SITAR—a useful instrument for growth curve analysis

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.