Abstract
Background: Growth trajectories are highly variable between children, making epidemiological analyses challenging both to the identification of malnutrition interventions at the population level and also risk assessment at individual level. We introduce stochastic differential equation (SDE) models into child growth research. SDEs describe flexible dynamic processes comprising: drift - gradual smooth changes - such as physiology or gut microbiome, and diffusion - sudden perturbations, such as illness or infection. Methods: We present a case study applying SDE models to child growth trajectory data from the Haydom, Tanzania and Venda, South Africa sites within the MAL-ED cohort. These data comprise n=460 children aged 0-24 months. A comparison with classical curve fitting (linear mixed models) is also presented. Results: The SDE models offered a wide range of new flexible shapes and parameterizations compared to classical additive models, with performance as good or better than standard approaches. The predictions from the SDE models suggest distinct longitudinal clusters that form distinct 'streams' hidden by the large between-child variability. Conclusions: Using SDE models to predict future growth trajectories revealed new insights in the observed data, where trajectories appear to cluster together in bands, which may have a future risk assessment application. SDEs offer an attractive approach for child growth modelling and potentially offer new insights.
Highlights
Growth trajectories are highly variable between children, making epidemiological analyses challenging both to the identification of malnutrition interventions at the population level and risk assessment at individual level
Linear mixed models and stochastic differential equation (SDE) mixed models Using individual child trajectory data over 0–24 months for ZWfL from all n=460 children from the two sites, the best fitting LMM model was a cubic polynomial with a single interaction term between age squared and site, which gave Akaike information criterion (AIC)=21913 and Bayesian information criterion (BIC)=21983
These are quantitatively similar except that the SDE correctly captures the initial shape of the mean, a short rapid increase decrease during the first six months in the Venda data, whereas the LMM estimates a steady decrease from birth through six months
Summary
Growth trajectories are highly variable between children, making epidemiological analyses challenging both to the identification of malnutrition interventions at the population level and risk assessment at individual level. Methods: We present a case study applying SDE models to child growth trajectory data from the Haydom, Tanzania and Venda, South Africa sites within the MAL-ED cohort. These data comprise n=460 children aged 0-24 months. The predictions from the SDE models suggest distinct longitudinal clusters that form distinct ‘streams’ hidden by the large between-child variability. Conclusions: Using SDE models to predict future growth trajectories revealed new insights in the observed data, where trajectories appear to cluster together in bands, which may have a future risk assessment application. SDEs offer an attractive approach for child growth modelling and potentially offer new insights
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