Linear spline multilevel models for summarising childhood growth trajectories: A guide to their application using examples from five birth cohorts

Abstract

Childhood growth is of interest in medical research concerned with determinants and consequences of variation from healthy growth and development. Linear spline multilevel modelling is a useful approach for deriving individual summary measures of growth, which overcomes several data issues (co-linearity of repeat measures, the requirement for all individuals to be measured at the same ages and bias due to missing data). Here, we outline the application of this methodology to model individual trajectories of length/height and weight, drawing on examples from five cohorts from different generations and different geographical regions with varying levels of economic development. We describe the unique features of the data within each cohort that have implications for the application of linear spline multilevel models, for example, differences in the density and inter-individual variation in measurement occasions, and multiple sources of measurement with varying measurement error. After providing example Stata syntax and a suggested workflow for the implementation of linear spline multilevel models, we conclude with a discussion of the advantages and disadvantages of the linear spline approach compared with other growth modelling methods such as fractional polynomials, more complex spline functions and other non-linear models.

Keywords: ALSPAC; Born in Bradford; Generation XXI; PROBIT; Pelotas; child; growth; height; longitudinal; multilevel models; spline; weight.

Figure 1.

Distribution of the ages at measurement in (a) ALSPAC and (b) Pelotas 2004 cohorts. a. ALSPAC: b. Pelotas 2004 cohort ALSPAC: The Avon Longitudinal Study of Parents and Children. Note: Illustrating the greater inter-individual variability in ages at measurement in ALSPAC compared with the Pelotas 2004 cohort. Other cohorts are shown in Supplementary Figure 1.

Figure 2.

Average predicted length/height and weight trajectories from the ALSPAC cohort; (a) Mean predicted height trajectories for males (dashed line) and females (solid line) in ALSPAC and (b) Mean predicted weight trajectories for males (dashed line) and females (solid line) in ALSPAC. ALSPAC: The Avon Longitudinal Study of Parents and Children.