estimate body composition of children is not an easy task , since the relationships between body components during growth are not constant as in adults .
anthropometric - based equations remain an adequate alternative for determining the body composition of pediatric populations in field settings .
however , the advent of new technologies has enabled new ways for body composition assessment , thus , rendering the traditional anthropometry inaccuracy as a representative standard .
there are some methodological concerns when using the current anthropometric models : several equations have been developed using a two - compartment model ( 2c model ) either using hydrostatic weighing [ 2 , 3 ] or other densitometric techniques ; however , this approach relies on assumptions , specifically concerning the fat - free mass ( ffm ) density ( 1.1  g / cc ) and hydration ( 73.2% of total - body water within the ffm ) that , although stable for adults , may vary substantially during growth .
in fact , from childhood through adolescence , total - body water ( tbw ) decreases whereas bone mass increases which means that ffm density is lower than 1.1  g / cc , at younger ages , approaching that value when chemical maturity is reached .
therefore , 2c models tend to overestimate fm and underestimate ffm in children , and their use as a criterion method for developing anthropometric - based models is inaccurate . for that reason , the use of 3c and 4c compartment models are preferred for determining the body composition in children , since fewer assumptions are used as more ffm components are measured .
the advent of dual - energy x - ray absorptiometry ( dxa ) , measures of fm , bone mineral content ( bmc ) , and lean soft tissue ( lst ) are obtained .
hence , dxa can be considered as a 3c model since the estimates of three components are obtained as follows : first by separating pixels into those with soft tissue only ( fm plus lst ) and those with soft tissue plus bmc , based on two different photon energies ( lower and higher energies , resp . ) .
the dxa provides precise [ 6 , 7 ] and accurate [ 811 ] measures of fm and ffm ( as lst plus bmc ) when compared to multicompartment models .
in addition , given its low risk and quick assessment , the dxa use has been implemented in large multicenter studies , including the national health and nutrition examination survey .
however , the availability of dxa in the clinical and fields settings is limited given its cost .
therefore , simple solutions are required for estimating body composition in children and anthropometric parameters , such as skinfolds and circumferences , which have been widely used as bedside techniques in different contexts .
thus , the aim of this study was to develop and cross - validate multicomponent - anthropometric - based equations to simultaneously estimate fm , bmc , and lst in a male pediatric population , using dxa as the criterion method .
the study followed a cross - sectional design , consisting of a sample of 408 young males between 8 and 18 years of age .
the subjects were recruited voluntarily from a population of students that could be engaged in systematic programs of sports , or not , considered as athletes and nonathletes , respectively .
the athletes came from sports centers ( n = 177 ) and nonathletes from schools ( n = 231 ) .
children with a regular sports practice were engaged in soccer field ( n = 143 ) , athletics ( n = 11 ) , football court ( n = 20 ) , and judo ( n = 3 ) .
the nonathletes came from public ( n = 142 ) and private ( n = 89 ) school .
medical examinations were conducted to assure that children were healthy and not taking medications that could affect metabolism , appetite , or growth .
the number of white participants was relatively higher ( n = 270 ) compared to blacks ( n = 79 ) , hispanics ( n = 50 ) , and asians ( n = 9 ) , classified by race self - declared .
this sample comes from a large ethnic mixture and previous analysis that showed no statistical differences in interracial body composition ( data not shown ) , so , the final samples ( n = 408 ) were considered as uniform . to determine the sample size
, we followed the bolfarine and bussab   recommendation , and based on a pilot analysis with subjects presenting a large variance in the dependent variable ( fm ) , the estimation of the desired error ( 1.25% ) and confidence interval ( 95% ) determined that at least 300 subjects would be required .
the study followed the guidelines and regulations of directing human research , and agreements were obtained from the parents or guardians to all procedures .
the approval was granted by the ethics in research department of the school of physical education and sport , university of so paulo ( cep332007/eefe/04.04.2007 - 2006/32 ) , which also adhere to the helsinki declaration .
each subject was evaluated in the laboratory , in the morning after an overnight fast , in a single session , and always by the same examiner , and all measurements , were performed during a period of three months . before the measurements the subjects were asked to empty their bladders .
dressed in shorts and shirt , the total - body dxa examination was applied using the system for total - body scan , according to manufacturer 's guidelines .
the anthropometric measures were performed according to the literature recommendations [ 14 , 15 ] , summarized below .  
whole and regional body composition was estimated with a dxa scanner lunar dpx - nt ( ge medical , software lunar dpx encore 2007 version 11.40.004 , madison , wi ) .
the software identified the physical characteristics of ethnicity , gender , and age and automatically adjusted the scan mode , speed , and images resolution .   body weight was determined from dxa , and the dependent variables of interest were fat mass ( fm , kg ) , bone mineral content ( bmc , kg ) , and lean soft tissue ( lst , kg ) .
the subject body mass , height , and seating height   were measured with a digital scale ( filizola , pl 200 , campo grande , ms ) and a fixed wall stadiometer ( sanny professional - es2020 , so paulo , sp ) , respectively . the skinfolds ( biceps , triceps , subscapular , chest , midaxillary , suprailiac , vertical abdominal , horizontal abdominal , mid - thigh , and medial calf ) , circumferences ( chest , relaxed arm , contracted arm , forearm , wrist , waist , abdominal , hip , proximal thigh , and calf ) , and breadths ( biacromial , biiliac , chest , elbow , bitrochanteric , wrist , knee , and bimalleolar ) were measured by conventional procedures stated in the literature [ 15 , 16 ] using sanny scientific equipment . 

the maturity offset was predicted by gender - specific regression equations based upon noninvasive techniques , using chronological age , height , body mass , sitting height , and leg length measurements .
the method predicts years from peak height velocity ( phv ) according to the mirwald et al .  
equation for boys : 
 ( 1)phv=9.236 + 0.0002708(lhsh)0.001663(alh)+0.007216(ash)+0.02292(wt / ht100 ) , 
 where lh stands for legs height ( cm ) , sh for seating height ( cm ) , a for age ( years ) , wt for body weight ( kg ) , and ht for height ( cm ) . 

chronological ages were based on birth year and grouped in decimal values adjusted to the nearest integer . to ensure the precision of the results , intra evaluator technical errors of measurement absolute ( tem ) and relative ( tem% ) were calculated ( table 1 ) . in subsequent days , duplicates for all measures were applied in thirteen subjects , when the results were always within the expected tolerance limits .
, chicago , il ) was used to analyze the data of descriptive statistics ( mean , standard deviation , range , technical error of measure relative , absolute , and the confidence interval 
ci 95% ) were used to describe the sample , and correlation coefficient was applied to verify the basic assumption of the relations between dependent and independent variables . for developing the multicomponent anthropometric equation ,
a multivariate regression model ( nym = nx(r+1)(r+1)m + nm ) was utilized as diagonal mutual analysis , parameter estimation , and the least squares errors method by r - free software . when the choice of remaining variables the following criteria were used ( a ) maintenance of a high correlation between independent and dependent variables , ( b ) uniformity of the data , ( c ) centralized distribution of the residuals , ( e ) reducing the number of independent variables while maintaining the highest levels of significance after stepwise , with adjustments by the pillai approach to test the f values , ( f ) multicollinearity tolerated , ( g ) determining the  values in a multivariate model , and ( h ) remaining of the high precision and validity of the final model .
for performing the validation of the models we used thepress statistic . from the deletion of an observation , proposed equations with the remaining sample are conducted , and the process is repeated .
the press statistic is defined as the sum of squares of residuals ( press ) in : 
 ( 2 ) 
 press 
 = i=1n[yiy^(i)]2 .
thus , a model with a high degree of predictability for excluded observations gives the value of the rpress ( close to 1 ) and a standard estimated error ( seepress ) near zero . in summary ,
the validation procedure that uses press is similar to the application of the equation to an independent sample .
characteristics of the total sample are shown in table 1 , including range ( minimum  maximum ) , tem , tem% , and confidence interval ( 95% ) . 

table 2 presents the correlation matrix within some of the 32 independents , including size measures , skinfolds , circumferences , breadths , and maturation by phv with and the dependent variables . a centered distribution of the residuals ( differences )
was observed for the response components ( figure 1 ) . from all 32 initial variables used as predictors of the dependent variables ,
a stepwise regression was performed individually for fm , bmc , and lst in order to select the common variables for all three components , with the higher significance level .
the number of predictor variables was reduced after 27 eliminations , and a final model was obtained with five independent variables and high precision ( r ) , meaning that the models largely explained the variance of the dependent variables ( table 3 ) . here
the estimated parameters vector (  ) of the model was obtained for each variable , resulting in a single model for all dependent variables ( table 3 ) . from the multivariate parameters , it was possible to predict simultaneously each body component ( fm , bmc , and lst ) , considering the interrelationship of dependent variables , unlike the traditional methods ( one - dimensional analysis ) .
multicollinearity within the final independent variables was tested , and cases were found in which the variables were highly collinear . in those cases , an independent variable in the model was eliminated and performed the ratio between the largest and the lowest eigenvalues , until resulting in a final product with only moderate multicollinearity (  = 167.0637 ) . 

table 4 summarizes mean values and standard deviations for the descriptive characteristics obtained from the dxa scan by age group .
the fm showed increases up to the age of 13 , which tend to stabilize .
all other significant differences for subsequent ages in bmc were found from 11- to 12-year - old age group ( p = 0.021 ) , from 13- to 14-year - old age group ( p = 0.001 ) , and from 14- to 15-year - old age group ( p = 0.001 ) ; for lst , the differences were found from 11- to 12-year - old age group ( p = 0.001 ) , from 13- to 14-year - old age group ( p = 0.001 ) , and from 14- to 15-year - old age group ( p = 0.001 ) .
the correlations between the predicted values ( of the model ) and those observed ( by dxa ) in fm , bmc , and lst ( figure 2 ) showed an increased dispersion at higher scores of body composition . the press related statistics ( r ) ,
adjusted coefficients of determination ( adj  r ) , and standard error of estimate ( seeresidual ) for residual analysis are showed in table 3 . in this study , the error was determined by the outcome of y - observed minus y - estimated .
parameters of internal validation included rpress statistic and seepress , as observed in table 3 .
the model is valid according to the assumptions defined in the methodology , where rpress should be close to  1  and seepress near  0  .
then , the final model for each dependent variable could be expressed as 
 ( 3)fm=  0.0857  height+0.3139  weight  + 0.1970  sksi+0.2350  skhab0.6571  phv , bmc=0.0032  height+0.0392  weight  0.0095  sksi0.0105  skhab+0.0525  phv , lst=0.0820  height+0.6419  weight  0.1964  sksi0.2321  skhab+0.7047  phv , 
 where sksi stands for suprailiac skinfold ( mm ) , skhab for horizontal abdominal skinfold ( mm ) , and phv for peak height velocity ( years ) .
the multicomponent model approach presented in this study showed a high correlation in most comparisons between independent and dependent variables ( table 2 ) , suggesting the possibility of using these variables as an alternative method .
the multicomponent determination of body composition during growth finds application in field and clinical settings allowing specific definition for the component of interest . in sports , for example ,
monitoring the training process to reduce fm or increase lean mass may be of interest to technicians , aiming to improve sports performance .
for most cases , the uncertainty of which component has contributed to an increase in body weight may compromise an adequate decision for exercise prescription , since the true relationships between fm and ffm are not known .
therefore , an accurate and precise body composition estimation is required using simple methods . in the present study ,
the greater associations of fm were observed with skinfolds , bmc , with growth components ( height , weight , breadth , and pvc ) and lst with growth components and circumferences ( table 2 ) , expressing the real expected relationships between the types of measurements and the components measured in a combined prediction .
this is so because the combined estimation of the parameters produces zero restrictions on coefficients of other equations .
the relationship between the predictors and the response variables must be strong .   however , the robustness of the model can be compromised if there is multicollinearity between independent variables .
therefore , the elimination of independent variables was required , and those who are not commonly used in the literature or without a high predictive significance were removed . apart from being a practical model , the least number of possible variables should be considered . in this case , the estimates of regression coefficients become very sensitive to small changes in the planning matrix .
the variations of the estimators are high , making testing of h0 : j = 0 versus ha : j  0  diff = 0 ; therefore , important independent variables could mistakenly be removed .
one of the assumptions of the linear model is that the rank of the matrix ( xx ) is equal to k + 1 .
thus , in addition to moderate multicollinearity (  = 167.0637 ) and near the bottom of this classification ( from 100 to 1000 )   and the determinant away from zero , the rank axis of xx matrix is complete . then , there is its classical inverse ( xx ) [ det ( xx )  0 ] , multiplied by the right side of the normal equation system , allowing the  obtaining the least squares estimator .
the classical inverse matrix procedure was calculated , resulting in the root close to the efficiency characteristic , once the issue of moderate multicollinearity was observed , near to lower limit .
the gain in predictive efficiency in the use of multivariate analysis in relation to various regressions is well proven . basically , this is true because the efficiency jointly estimates the parameters and produces zero restrictions on coefficients of other equations , with the same error as vectors of estimated betas , enhancing the prediction .
so far , only the fm has been predicted by pediatric anthropometric models , determined by anthropometric - based models which have been developed against densitometric techniques in children [ 2 , 3 , 2426 ] showing relatively low ability in predicting the variability of the reference method ( r < 0.80 ) when compared to those developed from the present study ( table 3 ) .
however , investigations can be controversial when very young or very obese children are involved in the observations , and the literature expresses caution in the estimation of body composition when bmi is high [ 1 , 28 , 29 ] .
the model proposed in this study was able to predict the body composition also of overweight subjects according to the cole et al .  
cutoff points ( 11 cases ) . even if these cases were removed , the accuracy of the model remained similar , confirming a possible generalization of the predictive equations for assessing overweight children .
the method of internal validity adopted   confirmed the effectiveness of the model to predict the components of body composition with a high internal validity ( rpress = 0.94 to 0.98 ) and low proportional errors of estimation ( seepress = 0.01 to 0.09 ) , that is , a score rpress = 0.9490 for fm ( table 3 ) may explain about 94.90% of the variability in predicting new observations in independent samples , compared with about 98.08% of variability in the original data , explained by the least squares ( r ) method .
also , the high independent rpress ( 94.02% and 98.04% ) , respectively , for bmc and lst indicates the strength of the model in predicting the lean body composition of young males between 8 and 18 years of age .
these results provide the generalizability of the model , even when the variance of body composition is high .
the low dispersion of the measured and predicted values for the body components ( figure 2 ) seems to confirm this hypothesis . to facilitate a better understanding of the practical utility of the model ,
we show the following example for predicting fm , bmc , and lst in a 13-year old boy ( table 5 ) . after obtaining , the measures ( independent variables ) of height , weight , maturation ( phv ) , and skinfolds ( suprailiac and horizontal abdominal )
the products of each measure , multiplied by its  coefficient regression , result in absolute values ( kg ) for fm , bmc , and lst .
a limitation of this study is that although dxa was used as a reference method to develop our model , this technique is not considered the gold standard for pediatric populations . a four - compartment model ( 4c model )
is actually the most strong model for accurately assesses body composition in children as it accounts for the variability of the main ffm components . though its use is recommended as criterion , this method is time - consuming and requires sophisticated equipment , specialized technicians , and high costs which make it difficult for use in large samples .
in addition , the 4c model is not free of errors , considering the number of required techniques necessary for determining the main ffm constituents ( water and mineral )
. therefore , the use of dxa is an alternative chosen by several investigators to develop predictive equations for children and adolescents [ 25 , 3338 ] .
in fact , a recent study revealed dxa as a precise and valid method for body composition assessment .
another limitation that needs to be addressed is the ethnical differences of this sample , who could limit the generalization of the equations to other populations .
therefore , further studies are recommended that examine the accuracy of the models before its application .  
concluding , new anthropometric - based model for assessing body composition of children and adolescent males was proposed . considering the unavailability of sophisticated instruments in field and clinical settings , these models proved to be a valid and alternative solution to estimate body composition in a male pediatric population .
 the aim of this study was to propose and cross - validate an anthropometric model for the simultaneous estimation of fat mass ( fm ) , bone mineral content ( bmc ) , and lean soft tissue ( lst ) using dxa as the reference method . 
 a total of 408 boys ( 818 years ) were included in this sample . 
 whole - body fm , bmc , and lst were measured by dxa and considered as dependent variables . 
 independent variables included thirty - two anthropometrics measurements and maturity offset determined by the mirwald equation . from a multivariate regression model ( ymn = x(r + 1)(r + 1)nm + nm ) , a matrix analysis was performed resulting in a multicomponent anthropometric model . 
 the cross - validation was executed through the sum of squares of residuals ( press ) method . 
 five anthropometric variables predicted simultaneously fm , bmc , and lst . 
 cross - validation parameters indicated that the new model is accurate with high rpress2 values ranging from 0.94 to 0.98 and standard error of estimate ranging from 0.01 to 0.09 . 
 the newly proposed model represents an alternative to accurately assess the body composition in male pediatric ages . 
1. Introduction
2. Methods
3. Results
4. Discussion