomes unspecified. We propose an estimating equation together with an expectation-maximization-type (expectation-substitution) algorithm. The consistency and the asymptotic distribution of the parameter estimates are established. The method is evaluated using extensive simulations and applied to a longitudinal nutrition data set from a large dietary intervention trial on breast cancer survivors, the Women's Healthy Eating and Living Study.

SUBMITTER: Proudfoot J

PROVIDER: S-EPMC5799029 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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A joint marginal-conditional model for multivariate longitudinal data.

Proudfoot James J Faig Walter W Natarajan Loki L Xu Ronghui R

Statistics in medicine 20171204 5

Multivariate longitudinal data frequently arise in biomedical applications; however, their analyses are often performed one outcome at a time, or jointly using existing software in an ad hoc fashion. A main challenge in the proper analysis of such data is the fact that the different outcomes are measured on different unknown scales. Methodology for handling the scale problem has been previously proposed for cross-sectional data, and here we extend it to the longitudinal setting. We consider mode ...[more]

PMID: 29205414

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Project description:BackgroundImmuno-epidemiologists are often faced with multivariate outcomes, measured repeatedly over time. Such data are characterised by complex inter- and intra-outcome relationships which must be accounted for during analysis. Scientific questions of interest might include determining the effect of a treatment on the evolution of all outcomes together, or grouping outcomes that change in the same way. Modelling the different outcomes separately may not be appropriate because it ignores the underlying relationships between outcomes. In such situations, a joint modelling strategy is necessary. This paper describes a pairwise joint modelling approach and discusses its benefits over more simple statistical analysis approaches, with application to data from a study of the response to BCG vaccination in the first year of life, conducted in Entebbe, Uganda.MethodsThe study aimed to determine the effect of maternal latent Mycobacterium tuberculosis infection (LTBI) on infant immune response (TNF, IFN-γ, IL-13, IL-10, IL-5, IL-17A and IL-2 responses to PPD), following immunisation with BCG. A simple analysis ignoring the correlation structure of multivariate longitudinal data is first shown. Univariate linear mixed models are then used to describe longitudinal profiles of each outcome, and are then combined into a multivariate mixed model, specifying a joint distribution for the random effects to account for correlations between the multiple outcomes. A pairwise joint modelling approach, where all possible pairs of bivariate mixed models are fitted, is then used to obtain parameter estimates.ResultsUnivariate and pairwise longitudinal analysis approaches are consistent in finding that LTBI had no impact on the evolution of cytokine responses to PPD. Estimates from the pairwise joint modelling approach were more precise. Major advantages of the pairwise approach include the opportunity to test for the effect of LTBI on the joint evolution of all, or groups of, outcomes and the ability to estimate association structures of the outcomes.ConclusionsThe pairwise joint modelling approach reduces the complexity of analysis of high-dimensional multivariate repeated measures, allows for proper accounting for association structures and can improve our understanding and interpretation of longitudinal immuno-epidemiological data.

Project description:BACKGROUND:Joint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. An underlying random effects structure links the survival and longitudinal submodels and allows for individual-specific predictions. Multiple time-varying and time-invariant covariates can be included to potentially increase prediction accuracy. The goal of this study was to estimate a multivariate joint model on several longitudinal observational studies of Huntington's disease, examine external validity performance, and compute individual-specific predictions for characterizing disease progression. Emphasis was on the survival submodel for predicting the hazard of motor diagnosis. METHODS:Data from four observational studies was analyzed: Enroll-HD, PREDICT-HD, REGISTRY, and Track-HD. A Bayesian approach to estimation was adopted, and external validation was performed using a time-varying AUC measure. Individual-specific cumulative hazard predictions were computed based on a simulation approach. The cumulative hazard was used for computing predicted age of motor onset and also for a deviance residual indicating the discrepancy between observed diagnosis status and model-based status. RESULTS:The joint model trained in a single study had very good performance in discriminating among diagnosed and pre-diagnosed participants in the remaining test studies, with the 5-year mean AUC?=?.83 (range .77-.90), and the 10-year mean AUC?=?.86 (range .82-.92). Graphical analysis of the predicted age of motor diagnosis showed an expected strong relationship with the trinucleotide expansion that causes Huntington's disease. Graphical analysis of the deviance-type residual revealed there were individuals who converted to a diagnosis despite having relatively low model-based risk, others who had not yet converted despite having relatively high risk, and the majority falling between the two extremes. CONCLUSIONS:Joint modeling is an improvement over traditional survival modeling because it considers all the longitudinal observations of covariates that are predictive of an event. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important in the timing of interventions, determining the qualification for appropriate clinical trials, and general genotypic analysis.

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A joint marginal-conditional model for multivariate longitudinal data.

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A joint marginal-conditional model for multivariate longitudinal data.

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