Application of growth models in the analysis of pathological growth data: The case of hypophosphatemic vitamin D‐resistant rickets

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Abstract
Growth in height of 16 patients suffering from hypophosphatemic vitamin D-resistant rickets (HR) was analyzed by means of three nonlinear growth models: the Preece Baines function, the JPPS model, and the triple logistic function. The data were purely longitudinal, covering age ranges from childhood to adulthood, with an average of 3 measurements per year. All three models proved to fit the growth pattern of HR patients with the same degree of accuracy as they do for healthy children, indicating that, despite their small height-for-age and their disproportionately short stature, these patients had a quite normal overall shape of their growth pattern. The JPPS model was particularly appropriate to describe the individual growth pattern of these patients, since the fit of this model was quite robust towards the choice of starting values for the numerical least-squares technique, and the model estimated biological variables in a fairly unbiased way. Analysis of the residuals suggested that in 5 of the 16 patients there was evidence of short-term variations in growth rate (mini-spurts), such as have been described in healthy children.