Open Access
March 2013 Clustering for multivariate continuous and discrete longitudinal data
Arnošt Komárek, Lenka Komárková
Ann. Appl. Stat. 7(1): 177-200 (March 2013). DOI: 10.1214/12-AOAS580


Multiple outcomes, both continuous and discrete, are routinely gathered on subjects in longitudinal studies and during routine clinical follow-up in general. To motivate our work, we consider a longitudinal study on patients with primary biliary cirrhosis (PBC) with a continuous bilirubin level, a discrete platelet count and a dichotomous indication of blood vessel malformations as examples of such longitudinal outcomes. An apparent requirement is to use all the outcome values to classify the subjects into groups (e.g., groups of subjects with a similar prognosis in a clinical setting). In recent years, numerous approaches have been suggested for classification based on longitudinal (or otherwise correlated) outcomes, targeting not only traditional areas like biostatistics, but also rapidly evolving bioinformatics and many others. However, most available approaches consider only continuous outcomes as a basis for classification, or if noncontinuous outcomes are considered, then not in combination with other outcomes of a different nature. Here, we propose a statistical method for clustering (classification) of subjects into a prespecified number of groups with a priori unknown characteristics on the basis of repeated measurements of several longitudinal outcomes of a different nature. This method relies on a multivariate extension of the classical generalized linear mixed model where a mixture distribution is additionally assumed for random effects. We base the inference on a Bayesian specification of the model and simulation-based Markov chain Monte Carlo methodology. To apply the method in practice, we have prepared ready-to-use software for use in R ( We also discuss evaluation of uncertainty in the classification and also discuss usage of a recently proposed methodology for model comparison—the selection of a number of clusters in our case—based on the penalized posterior deviance proposed by Plummer [Biostatistics 9 (2008) 523–539].


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Arnošt Komárek. Lenka Komárková. "Clustering for multivariate continuous and discrete longitudinal data." Ann. Appl. Stat. 7 (1) 177 - 200, March 2013.


Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171268
MathSciNet: MR3086415
Digital Object Identifier: 10.1214/12-AOAS580

Keywords: ‎classification‎ , functional data , Generalized linear mixed model , multivariate longitudinal data , repeated observations

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 1 • March 2013
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