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. 2016 Sep 7;16(1):117.
doi: 10.1186/s12874-016-0212-5.

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

Graeme L Hickey  1 , Pete Philipson  2 , Andrea Jorgensen  3 , Ruwanthi Kolamunnage-Dona  3
Affiliations

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

Graeme L Hickey et al. BMC Med Res Methodol. .

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.

Keywords: Joint models; Longitudinal data; Multivariate data; Software; Time-to-event data.

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Figures

Fig. 1
Fig. 1
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 W i(t) and the random effects, b i, are correlated, which gives rise to the joint model. T i 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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