Dataset Information

Modelling childhood growth using fractional polynomials and linear splines.

ABSTRACT:

Background

There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines).

Methods

We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age.

Results

Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased.

Conclusions

Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures.

SUBMITTER: Tilling K

PROVIDER: S-EPMC4264511 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Publications

Modelling childhood growth using fractional polynomials and linear splines.

Tilling Kate K Macdonald-Wallis Corrie C Lawlor Debbie A DA Hughes Rachael A RA Howe Laura D LD

Annals of nutrition & metabolism 20141118 2-3

<h4>Background</h4>There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines).<h4>Methods</h4>We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (A ...[more]

PMID: 25413651

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Project description:Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.

Project description:The Lives Saved Tool (LiST) is a widely used resource for evidence-based decision-making regarding health program scale-up in low- and middle-income countries. LiST estimates the impact of specified changes in intervention coverage on mortality and stunting among children under 5 years of age. We aimed to improve the estimates of the parameters in LiST that determine the rate at which the effects of interventions to prevent stunting attenuate as children get older.We identified datasets with serial measurements of children's lengths or heights and used random effects models and restricted cubic splines to model the growth trajectories of children with at least six serial length/height measurements. We applied WHO growth standards to both measured and modelled (smoothed) lengths/heights to determine children's stunting status at multiple ages (1, 6, 12, 24 months). We then calculated the odds ratios for the association of stunting at one age point with stunting at the next ("stunting-to-stunting ORs") using both measured and smoothed data points. We ran analyses in LiST to compare the impact on intervention effect attenuation of using smoothed rather than measured stunting-to-stunting ORs.A total of 21,786 children with 178,786 length/height measurements between them contributed to our analysis. The odds of stunting at a given age were strongly related to whether a child is stunted at an earlier age, using both measured and smoothed lengths/heights, although the relationship was stronger for smoothed than measured lengths/heights. Using smoothed lengths/heights, we estimated that children stunted at 1 month have 45 times the odds of being stunted at 6 months, with corresponding odds ratios of 362 for the period 6 to 12 months and 175 for the period 12 to 24 months. Using the odds ratios derived from the smoothed data in LiST resulted in a somewhat slower attenuation of intervention effects over time, but substantial attenuation was still observed in the LiST outputs. For example, in Mali the effect of effectively eliminating SGA births reduced prevalence of stunting at age 59 months from 44.4% to 43.7% when using odds ratios derived from measured lengths/heights and from 44.4% to 41.9% when using odds ratios derived from smoothed lengths/heights.Smoothing of children's measured lengths/heights increased the strength of the association between stunting at a given age and stunting at an earlier age. Using odds ratios based on smoothed lengths/heights in LiST resulted in a small reduction in the attenuation of intervention effects with age and thus some increase in the estimated benefits, and may better reflect the true benefits of early nutritional interventions.

Dataset Information

Modelling childhood growth using fractional polynomials and linear splines.

Background

Methods

Results

Conclusions

Publications

Modelling childhood growth using fractional polynomials and linear splines.

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