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CPS1954 Vincent C. et al.

Multiclass classification of growth curves using
Random Change Point Model with heterogeneity
in the random effects
1,3
1,5
Vincent Chin * 11,2 , Jarod Y. L. Lee , Louise M. Ryan 1,3,4, Robert Kohn , Scott A.
Sisson
1,2
1 Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers.
2 School of Mathematics and Statistics, University of New South Wales, Sydney, Australia.
3 School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney,
Australia.
4 Harvard T.H. Chan School of Public Health, Harvard University, Cambridge, USA.
5 School of Economics, University of New South Wales, Sydney, Australia.

Abstract
Faltering growth among young children is a nutritional problem prevalent in
low to medium income countries and is in general defined as slower rate of
growth compared to a reference healthy population of the same age and
gender. As faltering is closely associated with reduced physical, intellectual
and productive potentials, it is important to identify faltered children and be
able to characterise different growth patterns so that target-specific
treatments can be designed and administered. Our proposed multiclass
classification model in this paper is built upon the broken stick model which is
a piecewise linear model with breaks at the knots. Heterogeneity in the growth
behaviour between children is captured by extending the broken stick model
to mixture distributed random effects whereby the mixture components
determines the classification of children into subgroups. We model the
mixture distribution by a Dirichlet process prior. With this prior, we avoid
having to choose the “true” number of components. Considering that children
have different timings of growth stages, we propose replacing the fixed knots
in the broken stick model by child-specific random change points. We
illustrate our classification model on a longitudinal birth cohort from the
Healthy Birth, Growth and Development knowledge integration (HBGDki)
project funded by the Bill and Melinda Gates Foundation. Analysis on the
dataset reveals 8 subgroups of children within the population. The largest
subgroup consists of children with linear faltering trend while the others show
varying degrees of growth catch-up at different stages between birth and age
one.

Keywords
Bayesian non-parametric model; Child growth modelling; Dirichlet process
prior; Longitudinal data; Mixture modelling

* Corresponding author: vincent.chin@student.unsw.edu.au
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