Abstract
Summary
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 (MS2) 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 MS2 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 MS2 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.
Similar content being viewed by others
References
Peck W (1993) Consensus development conference: diagnosis, prophylaxis, and treatment of osteoporosis. Am J Med 94:646–650
Matkovic V, Illich J, Skugor M (1995) Calcium intake and skeletal formation. In: Burckhardt P, Heaney R (eds) Nutritional aspects of osteoporosis ‘94. Rome, Ares-Serono Symposia, pp 129–145
Farhat G, Yamout B, Mikati MA, Demirjian S, Sawaya R, El-Hajj Fuleihan G (2002) Effect of antiepileptic drugs on bone density in ambulatory patients. Neurology 58:1348–1353
Henderson C, Specker B, Sierra R, Campaigne B, Lovell D (2000) Total body bone mineral content in non-corticosteroid-treated postpubertal females with juvenile rheumatoid arthritis: frequency of osteopenia and contributing factors. Arthritis Rheum 43:531–540
Gordan C, Bachrach L, Carpenter T, Crabtree N et al (2008) Dual energy x-ray absorptiometry interpretation and reporting in children and adolescents: the 2007 ISCD pediatric official positions. J Clin Densitom 11:43–58
Kalkwarf H, Zemel B, Gilsanz V et al (2007) The bone mineral density in childhood study: bone mineral content and density according to age, sex, and race. J Clin Endocrinol Metab 92:2087–2099
Cole T, Green P (1992) Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med 11:1305–1319
Baptista F, Fragosa O, Vieira F (2007) Influence of body composition and weight-bearing physical activity in BMD of pre-pubertal children. Bone 40(Sup 1):S24–S25
Hogler W, Brioday J, Woodhead H, Chan A, Cowell C (2003) Importance of lean mass in the interpretation of total body densitometry in children and adolescents. J Pediatr 143:81–88
Hannon W, Cowen S, Wrate R, Barton J (1995) Improved prediction of bone mineral content and density. Arch Dis Child 72:147–149
Ellis K, Shypailo R, Hardin D et al (2001) Z score prediction model for assessment of bone mineral content in pediatric diseases. J Bone Miner Res 16:1658–1664
Horlick M, Wang J, Pierson R Jr, Thornton J (2004) Prediction models for evaluation of total body bone mass with dual-energy x-ray absorptiometry among children and adolescents. Pediatrics 114:E337–E345
Tanner J (1962) Growth at adolescence, 2nd edn. Blackwell Scientific, Oxford
Wainer H, Thissen D (1975) Multivariate semi-metric smoothing in multiple prediction. J Am Stat Assoc 70:568–573
Khamis H, Guo S (1993) Improvement in the Roche-Wainer-Thissen stature prediction model: a comparative study. Am J Hum Biol 5:669–679
Tukey J (1972) Exploratory data analysis, 2nd preliminary ed. Addison-Wesley, Reading, Chapter 8D
SAS Institute (2008) JMP statistics and graphics guide—fitting commands, JMP Version 8.0. SAS Institute, Cary
Tabachnick B, Fidell L (1996) Using multivariate statistics. Allyn & Bacon, Boston
Roche A (1992) Growth maturation, and body composition: the Fels longitudinal study. Cambridge University Press, Cambridge
Griffiths M, Noakes K, Pocock N (1997) Correcting the magnification error of fan beam densitometers. J Bone Miner Res 12:119–123
Moolgard C, Thomsen BL, Prentice A, Cole TJ, Michaelson KF (1997) Whole body bone mineral content in healthy children and adolescents. Arch Dis Child 76:9–15
Carter D, Bouxsein M, Marcus R (1992) New approaches for interpreting projected bone densitometry data. J Bone Miner Res 7:137–145
Draper N, Smith H (1998) Applied regression analysis. Springer, New York
Neter J, Wasserman W, Kutner M (1990) Applied linear statistical models. Irwin, Boston, pp 131–138
Acknowledgments
This work was funded by the National Institute of Child Health and Human Development (NICHD), contract number N01-HD-1-3328.
Conflict of interest
None
Author information
Authors and Affiliations
Corresponding author
Appendix 1: Statistical model creation
Appendix 1: Statistical model creation
For any data set, the total variation can be expressed as \( {\hbox{S}}{{\hbox{S}}_{\rm{tot}}} = \sum\nolimits_{i = 0}^n {{{\left( {{{\hbox{y}}_i} - \overline {\hbox{y}} } \right)}^2}}, \) where \( \overline y \) is the average of the set, and the degrees of freedom DoF tot as the total number of observations in the data set minus 1. For any model of that data set, the variation explained by the model can be expressed as \( {\hbox{S}}{{\hbox{S}}_{\rm{reg}}} = \sum\nolimits_{i = 0}^n {{{\left( {{{\hbox{y}}_i} - \widehat{\hbox{y}}} \right)}^2}}, \) where \( \widehat{y} \) is the predicted value from the model, and is equivalent to the sum of the squares of the ε’s in Eq. 1. The degrees of freedom of the model DoF reg is the number of parameters fit by the model. Finally, the variation in a data set unexplained by the model can be expressed as \( S{S_{\rm{err}}} = S{S_{\rm{tot}}} - S{S_{\rm{reg}}} \) and the degrees of freedom for the error as \( Do{F_{\rm{err}}} = Do{F_{\rm{tot}}} - Do{F_{\rm{reg}}} \).
The coefficient of determination, \( {R^2} = 1 - S{S_{\rm{err}}}/S{S_{\rm{tot}}} \), is a measure of how well the model fits the data. When adding terms to a model, R 2 always increases, even if the extra terms are not significantly adding explanatory value to the model. The adjusted coefficient of determination, adjusted \( {R^2} = 1 - \left( {S{S_{\rm{err}}}/S{S_{\rm{tot}}}} \right)/\left( {Do{F_{\rm{err}}}/Do{F_{\rm{tot}}}} \right) \), penalizes the statistic by accounting for the number of explanatory variables used in the model. It approximately measures the percentage of variation in the data accounted for by the model in a way that can be compared between competing models [23].
The root mean squared error, \( {\text{RMSE}} = {\sqrt {\frac{{SS_{\text{err}} }}{{DoF_{\text{err}} }}} } \), provides an estimate of the error for the model. The overall RMSE for the entire model is formed by using the total SS err and its degrees of freedom. In addition, each of the 64 age/gender/race subgroups also has an individual RMSE, formed by using each of the subgroups’ SS err and their respective degrees of freedom.
When more significant parameters are added to the model, the adjusted R 2 increases and the total RMSE usually decreases. When comparing two models, where model x is a more complex model and model z is a simpler model, the ratio of ((SS errz – SS errx )/SS errx)/((DoF errz – DoF errx)/DoF errx) becomes an F statistic that can be used to judge if adding the extra parameters makes model x a better fit for the data than model z [24].
Rights and permissions
About this article
Cite this article
Short, D.F., Zemel, B.S., Gilsanz, V. et al. Fitting of bone mineral density with consideration of anthropometric parameters. Osteoporos Int 22, 1047–1057 (2011). https://doi.org/10.1007/s00198-010-1284-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00198-010-1284-4