Abstract Body

During infancy and puberty, longitudinal growth in height or weight is complicated to model because the growth curves representing individual growth patterns vary considerably in shape. A popular way to analyse such data is to convert the measurements to z-scores—it removes the age trend and linearises the curves. However it also discards useful information about the shape of the growth curve and complicates the analysis of growth during puberty. This talk focuses instead on the measurement scale, and describes a relatively novel growth model called SITAR (Cole et al, 2010).

Two general features of the growth pattern are useful to summarise: a) the shape of the mean growth curve, and b) the nature and extent to which individuals deviate from the mean curve. But this poses a problem—how can one average curves that differ in shape? The trick is to assume that the curves all have the same underlying shape, and that they differ from each other only in simple ways.

SITAR achieves this by estimating a mean growth curve from which individual growth curves differ in just three respects: size (i.e. the extent to which the individual is consistently taller/shorter or heavier/lighter than average); timing (by how much their age at peak growth velocity is earlier or later than average), and intensity (by how much their average growth velocity is higher or lower than average). So individual growth patterns are summarised on three scales: size = small/big, timing = early/late and intensity = slow/fast. Geometrically, size and timing correspond to shifting the curve down/up and left/right, while intensity rotates the curve. SITAR (SuperImposition by Translation and Rotation) is a nonlinear mixed effects model that estimates size, timing and intensity as random effects, while the mean growth curve is a natural cubic spline. It differs from growth models like Jenss-Bayley, Preece-Baines or Karlberg’s ICP which use parametric forms of curve—the advantage of a cubic spline curve is that its shape is defined purely by the data, and hence can be relatively complex, unconstrained by a prespecified mathematical form.

Applied to studies of height in puberty, SITAR fits the data extremely well. The residual standard deviation is typically less than one tenth of the population standard deviation, so the model explains over 99% of the variance. It estimates mean curves for distance and velocity, from which mean final height and mean ages and values of height velocity at take-off and peak can be extracted. It also compares growth summary statistics across two or more groups. Published examples of SITAR include randomised clinical trials testing the effect on attained height of oxandrolone in girls with Turner syndrome, and of calcium supplementation in boys and girls from The Gambia subsisting on a low calcium diet.

Separately SITAR addresses questions concerning the life course, where individual growth patterns in childhood—as summarised by size, timing and intensity—are viewed as exposures relating to later life adverse outcomes. An example here links the age at peak height velocity to bone health in later life, showing that an early puberty is associated with stronger bones at age 60.

SITAR is very effective at summarising the complexity of growth. This may be because it mimics the biology of growth as championed by J M Tanner, focussing on the growth spurt in terms of peak velocity and age at peak velocity.