SITAR--a useful instrument for growth curve analysis

Abstract

Background: Growth curve analysis is a statistical issue in life course epidemiology. Height in puberty involves a growth spurt, the timing and intensity of which varies between individuals. Such data can be summarized with individual Preece-Baines (PB) curves, and their five parameters then related to earlier exposures or later outcomes. But it involves fitting many curves.

Methods: We present an alternative SuperImposition by Translation And Rotation (SITAR) model, a shape invariant model with a single fitted curve. Curves for individuals are matched to the mean curve by shifting their curve up-down (representing differences in mean size) and left-right (for differences in growth tempo), and the age scale is also shrunk or stretched to indicate how fast time passes in the individual (i.e. velocity). These three parameters per individual are estimated as random effects while fitting the curve. The outcome is a mean curve plus triplets of parameters per individual (size, tempo and velocity) that summarize the individual growth patterns. The data are heights for Christ's Hospital School (CHS) boys aged 9-19 years (N = 3245, n = 129,508), and girls with Turner syndrome (TS) aged 9-18 years from the UK Turner Study (N = 105, n = 1321).

Results: The SITAR model explained 99% of the variance in both datasets [residual standard deviation (RSD) 6-7 mm], matching the fit of individually-fitted PB curves. In CHS, growth tempo was associated with insulin-like growth factor-1 measured 50 years later (P = 0.01, N = 1009). For the girls with TS randomized to receive oxandrolone from 9 years, velocity was substantially increased compared with placebo (P = 10(-8)).

Conclusions: The SITAR growth curve model is a useful epidemiological instrument for the analysis of height in puberty.

Figure 1

Illustration of the SITAR model for height in puberty. The solid line is the mean growth curve; the short dashed lines indicate a vertical or height shift in the curve corresponding to size (α); the long dashed lines indicates a horizontal or age shift corresponding to tempo (β) and the dot-dashed lines represent a shrinking–stretching of the age scale reflecting velocity (γ)

Figure 2

CHS data—3245 height growth curves and 129 508 heights from 9 to 19 years

Figure 3

The effect on Figure 2 of adjusting in turn for (a) size α (shifting curves vertically), (b) tempo β (shifting curves horizontally), (c) velocity γ (shrinking–stretching age scales), and (d) extreme outliers

Figure 4

Turner Study data. Left: 105 height growth curves and 1321 heights from 9 to 19 years as randomized (oxandrolone red solid lines, placebo blue dashed lines). Right: the same curves after SITAR adjustment

Figure 5

Turner Study. Comparison of the SITAR growth parameters by trial arm. Velocity is far greater for oxandrolone (P = 10^–8)

Figure 6

Turner Study. The mean growth curves for the two arms, indicating the greater velocity for oxandrolone