Estimating Mean Growth Trajectories When Measurements Are Sparse and Age Is Uncertain

Comparing children's growth across the world and at different moments in history can yield insight into both health challenges and healthy morphological variation in humans. A difficulty of such comparative analyses is that, in marginalized populations, there are often logistical complications to obtaining repeat measures of individual children's height and weight. The problem is even more acute for historical populations: bioarcheological datasets comprise single measures of individuals at death. Additionally, for both contemporary and historical populations, there is often non-trivial uncertainty about children's ages. Both of these factors complicate estimation of growth trajectories. Here we evaluate the degree to which we can accurately estimate a population-mean growth trajectory using only a small number of (randomly) uncertain measurements, like those that compose many contemporary and bioarcheological datasets.

We recently derived a causal model of human growth from fundamental principles of metabolism and allometry, permitting exploration of genetic and environmental contributions to children's growth. Here, we fit this model in a Bayesian framework to simulated cross-sectional and longitudinal datasets of varying size, where age is uncertain.

For large-scale comparisons, reasonably accurate population-mean growth trajectories may be obtained from single height measures of 100 children of a given sex and a range of ages. However, detailed analyses of pubertal growth spurts and the metabolic and allometric parameters underlying growth require longitudinal datasets.

We conclude that this new model and estimation strategy constitute a potentially useful toolkit for comparing mean growth trajectories across contemporary and historical populations.