A comparative study of the fit of four different functions to longitudinal data of growth in height of Belgian girls

Abstract

We have fitted Preece-Baines model 1, double logistic, logistic and Gompertz functions to longitudinal data on the growth in height of 35 Belgian girls, followed from birth to 18.0 years. The Preece-Baines model 1 showed significantly lower residual mean squares than the double logistic function, when fitted to data beyond the age of 1.0 year. The former model was also most robust towards variations in the lower age bound by the subject's data series and always described the adolescent spurt better than the latter. Both models fitted the data badly when measurements before the age of 1.0 year were included, and they usually estimated the point at take-off too early. Over the adolescent cycle, only, the logistic function fitted our data slightly better than the Gompertz function, with significantly lower pooled residual mean squares, though a slightly worse performance in the runs-test.

Total Pubertal Growth and Markers of Puberty Onset in Adolescents with GHD: Comparison between Mathematical Growth Analysis and Pubertal Staging Methods

“…Although acceleration in height gain is generally the first sign of puberty, it is not conventionally used to determine the onset of puberty in endocrinological practice. This anthropometric approach has been considered to be the best way to determine ‘real’ TPG in normal adolescents, although the results obtained may depend on the mathematical approach applied [8, 9, 14, 16,18,19,20,21,22,23]. …”

“…PB1 fits prepubertal as well as pubertal growth but, does not allow for the rather elusive mid-growth spurt discussed by Gasser et al [23] (in their discussion of non-parametric regression analysis, Gasser et al noted that the mid-growth spurt is often small, almost drowned in random noise). Moreover, several children have more than one prepubertal spurt, which tend to be smoothed out into one single long-lasting raise in growth velocity by using growth modeling [20]. Finally, models designed to describe a prepubertal spurt may generate such a spurt even if the raw data shows no sign of it [20, 23].…”

Adolescent height growth of girls in Tokyo

“…Finally, comparisons were made with seven other populations whose reports are available in the literature and their growth curves fitted by the PB1 function. These were two European groups [British and Belgian; Preece and Baines (1978) and Hauspie et al (1980a), respectively], one South Asian group [West Bengal; Hauspie et al (1980b)], one African group [Gambia;Billewicz and McGregor (1982)], one Australian aboriginal group [Brown and Townsend (1982)], and two US groups [Americans in Massachusettes and the Fels Institute; Zacharias and Rand (1983) and Guo et al (1992), respectively]. Results from a Polish girl group (ChrzastekSpruch et al, 1990) have also been reported, but we did not include these in the present comparisons because they were presented as percentile data.…”

“…This was the report in which four mathematical functions were described, and model 1 (PB1) among the four was indicated as the best by the authors. The 35 individual data of Belgian girls mentioned above were fitted to the PB1 and other functions as outlined above (Hauspie et al, 1980a). Mixed longitudinal data of 303 Indian (West Bengal) boys and 260 girls showed that the adolescent growth spurt in the population was similar to that of the British Harpenden children (Hauspie et al, 1980b).…”

“…He also mentioned that structural models were nonlinear in their constants and provided a good description of growth patterns with a relatively small number of parameters, although by the nature of their mathematical function they may be unable to represent certain growth events, such as the mid-childhood spurt. Hauspie et al (1980a) fitted the double logistic, Gompertz and PB1 functions to the longitudinal height growth data of 35 Belgian girls, from birth to 18.0 years. The authors of that study concluded that the PB1 model showed significantly lower residual mean squares when fitted to data beyond age 1.0, was more robust towards variations in the lower age bounds, and described the adolescent spurt better than the double logistic function.…”