Introducing a drift and diffusion framework for childhood growth research

Benjamin J.J. McCormick*, Fraser I. Lewis, Godfrey Guga, Paschal Mdoe, Esto Mduma, Cloupas Mahopo, Pascal Bessong, Stephanie A. Richard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalGates Open Research
Issue number71
Early online date29 Jun 2020
Publication statusPublished - 26 Nov 2020

Bibliographical note

We thank the participants and staff of the MAL-ED study for their vital contributions and we thank Prof. Laura Caulfield for her insightful and constructive input. The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the U.S. National Institutes of Health or Department of Health and Human Services.

Publisher Copyright:
© 2020 Lewis FI et al.


  • Child growth
  • Dynamic modelling
  • MAL-ED
  • Stochastic differential equations


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