Statistical Modelling 21 (1-2) (2021), 115–136

Pairwise estimation of multivariate longitudinal outcomes in a Bayesian setting with extensions to the joint model

Katya Mauff,
Department of Biostatistics,
Erasmus University Medical Center,
Rotterdam,
the Netherlands
e-mail: katya.mauff@gmail.com

Nicole S Erler,
Department of Biostatistics,
Erasmus University Medical Center,
Rotterdam,
the Netherlands


Isabella Kardys,
Department of Cardiology,
Erasmus Medical Center,
Rotterdam,
the Netherlands


Dimitris Rizopoulos,
Department of Cardiology,
Erasmus Medical Center,
Rotterdam,
the Netherlands


Abstract:

Multiple longitudinal outcomes are theoretically easily modelled via extension of the generalized linear mixed effects model. However, due to computational limitations in high dimensions, in practice these models are applied only in situations with relatively few outcomes. We adapt the solution proposed by Fieuws and Verbeke (2006) to the Bayesian setting: fitting all pairwise bivariate models instead of a single multivariate model, and combining the Markov Chain Monte Carlo (MCMC) realizations obtained for each pairwise bivariate model for the relevant parameters. We explore importance sampling as a method to more closely approximate the correct multivariate posterior distribution. Simulation studies show satisfactory results in terms of bias, RMSE and coverage of the 95% credible intervals for multiple longitudinal outcomes, even in scenarios with more limited information and non-continuous outcomes, although the use of importance sampling is not successful. We further examine the incorporation of a time-to-event outcome, proposing the use of Bayesian pairwise estimation of a multivariate GLMM in an adaptation of the corrected two-stage estimation procedure for the joint model for multiple longitudinal outcomes and a time-to-event outcome (Mauff et al., 2020, Statistics and Computing). The method does not work as well in the case of the corrected two-stage joint model; however, the results are promising and should be explored further.

Keywords:

pairwise; multivariate mixed effects; bayesian, joint; importance sampling.

Downloads:

Code and supplementary material in Google drive archive. For the article's respective data, interested readers can contact Isabella Kardys should they wish to replicate the analysis.
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