Fitting of bone mineral density with consideration of anthropometric parameters

Abstract

A new model describing normal values of bone mineral density in children has been evaluated, which includes not only the traditional parameters of age, gender, and race, but also weight, height, percent body fat, and sexual maturity. This model may constitute a better comparative norm for a specific child with given anthropometric values.

Introduction: Previous descriptions of children's bone mineral density (BMD) by age have focused on segmenting diverse populations by race and gender without adjusting for anthropometric variables or have included the effects of anthropometric variables over a relatively homogeneous population.

Methods: Multivariate semi-metric smoothing (MS(2)) provides a way to describe a diverse population using a model that includes multiple effects and their interactions while producing a result that can be smoothed with respect to age in order to provide connected percentiles. We applied MS(2) to spine BMD data from the Bone Mineral Density in Childhood Study to evaluate which of gender, race, age, height, weight, percent body fat, and sexual maturity explain variations in the population's BMD values. By balancing high adjusted R (2) values and low mean square errors with clinical needs, a model using age, gender, race, weight, and percent body fat is proposed and examined.

Results: This model provides narrower distributions and slight shifts of BMD values compared to the traditional model, which includes only age, gender, and race. Thus, the proposed model might constitute a better comparative standard for a specific child with given anthropometric values and should be less dependent on the anthropometric characteristics of the cohort used to devise the model.

Conclusions: The inclusion of multiple explanatory variables in the model, while creating smooth output curves, makes the MS(2) method attractive in modeling practically sized data sets. The clinical use of this model by the bone research community has yet to be fully established.

Fig. 1

Number of subjects in each of the four groups by age

Fig. 2

Smoothed coefficients by age for the four groups based on model D; a for height, b for percent body fat, c for height, and d for intercept

Fig. 2

Smoothed coefficients by age for the four groups based on model D; a for height, b for percent body fat, c for height, and d for intercept

Fig. 3

Expected BMD distributions using model D; a for 16-year-old non-black boys with various anthropometric measurements based on CDC charts for height and weight and b for 14-year-olds with CDC average weight and height. For all models, the group sample average for percent body fat was used

Fig. 4

RMSE for black boys by age. Model D has a consistently lower RMSE

Fig. 5

BMD vs. age for model A and model D using a group 50% body fat value from the data sample; a for non-black girls having CDC 50% values for weight and b for a non-black boys having CDC 75% values for weight and height

Fig. 6

Spine Z-scores of two Caucasian girls from an independent data set [19]. The difference between the sparse and full models can be positive or negative and can be as large or larger than one Z-score unit