TRACK: a FORTRAN program for calculating the Foulkes-Davis tracking index

GTRACK: a PC program for computing Goldstein's growth constancy index and an alternative measure of tracking

This paper reviews Goldstein's 'growth constancy index,' Xi, a measure of tracking which can be used to determine whether or not individuals maintain their relative positions in the distribution of a given measurement as that distribution changes over time. We suggest that Xi is an appropriate measure of tracking when the (standardized) measurements arise in the context of a Model I ANOVA, but that the intraclass correlation coefficient, rI, may be preferred when a Model II ANOVA is applicable. We also describe--and make available--a PC program which allows the user to choose between Model I and Model II, and computes the appropriate tracking index and confidence intervals for the corresponding parameter.

The distribution of body fat from childhood to adulthood in a longitudinal study population

Body fat distribution, its continuity from childhood (4-6 years) to 30 years of age, and its link to that of parents is described in a longitudinal study population. A computer-assisted image analysis technique was used to measure body fat distribution (as measured by waist and hip diameters) from somatotype photographs. Pearson correlation coefficients were used to assess the association between the waist/hip diameter ratio (WHDR) and the body mass index (BMI) at all ages and between the WHDR of parents and offspring. Both Pearson correlation coefficients and the Foulkes-Davis tracking index were used to assess tracking of the WHDR from childhood to age 30 years. Stepwise regression analyses were performed to determine the predictability of the WHDR at age 30 years from WHDRs in childhood and adolescence. Among both sexes the WHDR decreased and BMIs increased with age from childhood to 18 years, then both increased from age 18 to 30 years. The correlation between the WHDR and BMI was significant only at 30 years for males (r = 0.37; p < 0.05) and during all stages of adolescence in females (p < 0.05). Age-to-age correlations were high for both sexes (p < 0.0001), and remained significant over a span of up to 25 years. Using the Foulkes-Davis tracking index, tracking from the year of peak height velocity to 30 years (a span of approximately 20 years) was strong for both sexes. Parent and child WHDRs were correlated and differed by sex. Father-son correlations were not significant in childhood, but reached significance in early adolescence (2 years before the year of peak velocity) and remained significant to 30 years (p < 0.05). Mother-daughter correlations were significant at all ages (p < 0.05). The level of the WHDR at the peak of the pubertal growth spurt (year of peak height velocity) predicted up to 58% of the variance in males and 51% of the variance in females of the WHDR at 30 years. We conclude that the adult WHDR (a proxy for the waist/hip ratio) becomes evident by the year of the pubertal growth spurt in height.

Data analysis in craniofacial biology with special emphasis on longitudinal studies

Recommendations are made for strengthening data description and analysis in craniofacial biology. Special emphasis is placed on longitudinal data, and PC programs for accomplishing appropriate analyses in this context are described and made available to interested readers. Some more general recommendations are treated in less detail. These include the effective description of data using stem-and-leaf displays and/or boxplots, the use of decision-analytic methods in the management of patients with dentofacial deformities, and the valid application of certain statistical methods in single-subject studies. Finally, it is conjectured that computer-intensive methods such as randomization tests and jackknifing will play an increasingly prominent role in craniofacial research.

A GAUSS program for computing the Foulkes-Davis tracking index for polynomial growth curves

We have previously published a GAUSS program for computing the Foulkes-Davis tracking index, gamma, from a one-sample longitudinal data set when no assumptions were made concerning the structure of the individual growth curves (Schneiderman et al., Am J Hum Biol, 4 (1992) 417-420). In this paper we consider the computation of the Foulkes-Davis index assuming that each individual growth curve may be adequately represented by a polynomial function in time and a GAUSS program performing these computations is made available. As with the two other tracking indices we have described, gamma and kappa (Schneiderman et al., Am J Hum Biol, 2 (1990) 475-490), this one can be used to evaluate regularity in patterns of growth or adaptation. An example is presented where statural growth in the same three groups considered in the earlier papers are analyzed. The small disparities between these and the earlier results are discussed in view of the different assumptions of the models and the differences in how they operationalize the concept of tracking.