Research Article: Conditional random slope: A new approach for estimating individual child growth velocity in epidemiological research

Date Published: April 21, 2017

Publisher: John Wiley and Sons Inc.

Author(s): Michael Leung, Diego G. Bassani, Amy Racine‐Poon, Anna Goldenberg, Syed Asad Ali, Gagandeep Kang, Prasanna S. Premkumar, Daniel E. Roth.


Conditioning child growth measures on baseline accounts for regression to the mean (RTM). Here, we present the “conditional random slope” (CRS) model, based on a linear‐mixed effects model that incorporates a baseline‐time interaction term that can accommodate multiple data points for a child while also directly accounting for RTM.

In two birth cohorts, we applied five approaches to estimate child growth velocities from 0 to 12 months to assess the effect of increasing data density (number of measures per child) on the magnitude of RTM of unconditional estimates, and the correlation and concordance between the CRS and four alternative metrics. Further, we demonstrated the differential effect of the choice of velocity metric on the magnitude of the association between infant growth and stunting at 2 years.

RTM was minimally attenuated by increasing data density for unconditional growth modeling approaches. CRS and classical conditional models gave nearly identical estimates with two measures per child. Compared to the CRS estimates, unconditional metrics had moderate correlation (r = 0.65–0.91), but poor agreement in the classification of infants with relatively slow growth (kappa = 0.38–0.78). Estimates of the velocity‐stunting association were the same for CRS and classical conditional models but differed substantially between conditional versus unconditional metrics.

The CRS can leverage the flexibility of linear mixed models while addressing RTM in longitudinal analyses.

Partial Text

Estimation of the rate of change over time in a child’s physical size is essential for epidemiological studies of the determinants and consequences of variations in child growth. Methods to estimate growth velocity in early life are particularly relevant to the developmental origins of health and disease (DOHaD) hypothesis; for example, the pace of early postnatal growth or weight gain may influence the risk of obesity and cardiometabolic diseases later in life (Victora et al., 2008). However, there is currently a lack of consensus on the operational definition of growth velocity, leading to inconsistent use of statistical strategies to quantify growth in epidemiology.

The CRS is a novel approach for estimating conditional growth velocity based on a LME model that incorporates a baseline size‐age interaction term. This model is straightforward, leverages the flexibility of a longitudinal mixed model while addressing RTM, and is a generalization of the classical formulation of the conditional SDS model (Cole, 1995, 1998; Keijzer‐Veen et al., 2005). We demonstrated that when more than two measurements per child are available for an age interval of interest, CRS models provide a feasible approach for quantifying inter‐individual variations in child growth while accounting for RTM.

The authors thank the colleagues in the Healthy Birth, Growth, and Development Knowledge integration (HBGDki) consortium, and HBGDki staff at the Bill and Melinda Gates Foundation. They also acknowledge Wellcome Trust and the Bill and Melinda Gates Foundation for supporting the original cohort studies. They also thank the AJHB reviewer for valuable feedback on a previous version of this article.

ML, DGB, AR, AG, and DER designed the study, developed the methodology, performed the analyses and wrote the manuscript. SAA, GK, and PSP collected the data. Each author has seen and approved the contents of the submitted manuscript.




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