  Faltering growth among children is a nutritional problem prevalent in low to
medium income countries; it is generally defined as a 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
economic productivity potential, it is important to identify faltered children
and be able to characterise different growth patterns so that targeted
treatments can be designed and administered. We introduce a multiclass
classification model for growth trajectory that flexibly extends a current
classification approach called the broken stick model, which is a piecewise
linear model with breaks at fixed knot locations. Heterogeneity in growth
patterns among children is captured using mixture distributed random effects,
whereby the mixture components determine the classification of children into
subgroups. The mixture distribution is modelled using a Dirichlet process
prior, which avoids the need to choose the "true" number of mixture components,
and allows this to be driven by the complexity of the data. Because children
have individual differences in the onset of growth stages, we introduce
child-specific random change points. Simulation results show that the random
change point model outperforms the broken stick model because it has fewer
restrictions on knot locations. We illustrate our model on a longitudinal birth
cohort from the Healthy Birth, Growth and Development knowledge integration
project funded by the Bill and Melinda Gates Foundation. Analysis reveals 9
subgroups of children within the population which exhibit varying faltering
trends between birth and age one.
