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Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues

View Article: PubMed Central - PubMed

ABSTRACT

Background: Available methods for the joint modelling of longitudinal and time-to-event outcomes have typically only allowed for a single longitudinal outcome and a solitary event time. In practice, clinical studies are likely to record multiple longitudinal outcomes. Incorporating all sources of data will improve the predictive capability of any model and lead to more informative inferences for the purpose of medical decision-making.

Methods: We reviewed current methodologies of joint modelling for time-to-event data and multivariate longitudinal data including the distributional and modelling assumptions, the association structures, estimation approaches, software tools for implementation and clinical applications of the methodologies.

Results: We found that a large number of different models have recently been proposed. Most considered jointly modelling linear mixed models with proportional hazard models, with correlation between multiple longitudinal outcomes accounted for through multivariate normally distributed random effects. So-called current value and random effects parameterisations are commonly used to link the models. Despite developments, software is still lacking, which has translated into limited uptake by medical researchers.

Conclusion: Although, in an era of personalized medicine, the value of multivariate joint modelling has been established, researchers are currently limited in their ability to fit these models routinely. We make a series of recommendations for future research needs.

Electronic supplementary material: The online version of this article (doi:10.1186/s12874-016-0212-5) contains supplementary material, which is available to authorized users.

No MeSH data available.


Graphical representation of a joint model of a time-to-event submodel and K-multivariate longitudinal outcomes submodel. Square boxes denote observed data; circles denote unobserved (including random) terms. The black-dashed box indicates that covariates can be shared between both submodels. The red-dashed box indicates that the process Wi(t) and the random effects, bi, are correlated, which gives rise to the joint model. Ti is the failure time, which may or may not be observed, in which case a censoring time is observed. All other notation is defined as above
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Fig1: Graphical representation of a joint model of a time-to-event submodel and K-multivariate longitudinal outcomes submodel. Square boxes denote observed data; circles denote unobserved (including random) terms. The black-dashed box indicates that covariates can be shared between both submodels. The red-dashed box indicates that the process Wi(t) and the random effects, bi, are correlated, which gives rise to the joint model. Ti is the failure time, which may or may not be observed, in which case a censoring time is observed. All other notation is defined as above

Mentions: In principle, each submodel can be fitted separately. However, this can result in biased estimates and a loss of efficiency when the processes are correlated. When bik and Wi(t) are jointly modelled, it leads to the so-called shared random effects joint model. A graphical representation of this model is shown in Fig. 1. Joint models might also fall under the umbrellas of pattern-mixture models or selection models depending on the factorization of the joint distribution of event time and longitudinal data [31, 32]. Furthermore, modelling approaches might also fall under the umbrellas of joint latent class models [33], semiparametric [34], and fully parametric models [35]. We note also that the topic of missing values in longitudinal data analyses has its own literature [36]. In the MVJM literature, focus has mainly been towards shared random effects models. We review the different submodels, including distributional assumptions and correlation structures, latent association structures, estimation techniques, software implementations, and give clinical examples of application.Fig. 1


Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues
Graphical representation of a joint model of a time-to-event submodel and K-multivariate longitudinal outcomes submodel. Square boxes denote observed data; circles denote unobserved (including random) terms. The black-dashed box indicates that covariates can be shared between both submodels. The red-dashed box indicates that the process Wi(t) and the random effects, bi, are correlated, which gives rise to the joint model. Ti is the failure time, which may or may not be observed, in which case a censoring time is observed. All other notation is defined as above
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC5015261&req=5

Fig1: Graphical representation of a joint model of a time-to-event submodel and K-multivariate longitudinal outcomes submodel. Square boxes denote observed data; circles denote unobserved (including random) terms. The black-dashed box indicates that covariates can be shared between both submodels. The red-dashed box indicates that the process Wi(t) and the random effects, bi, are correlated, which gives rise to the joint model. Ti is the failure time, which may or may not be observed, in which case a censoring time is observed. All other notation is defined as above
Mentions: In principle, each submodel can be fitted separately. However, this can result in biased estimates and a loss of efficiency when the processes are correlated. When bik and Wi(t) are jointly modelled, it leads to the so-called shared random effects joint model. A graphical representation of this model is shown in Fig. 1. Joint models might also fall under the umbrellas of pattern-mixture models or selection models depending on the factorization of the joint distribution of event time and longitudinal data [31, 32]. Furthermore, modelling approaches might also fall under the umbrellas of joint latent class models [33], semiparametric [34], and fully parametric models [35]. We note also that the topic of missing values in longitudinal data analyses has its own literature [36]. In the MVJM literature, focus has mainly been towards shared random effects models. We review the different submodels, including distributional assumptions and correlation structures, latent association structures, estimation techniques, software implementations, and give clinical examples of application.Fig. 1

View Article: PubMed Central - PubMed

ABSTRACT

Background: Available methods for the joint modelling of longitudinal and time-to-event outcomes have typically only allowed for a single longitudinal outcome and a solitary event time. In practice, clinical studies are likely to record multiple longitudinal outcomes. Incorporating all sources of data will improve the predictive capability of any model and lead to more informative inferences for the purpose of medical decision-making.

Methods: We reviewed current methodologies of joint modelling for time-to-event data and multivariate longitudinal data including the distributional and modelling assumptions, the association structures, estimation approaches, software tools for implementation and clinical applications of the methodologies.

Results: We found that a large number of different models have recently been proposed. Most considered jointly modelling linear mixed models with proportional hazard models, with correlation between multiple longitudinal outcomes accounted for through multivariate normally distributed random effects. So-called current value and random effects parameterisations are commonly used to link the models. Despite developments, software is still lacking, which has translated into limited uptake by medical researchers.

Conclusion: Although, in an era of personalized medicine, the value of multivariate joint modelling has been established, researchers are currently limited in their ability to fit these models routinely. We make a series of recommendations for future research needs.

Electronic supplementary material: The online version of this article (doi:10.1186/s12874-016-0212-5) contains supplementary material, which is available to authorized users.

No MeSH data available.