Z Score Prediction Model for Assessment of Bone Mineral Content in Pediatric Diseases*


  • Kenneth J. Ellis,

    Corresponding author
    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
    • Address reprint requests to: Kenneth J. Ellis, Ph.D., Body Composition Laboratory, U.S. Department of Agriculture/Agricultural Research, Service Children's Nutrition Research Center, 1100 Bates Street, Houston, TX 77030–2600, USA
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  • Roman J. Shypailo,

    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
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  • Dana S. Hardin,

    1. Department of Pediatrics, University of Texas Health Science Center, Houston, Texas, USA
    2. Texas Children's Hospital, Houston, Texas, USA
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  • Maria D. Perez,

    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
    2. Texas Children's Hospital, Houston, Texas, USA
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  • Kathleen J. Motil,

    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
    2. Texas Children's Hospital, Houston, Texas, USA
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  • William W. Wong,

    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
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  • Steven A. Abrams

    1. U.S. Department of Agriculture/Agricultural Research Service Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, Houston, Texas, USA
    2. Texas Children's Hospital, Houston, Texas, USA
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  • *

    This work is a publication of the USDA/ARS Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, and Texas Children's Hospital, Houston, TX. The contents of this publication do not necessarily reflect the views or policies of the USDA, nor does mention of trade names, commercial products, or organizations imply endorsement


The objective of this study was to develop an anthropometry-based prediction model for the assessment of bone mineral content (BMC) in children. Dual-energy X-ray absorptiometry (DXA) was used to measure whole-body BMC in a heterogeneous cohort of 982 healthy children, aged 5–18 years, from three ethnic groups (407 European- American [EA], 285 black, and 290 Mexican-American [MA]). The best model was based on log transformations of BMC and height, adjusted for age, gender, and ethnicity. The mean ± SD for the measured/predicted ln ratio was 1.000 ± 0.017 for the calibration population. The model was verified in a second independent group of 588 healthy children (measured/predicted ln ratio = 1.000 ± 0.018). For clinical use, the ratio values were converted to a standardized Z score scale. The whole-body BMC status of 106 children with various diseases (42 cystic fibrosis [CF], 29 juvenile dermatomyositis [JDM], 15 liver disease [LD], 6 Rett syndrome [RS], and 14 human immunodeficiency virus [HIV]) was evaluated. Thirty-nine patients had Z scores less than −1.5, which suggest low bone mineral mass. Furthermore, 22 of these patients had severe abnormalities as indicated by Z scores less than −2.5. These preliminary findings indicate that the prediction model should prove useful in determining potential bone mineral deficits in individual pediatric patients.


DUAL-ENERGY X-RAY absorptiometry (DXA) has become a standard technique for the measurement of bone mineral density (BMD) of the lumbar spine, femur, forearm, and whole body.(1, 2) Although these data have contributed significantly to our basic understanding of the physiological processes of growth and aging, the comparison of an individual's value with a reference range has gained the most widespread clinical use. For adults, the two most common comparisons are called the Z score and T score, respectively.3-5) The Z score provides a comparison with healthy subjects of the same age, while the T score provides a comparison with healthy young adults (20-29 years). The intent of the T score for adults is not to provide an age-matched comparison, but to estimate the loss of bone relative to peak density.(4, 5) For children, the T score concept cannot be used, because peak bone density is not reached until late adolescence or early adulthood. A prediction model that uses only age may not be sufficient because it would not account for the wide variations in growth patterns during childhood. Therefore, we are proposing that an anthropometric-based model for the prediction of bone mineral mass of children is needed.

For adults, clinical evaluations of bone status are based on BMD, defined as the ratio of bone mineral content (BMC) to the two-dimensional projected image of bone area (BA). The size and geometry of the adult skeleton remains relatively stable over many years; thus, BA remains relatively constant for the individual. BMD has a lower variance than BMC; therefore, it has evolved as the bone parameter to assess abnormal conditions. This approach at normalization of BMC is unsatisfactory for use in children, because both BMC and BA are changing during growth.(6) Some investigators have introduced variations of the basic BMC/BA ratio in an effort to account for the true bone volume, but these models have met with limited success and are difficult to interpret when the whole body is measured.(7, 8)

The ability to obtain DXA scans in children in a few minutes with good precision and accuracy(9, 10) has contributed to its increasing clinical use in pediatrics. For the spine or femur measurement, an age-matched Z score rating usually is provided; however, no rating is available for whole-body pediatric measurements. Any normalization procedure for DXA measurements in children should be based on a model derived from a reference population of healthy children.11-14) The specific aims of this study were (1) to develop and verify an anthropometric-based prediction model for whole-body BMC in children, and (2) to assess the bone status of children with various diseases.


Reference population

A total of 982 healthy children, aged 5-18 years, participated in this study. There were 537 females and 445 males distributed among three ethnic groups: 407 European-Americans (EA), 285 blacks (AA), and 290 Mexican-Americans (MA). Trained pediatric research nurses performed all anthropometric measurements. Body weight (Wt) was measured on a calibrated digital scale to ±0.1 kg; height (Ht) was recorded to the nearest ±0.5 cm using a stadiometer (Holtain, Ltd., Crymmych, Pembs, UK). The protocol for the reference population was approved by the Baylor College of Medicine Institutional Review Board for Human Studies, and informed consent was obtained from a parent or guardian of each subject.

Clinical groups

A total of 106 children who had cystic fibrosis (CF), juvenile dermatomyositis (JDM), liver disease (LD), Rett syndrome (RS), or tested positive for the human immunodeficiency virus (HIV) were examined. These children represented a broad spectrum of clinical conditions that varied in duration and severity of illness, types of clinical treatments, and length of therapy. Wt was measured to ±0.1 kg, and Ht was measured to ±0.5 cm. All clinical research protocols were approved by Baylor's Institutional Review Board for Human Studies and informed consent was obtained from a parent or guardian.

Bone mineral measurements

Whole-body DXA scans were obtained using a Hologic QDR-2000W instrument operated in the pencil-beam mode and analyzed using body composition software version 5.56 (Hologic, Inc., Waltham, MA, USA). Certified DXA technologists performed all measurements. Three bone parameters were recorded: BMC, BA, and BMD. For children, the precision for BMC and BA has been shown to be 1-2%.(9, 10)

Statistical analyses

Statistical analyses were performed using MINITAB (version 12; Minitab, Inc., State College, PA, USA). Values provided in the tables are mean ± SD and differences among groups were tested using t-test statistics. The SE of the estimate (SEE) was obtained for linear regression analysis, and used to define the 95% confidence limits in figures. The general linear model was used in the analysis of variance (ANOVA) to test for gender and ethnic differences. The selection for parameters to include in the prediction model was based on stepwise multiple regression analysis with and without log transformation of the data. A value of p < 0.05 was considered significant.

Prediction model

Whole-body BMC was used as the dependent parameter for all prediction models. The independent or prediction variables were age, Ht, Wt, gender, and ethnicity. Models were tested with and without log transformation of the Ht, Wt, and BMC data. Log transformations were used to account for the curvilinear relationship observed between bone mineral and body size.(11, 12) The prediction model was derived for a reference (calibration) population of 982 healthy children. The best prediction model, defined based on the lowest SEE value, was achieved using natural log transformations for BMC and Ht. The form of the prediction model was ln BMC = α1 × ln Ht + α2 × age + α3 × ethnicity (r2 = 0.93-0.95; p < 0.00001), where ln denotes the natural log. The values for the constants (αi) were gender dependent, while ANOVA showed that the ethnicity code could be reduced to two levels (AA vs. EA + MA). The accuracy of the prediction model for the calibration population was tested using the ln ratio, defined as lnBMCmeasured/lnBMCpredicted. The ln ratio was used because the lnBMC-lnHt relationship was linear, and the conversion of the SEE to the BMC scale would result in a nonuniform interval. Validation of the prediction model was tested using an independent (validation) group of 588 healthy children. For clinical assessment, the mean and SD values for the ln ratio were converted to a standardized Z score scale.


The basic anthropometric data and bone mineral values for the calibration population are given in Table 1. Although there were differences in the mean values for boys among the ethnic groups, only the BMD of the AA group reached statistical significance (p ≤ 0.05) when compared with the EA group. For the girls, more of the ethnic differences were statistically significant. The AA girls were heavier by about 7 kg (p < 0.001), while the MA girls were shorter by about 5 cm (p < 0.01) when compared with the EA girls. These differences resulted in the higher body mass index (BMI) values (p < 0.001) for both the AA and MA girls when compared with the EA group. The mean BMC and BMD values for the AA girls also were significantly higher (p < 0.001) when compared with the EA and MA groups.

Table Table 1.. Anthropometric and Bone Mineral Values for the Calibration Population (Mean ± SD)
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The relation between measured and predicted values for whole-body BMC are shown in Fig. 1 for the girls in the calibration and validation populations. For the female calibration population, the mean ln-ratio was 1.000 ± 0.0175; the ln ratio for the male calibration population was 1.000 ± 0.0180. It is expected that the mean ratios would be one for these two groups because they were used to derive the prediction models. The SD values show the degree of discordance between the measured and predicted values. At 2 SD or approximately 95% of the calibration population, there was agreement to within ±3.5% for the ln ratio. The validity of the prediction model was tested in a second independent group of 588 healthy children. The mean ± SD for the ln ratio for this second group (validation population) was 0.996 ± 0.018, which confirmed the accuracy of the prediction model for healthy children.(15)

Figure FIG. 1.

Relation between the measured and predicted whole-body BMC for healthy females in the calibration (○) and validation (▪) populations.

The anthropometric data and DXA results for the different clinical groups are summarized in Table 2. For the males, only the CF group had a lower mean Wt (p < 0.01) than healthy controls. Ht for boys with CF (p < 0.02) and LD (p < 0.005) were lower than observed of the healthy population. Only the CF males, as a group, had a lower BMC (p < 0.003) than healthy males, whereas the CF, HIV, and LD groups had lower BMD values (p < 0.03-0.002).

Table Table 2.. Anthropometric and Bone Mineral Values for the Clinical Groups (Mean ± SD)
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In the clinical groups we examined, differences related to ethnicity tended to be statistically significant more often for the girls than for the boys. As a group, the HIV+ females were younger (p < 0.01) than the reference population. All the female clinical groups, except for the JDM girls, had lower Wt (p < 0.05-0.003) than the reference healthy girls. The CF, HIV, and LD female groups also had shorter stature (p < 0.05-0.001). Because Wt and Ht were below normal for age for many of the children in the clinical groups, it is not surprising that mean BMI also was outside of the normal range (p < 0.05-0.001). The children in the CF, HIV, LD, and RS groups had significantly lower mean BMC compared with healthy controls. Only the JDM and CF groups had mean BMD results that were within a normal range.

It is a relatively common pediatric practice to make only age-based comparisons among children. In Fig. 2 (panel A, boys; panel B, girls), we have presented the whole-body BMC values as a function of age for the different clinical groups. The two outer lines in the figures represent the upper and lower 95% confidence limits based on the healthy EA reference populations; the center line represents the average values for these populations. It is evident that many of the male patients (Fig. 2A) had BMC values that were below the average but still within the 95% confidence range. However, 9 boys (2 JDM, 5 CF, and 2 LD) did have BMC values below the lower limit. Ten girls (5 CF, 1 JDM, 2 LD, and 2 RS) also had BMC values below the lower limit (panel B). The distribution of BMC values between the two limits for the girls in the clinical groups showed no strong bias toward lower values, as was observed for the boys. The presentation of the BMC data in these graphs do not take into consideration the patient's stature or ethnicity.

Figure FIG. 2.

Whole-body BMC versus age for (A) boys and (B) girls. The two outer lines represent the 95% confidence limits about the average value (center curve) for healthy white children. The disease groups are CF, JDM, LD, HIV, and RS.

The results for the clinical groups, based on a comparison using the prediction model that considers Ht, age, gender, and ethnicity are shown in Fig. 3. The individual Z scores for the 106 patients ranged from +1.8 to −7.5. The results among the clinical groups differed. For the CF patients, the Z scores varied from +1.5 to −4.0, while the values for the HIV and JDM children was basically within ±2. Most (14/15) of the LD children had negative Z scores including the lowest value (−7.5) observed for all the clinical patients. The RS girls had the most significant bone mineral deficit because all 6 patients had Z scores below −3. When the 106 patients were considered together as a single group, there was evidence of a gradual decline in Z scores with increasing age at the rate of 1 U per 5- to 6-year period (p < 0.01).

Figure FIG. 3.

Relative Z score (adjusted for Ht, age, gender, and ethnicity) for whole-body BMC for children with CF, JDM, LD, HIV, and RS.

The mean Z scores and SD for each clinical group are summarized in Table 3. The mean Z score values for the CF, JDM, and LD groups were approximately −1, whereas the value for the HIV group was slightly positive. As noted previously in Fig. 3, the RS group clearly had the most significant bone mineralization defect with a mean Z score of −4.9. Additional information about the relative distribution of Z score values within a clinical group is provided in Table 3. Three ranges for the Z score for whole-body BMC were selected: Z > −1.5 (normal), −2.5 < Z ≤ −1.5 (osteopenia), Z ≤ −2.5 (osteoporosis). Using these classifications, about 1 in 4 of the JDM children, 1 in 3 of the LD children, and 1 in 2 of the CF children had Z scores below the normal range. All of the RS girls had whole-body BMC values that classified them in the most severe range.

Table Table 3.. Z Score Results for Whole-Body BMC for Pediatric Clinical Groups
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We have developed an anthropometry-based prediction model for the assessment of whole-body BMC in children. The dominant prediction parameter was Ht, followed by age, with adjustments needed for gender and ethnicity. The mean and SD values we obtained for the ln ratio (lnBMCmeas/lnBMCpred = 1.000 ± 0.017) for the calibration population of 982 healthy children showed the prediction accuracy of the model for an individual child within that population. Furthermore, we confirmed the accuracy of the prediction model when it was tested using the validation population (second independent group of 588 healthy children). The log transformation of the BMC and Ht values in the model also confirmed the curvilinear relationship between stature and bone mineral mass during normal growth. The age term in the model suggests that some aspects of bone mineralization may be timed differently than those that determine stature. That is, if two children have the same Ht, the older child will tend to have a higher BMC. Furthermore, inclusion of gender and ethnicity in the prediction model validates each factor's independent influences on the mineralization process. The need for gender-specific coefficients for each term of the model confirms the known differences in bone mineral mass between boys and girls.11-13) Likewise, further refinement of the prediction model was achieved by inclusion of the term for ethnicity. This indicates that black children on average will have higher BMC values than age- and Ht-matched EA or MA children. We conclude that all of these factors (Ht, age, gender, and ethnicity) need to be taken into consideration when normalization of whole-body BMC data between groups is desired.

Although Ht is the dominant parameter in the prediction model, the effects of age and ethnicity within a gender group are of sufficient magnitude that they should not be ignored. Exclusion of these indices would only increase the SD for the ln ratio calculation, which in turn would reduce the accuracy of a Z score for the patient. To simply match patients with healthy controls of the same age is not adequate, nor would it be appropriate to match patients based only on Ht without consideration of differences in age.

We have previously shown that whole-body BMC is highly correlated with the body's lean tissue mass (LTM) and BA.(11, 12) Initially we considered using these parameters in the prediction model, but in the final analysis chose to limit our selection to anthropometric indices that are obtained routinely. Our reasoning for exclusion of LTM and BA from the prediction model was 2-fold. First, LTM and/or BA could be abnormal themselves in some clinical conditions. Thus, it would make no sense to evaluate bone relative to an abnormal reference. Second, LTM and BA are derived from the same measurement as BMC, whereas any reference parameters used in a prediction model should be obtained independent of BMC. We also tested the inclusion of Wt as a prediction parameter, but found that it reduced the total variance by only a few percent. Furthermore, we were concerned that some diseases might dramatically alter body Wt (e.g., Prader-Willi syndrome or anorexia nervosa), which would introduce an unwanted bias in the predicted value. Thus, if a patient had a rapid Wt change, it would alter the predicted BMC value significantly, which in turn would make it difficult to detect a true change in BMC.

Only a few studies have reported relationships between anthropometric body indices and BMC or BMD in healthy children.11-14, 16-18) In most instances, only simple linear regressions were used. No attempt to account for the nonlinear relationship between BMC and Ht has been reported. For example, Molgaard et al.(16) provided mean BMC estimates for age and Ht groups separately, but not for the two parameters combined. Nelson et al.(17) reported prediction equations for BMC of children aged 8-10 years as a function of lnWt adjusted for ethnicity. On the other hand, Goulding et al.(18) reported a relation for lnBMC versus lnWt in white children. When we tested this relationship in our EA children, we obtained the same results for girls as reported by Goulding et al.,(18) but not for boys. Hannan et al.(13) provided three different prediction equations for whole-body BMC for adolescent girls (aged 11-18 years) based on age, Wt, Ht, and shoulder width. When only age was used, the mean prediction error was 291 g, which was reduced to 151 g when Wt and Ht were included. The addition of shoulder width reduced the error to 134 g. In a preliminary study of the females in our reference population, we reported an SEE of 160 g for EA girls when age, Wt, and Ht were used in a linear model.(11)

DXA is most commonly used to assess BMD of the lumbar spine or femur, which has proven useful for assessing the risk of osteoporosis in peri- and postmenopausal women. By comparison, only a few clinical centers perform DXA measurements in children. Several reasons probably contribute to this fact. First, most clinical centers performing DXA scans do not routinely examine children; thus, the staff is not trained properly. Second, Z score results are available only for BMD of the lumbar spine for children. That is, no Z score rating scheme for whole-body BMC measurement in children has been previously developed. Consequently, it is difficult to make direct comparisons of our findings for the different clinical groups with other studies. In one study, 1 in 3 CF patients had low BMD Z scores (≤ −2) at one or more regional skeletal sites, while in another study whole-body BMC values were significantly lower than those of gender- and age-matched healthy controls.(19, 20) In a third CF study, a BMC deficit of about 19% was reported for children and adolescents.(21) In contrast, Salamoni et al.(22) reported that whole-body BMC values of well-nourished CF children were not different from those of healthy controls.

There is a paucity of data in the literature to compare the BMC data for the children with the other diseases that we examined. Increased bone loss has been reported in adults who tested positive for HIV while receiving antiretroviral therapy,(23) which may raise concerns for the long-term effects of these drugs if used in children. Bone disorders present a significant complication of chronic LD.(24) BMC values for the radius of LD children, for example, can be 2-4 SDs below the mean when compared with those of age-matched healthy controls.(25) Regional BMD values for patients with RS have reported as abnormally low, in confirmation of our assessment of the whole-body BMC of girls with this diagnosis.(26)

We have developed an effective model for the prediction of whole-body BMC in children. We have shown that the DXA measurements of children with diseases, when standardized with this reference model, can provide a useful assessment of the patient's bone mineral status. That is, we believe that obtaining the BMC value without some means of comparing it to a reference or normal range is of limited use. We have confirmed the accuracy of our model in that the prevalence rates for abnormal bone mineral status in these diseases are consistent with those reported in the literature. The practical use of our Z score index also has been satisfactorily tested at other pediatric clinical research centers in the United States and Europe.(27, 28) We will continue to investigate whether further refinements to the prediction model are needed as we test its performance with more pediatric patients who may have potential bone mineralization abnormalities. In the interim, a Web site (http://www.bcm.tmc.edu/cnrc/bodycomplab) is available in which a Z score rating can be obtained by entering the appropriate anthropometric and DXA data.


We acknowledge the contributions of J.A. Pratt and K.E. Molina for the DXA measurements, the nursing staff of the Metabolic Research Unit for performing the anthropometric measurements, and L. Loddeke for editorial assistance in the preparation of this article. This work is supported by the U.S. Department of Agriculture, Agricultural Research Service under Cooperative Agreement 58-6250-6-001 with Baylor College of Medicine.