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Original Research Communications |
1 From the Departments of Exercise Science and Foods and Nutrition, The University of Georgia, Athens.
| ABSTRACT |
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Objective: Estimates of changes in percentage body fat (%BF) from dual-energy X-ray absorptiometry (DXA), skinfold thicknesses (SFTs), bioelectrical impedance analysis (BIA), and body mass index (BMI; in kg/m2) were compared with estimates from a 4-component (fat, water, mineral, and protein) model (%BFd,w,m), a more accurate method.
Design: Determinations of body density from hydrostatic weighing, body water from deuterium dilution, bone mineral and %BF from whole-body DXA, resistance from BIA, and anthropometric measures were made in 27 obese women (BMI: 31.1 ± 4.9) assigned to 1 of 3 groups: control (C; n = 9), diet only (DO; n = 9), or diet plus aerobic exercise (DE; n = 9).
Results: After the 16-wk intervention, changes in body mass (BM) averaged 0.5 ± 2.0, -7.2 ± 7.4, and -4.0 ± 3.3 kg and changes in %BFd,w,m averaged 2.1 ± 1.0%, -1.2 ± 1.4%, and -2.4 ± 1.6% in the C, DO, and DE groups, respectively. Compared with changes in %BFd,w,m, the errors (SD of bias) for estimates of changes in %BF by DXA, BIA, SFTs, and BMI were similar (range: ±2.02.4% of BM). BIA, SFTs, and BMI provided unbiased estimates of decreases in %BFd,w,m, but DXA overestimated decreases in %BF in the DO and DE groups.
Conclusions: DXA, BIA, SFTs, and BMI are comparably accurate for evaluating body-composition changes induced by diet and exercise interventions; however, small changes in %BF may not be accurately detected by these clinical methods.
Key Words: Bioelectrical impedance analysis BIA body mass index dual-energy X-ray absorptiometry DXA multicomponent models anthropometric measures skinfold thickness weight loss body composition exercise humans
| INTRODUCTION |
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Most methods available to clinicians for estimating body-composition changes, including estimates from dual-energy X-ray absorptiometry (DXA), bioelectrical impedance analysis (BIA), skinfold thicknesses (SFTs), and body mass index (BMI; in kg/m2) have been validated against estimates from densitometry, which has been considered the gold standard of indirect laboratory methods (2). Estimation of body fatness from body density (db) assumes that the density of fat is 0.9 kg/L and that the density of FFM (DFFM) is 1.1 kg/L (3). The assumption that the DFFM is 1.1 kg/L is, in theory, based on the assumption that the proportions and densities of the constituents of FFM are uniform across individuals. The SD of
0.01 kg/L for the DFFM suggests that its assumed constancy leads to an error in estimating body composition of approximately ±4% in the general population (4).
Body-composition estimates from a 4-component model (fat, water, mineral, and protein) account for variation in the water and mineral fractions of FFM, the largest sources of variability in the DFFM. Therefore, 4-component models provide more accurate estimates of body composition than do other methods and are a better criterion measure for validating other methods used to estimate body composition (4). Few studies have validated clinical methods used to evaluate changes in body composition resulting from weight loss using estimates from a 4-component model as the criterion (5, 6). Because of the inadequate criteria used to validate these clinical methods, it is possible that they may be more or less accurate for assessing body-composition changes than thought previously.
Research suggests that the composition of the weight lost as a result of diet combined with exercise is different from that lost as a result of energy restriction alone: with the former intervention there is a greater loss of FM, and FFM is maintained (7, 8). However, this conclusion is based almost entirely on studies that used laboratory and clinical methods based on a 2-component model to assess body composition. Whether or not clinical methods accurately assess alterations in the composition of the weight lost with diet alone compared with diet plus exercise is unknown. Thus, the purpose of this study was to compare estimates of change in percentage body fat (%BF) from DXA, SFTs, BIA, and BMI with estimates from a 4-component (fat, water, mineral, and protein) model (%BFd,w,m) after moderate weight loss induced by diet or diet plus aerobic exercise.
| SUBJECTS AND METHODS |
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3 mo postpartum, not involved in a structured physical activity program in the month previous to the start of the study, nonsmoking, no known medical or nutritional conditions or medication use known to affect body-composition measures, no known cardiopulmonary or metabolic diseases, no signs or symptoms suggestive of possible cardiopulmonary or metabolic disease, and not currently following a weight-reducing diet. Oral contraceptive users (25.9% of the study subjects) were allowed to participate, although they were required to continue their oral contraceptive use throughout the study. Of the study population, 81.5% were white, 11.1% were black, and 7.4% were Hispanic or Asian. The study was approved by the university's Institutional Review Board, and written consent was obtained from the participants before data collection began. Seventy-four subjects who met the inclusion criteria were recruited. Subjects were matched for BMI and assigned to 1 of 3 treatment groups: control (C), diet only (DO), or diet plus aerobic exercise (DE). Forty-five subjects dropped out of the study. Twenty-nine subjects successfully completed the interventions and posttest data-collection procedures; however, 2 subjects did not meet the exercise-session-attendance criteria (75%) and were excluded from the sample, resulting in 27 subjects whose data were used in the analysis (C group: n = 9; DO group: n = 9; and DE group: n = 9). Errors with the body-composition methods were evaluated in an independent group of 9 subjects (4 women and 5 men aged 24 ± 3.8 y, 16.6 ± 11.6 %BFd,w,m), who were tested on 2 occasions 1 wk apart.
Data collection
Baseline and postintervention data were collected by using the same protocol. Physical characteristics, physical activity history, body density, total body water, total-body bone mineral and body composition from DXA, body resistance from BIA, and anthropometric measures were determined during a single test session lasting
3.5 h. Subjects were asked to arrive at the laboratory well hydrated after 12 h without food and beverages except water, which was consumed based on personal preference and habit. A baseline urine sample, the second void of the morning, was collected to assess hydration status. On average, the subjects were adequately hydrated as evidenced by their ability to give urine samples and a urine specific gravity of 1.019 ± 0.008 kg/L pretest and 1.020 ± 0.006 kg/L posttest (normal range: 1.0101.025 kg/L) (9). No food or beverages, including water, were consumed during the testing session. For a given subject, baseline and postintervention data were collected during the same phase of the menstrual cycle or oral contraceptive pill sequence to control for changes in body water due to hormonal fluctuations. Menstrual cycle status was determined by self report.
Body-composition measures
Anthropometric measures
Body mass (BM) in air was determined with an electronic scale to the nearest 0.01 kg with subjects wearing the attire to be worn while being weighed underwater. Barefoot standing height was measured to the nearest 0.1 cm with a stadiometer. Maximal chest depth was measured with an anthropometer (Holtain Ltd, Crymych, United Kingdom) after a normal inhalation with the subject in a supine position. SFTs were measured 3 times (to the nearest 0.1 mm) with a Harpenden caliper (British Indicators, Ltd, London) at the triceps, biceps, subscapular, and suprailiac sites as described in the Anthropometric Standardization Reference Manual (10); the mean of 3 trials was used to calculate %BF. The within-subjects SD of replicate measurements of the sum of SFTs on 2 d
7 d apart in 9 subjects was 1.0 mm.
Resistance
Body resistance was measured according to standard procedures with a standard whole-body tetrapolar bioimpedance analyzer (RJL Systems, Inc, Detroit) on the right side of the body after subjects rested supine for 1015 min (11, 12). The within-subjects SD of replicate measurements of body resistance on 2 d
7 d apart in 9 subjects was 24.4
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Densitometry
Body density was measured by underwater weighing and by using the Archimedes' principle to determine body volume. Underwater body weight was determined with a Chatillon (Greensboro, NC) autopsy scale to the nearest 0.25 kg, with residual lung volume measured simultaneously with a closed-circuit, oxygen-rebreathing, nitrogen-dilution technique that was a modified version of Goldman and Buskirk's method (13). The volume of gas in the gastrointestinal tract was assumed to be 0.1 L. The within-subjects SD of replicate measurements of body density on 2 d
7 d apart in 9 subjects was 0.0013 kg/L.
Body water
Total body water was measured by using deuterium oxide dilution according to the technique of Davis et al (14). After a baseline blood sample was taken, subjects ingested a known quantity of 2H2O (0.3 g 2H2O/kg BM) in 100 mL distilled water. Another 100 mL distilled water was used as a rinse and then consumed to ensure complete ingestion of the tracer. After a 3-h equilibrium period during which all urine was collected, another blood sample was taken. Blood samples were centrifuged at 1670 x g and 0° C for 20 min and plasma was stored at -70°C. Plasma samples were purified by diffusion by incubating equal volumes of plasma and deionized water at 37°C for 48 h in incubation dishes (Bel-Air Products, Pequannock, NJ) (15). Isotope abundance in the purified plasma sample was determined in duplicate with an isotope ratio mass spectrometer (MAT 251; Finnigan, Bremen, Germany). Total body water was corrected for 2H2O loss in urine and decreased 4% to account for hydrogen exchange with protein and carbohydrate during the 3-h equilibrium period (16).
The within-subjects SD of replicate measurements of body water on 2 d
7 d apart in 9 subjects was 0.50 L. The within-subjects SD of 2 measurements of body water from the same blood sample on a given day was 0.25 L, which was considered to be the technical error associated with the measurement of total body water.
Bone mineral
Bone mineral ash and %BF were determined with whole-body scans by DXA (QDR-1000W, enhanced whole-body analysis software version 5.71; Hologic, Inc, Waltham, MA). Bone mineral ash was multiplied by 1.2741 to estimate the total-body bone mineral content. The constant 1.2741 assumes that 4.18% of the bone mineral is lost during the ashing process and that nonosseous mineral mass is 23.049% of bone mineral ash (17). The within-subjects SD of replicate measurements of bone mineral content and %BFDXA on 2 d
7 d apart were 11.6 g and 0.5% of BM, respectively.
Body-composition calculations
In addition to the estimates of %BFDXA, 5 estimates of %BF from different methods were calculated. %BF was estimated from db, (%BFd) by using the Siri equation (18) based on a 2-component (FM and FFM) model:
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| (1) |
1 wk apart in 9 subjects was 0.6% of BM.
%BF was estimated from db, total body water, and total body mineral by using the following equation from Lohman (4), which is based on a 4-component model (fat, water, mineral, and protein):
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1 wk apart in 9 subjects was 0.6% of BM.
FFM was calculated from %BFd,w,m and BM. The protein content of FFM was calculated as follows: protein mass = FFM water mass mineral mass. The DFFM was estimated from the water, mineral, and protein fractions of FFM (estimated from the 4-component model) and their respective densities by using the following equation:
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1 wk apart in 9 subjects was 0.0015 kg/L.
%BF was estimated from the sum of 4 SFT measurements by using the equation of Durnin and Womersley (19):
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S is the sum of the triceps, biceps, subscapular, and suprailiac SFTs. The within-subjects SD of replicate measurements of %BFSFT on 2 d
1 wk apart in 9 subjects was 0.5% of BM.
%BF was estimated from BIA by using the equation of Segal et al (20) for obese individuals:
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1 wk apart in 9 subjects was 0.5% of BM. %BF was also estimated from BMI by using the equation of Deurenberg et al (21):
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1 wk apart in 9 subjects was 0.1% of BM.
Diet and exercise regimens
Dietary protocol
Resting energy expenditure was estimated from FFM (22), increased 10% to account for the thermic effect of food, and then corrected by a factor of 1.5 for daily activity (23) to obtain an estimate of 24-h energy expenditure. FFM was estimated by using the DXA estimates of body composition that were available immediately on completion of the baseline testing. For the 16-wk intervention period, subjects in the DO and DE groups were prescribed a diet that reduced their estimated daily energy requirements by 4.19 MJ/d (1000 kcal/d). The prescribed diet followed the American Diabetic Association exchange system. No subject was prescribed a diet providing <5.02 MJ/d (1200 kcal/d). Subjects were requested to limit their fat intake to
30% of total energy. The foods consumed were self-selected and no supplements were prescribed. At baseline, 5 and 10 wk of the intervention, and posttesting, 3-d dietary food records (2 weekdays and 1 weekend day) were completed at home. In addition, 24-h dietary recalls were completed through an interview and by using food models to represent portion sizes to assess compliance with the diet. Because there was no significant difference in reported energy intakes between the average of the 3-d diet records and the 24-h interview, the average of the 4 d (3-d diet record and 1 24-h recall) was used in the data analysis. Total energy and macronutrient contents were calculated by analyzing the food records with THE FOOD PROCESSOR software (ESHA, Salem, OR). All subjects were strongly encouraged to attend weekly group meetings for dietary education and assistance with individual success strategies. All subjects consuming the energy-restricted diet were requested to maintain the prescribed diet until the posttest was conducted.
Aerobic exercise protocol
In addition to the energy-restricted diet described above, women in the DE group participated in walking-jogging classes on an indoor track 4 times/wk. Subjects were prescribed a walking-jogging protocol in which
1.47 MJ (350 kcal) was expended per session on the basis of walking-jogging speed and BM (24, 25) for an approximate weekly energy expenditure of
5.86 MJ (1400 kcal). Subjects progressed to the prescribed energy expenditure according to individual capabilities over the initial 3 wk. Exercise sessions were supervised by the investigator. Exercisers maintained the prescribed exercise program until the posttest was conducted.
Physical activity assessment
Daily physical activity, excluding the prescribed exercise, was assessed by using the 7-d Physical Activity Recall Interview (26). Physical activity was assessed at baseline, 5 and 10 wk of the intervention, and posttest. All subjects were requested to maintain normal daily physical activity. Subjects assigned to the C and DO groups were specifically requested to abstain from any structured exercise.
Statistical analysis
Data were analyzed with SPSS for Windows version 7.0 (SPSS Inc, Chicago). One-way analysis of variance was used to assess the significance of differences among groups on variables of interest pretest. A two-way (group-by-time) mixed-model analysis of variance and follow-up tests for simple effects were used to determine the significance of differences in daily physical activity, dietary energy intake, and dietary composition. Analysis of variance on change scores was used to assess the significance of differences among groups on body-composition measures (4-component model); Tukey's post hoc analysis was performed if there was a significant finding. Analysis of variance and Tukey's post hoc analysis (among groups within method) and planned comparisons (all clinical estimates compared with %BFd,w,m) were used to determine the significance of differences in %BF pretest and changes in %BF. Individual agreement between clinical estimates of change in %BF and changes in %BFd,w,m was assessed by using the Bland-Altman approach (27). Relations between variables were described by using simple linear regression analysis. An experiment-wise
level of 0.05 was used. Bonferonni correction was used to control the family-wise error rate (Pfw) when multiple comparisons were conducted.
| RESULTS |
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2.1 MJ (500 kcal) from baseline values at each time point. Because self report was used to assess dietary compliance, the validity of the data was questionable. In addition, because dietary compliance was sampled monthly, sensitivity to more frequent changes in energy intake was lacking. The decrease in reported energy intake in the absence of weight change in the control group supports this contention. For the DE group, attendance at the exercise sessions averaged 86 ± 5%. Total energy expenditure for the intervention averaged 86.1 ± 10.9 MJ (20562 ± 2603 kcal) with an average energy expenditure per exercise session of 1.4 ± 0.1 MJ (329 ± 26 kcal). Total walking distance averaged 352 ± 45 km (219 ± 28 miles), with an average distance per exercise session of 5.6 ± 0.5 km (3.5 ± 0.3 miles). Daily physical activity (in kJkg-1,min-1), excluding the prescribed exercise, assessed by using the 7-d Physical Activity Recall Interview (26) was not significantly different among groups or across time points (baseline: 150.7 ± 16.3; 5 wk: 148.6 ± 10.0; 10 wk: 145.3 ± 7.5; posttest: 145.3 ± 11.3). This nonsignificant finding suggested that the DE group did not change their spontaneous, nonexercise daily physical activity when initiating the walking program. In addition, it suggests that because daily physical activity did not differ significantly among groups and remained constant in all groups throughout the intervention, it did not significantly affect differences in body-composition changes during the intervention period.
Physical characteristics of the subjects at baseline are presented in Table 1
. There were no significant differences between groups in age, height, mass, BMI, or %BFd,w,m before the intervention. Changes in BM and body composition based on a 4-component model are presented in Table 2
. There were no significant differences between groups in any component pretest. BM changed 0.5%, -7.9%, and -4.8% in the C, DO, and DE groups, respectively. There was a significant difference in the change between the C and DO groups. When data for the one individual who lost
25 kg was removed from the analysis, the difference in BM change between the C and DO groups remained significant (DO: -4.9 ± 3.4 kg). There was a significant difference in BM change between the C and DE groups; however, no significant difference in BM change existed between the DO and DE groups. FM decreased 11% in the DO group and 10% in the DE group. These decreases were significantly greater than those in the C group, but were not significantly different from each other. The composition of the BM loss differed markedly, with
60% and
90% of the loss being FM in the DO and DE groups, respectively. There were no significant differences among the groups in changes in FFM, water, mineral, and protein mass.
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To evaluate whether changes in the water fraction of FFM affected the discrepancy between changes in %BFd,w,m and %BFDXA, the water fraction of FFM was calculated by using FFMDXA to avoid a spurious relation resulting from the common influence of water on the numerator and denominator in the water fraction of FFM when FFM is estimated by using the 4-component model. The difference in %BF change estimated with the 4-component model and with DXA was significantly related to a change in the water fraction of FFM (Figure 1
; r = -0.71, P < 0.05). The discrepancy between the change in %BFd,w,m and the change in %BFDXA was not related to change in body depth (r = -0.27, P > 0.05).
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(±SD) difference: 1.3 ± 2.1% of BM]. Individual disagreement between changes in %BFd,w,m and %BFBIA (-3.6% to 4.8% of BM; 0.8 ± 2.1% of BM) and between changes in %BFd,w,m and %BFSFT (-3.6% to 4.2% of BM; 1.0 ± 2.0% of BM) were similar and unbiased (Figure 2,
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50% of the loss was FM (on the basis of the 4-component model); therefore, BMI greatly overestimated the change in %BF. Reanalysis of the data without this subject's data improved the agreement between changes in %BFd,w,m and %BFBMI (-4.1% to 3.0% of BM; 0.3 ± 1.9% of BM) and resulted in changes in %BFBMI that agreed the closest with changes in %BFd,w,m when there was moderate weight loss. | DISCUSSION |
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Estimates of change in %BF by DXA overestimated the loss in %BF and underestimated the gain in %BF. Compared with changes estimated with the 4-component model, the magnitude of error was similar to that of less-sophisticated clinical methods. The biased estimation of change in %BF compared with a 4-component model was contradictory to the findings of Albu et al (6) and Fogelhom et al (5), who found that dual-photon absorptiometry and DXA, respectively, provided an accurate estimation of the mean change in %BF. Data from the present study agree with Fogelholm et al's finding that errors with DXA were comparable with errors with BIA, SFT, and BMI estimates of the change in %BF.
Errors in %BFDXA associated with the assumption of a constant hydration of the soft lean tissue mass may have contributed to the discrepancy of estimates of change in %BFDXA compared with the 4-component model. Whole-body composition estimates with DXA assume a constant hydration of lean soft tissue with any deviation causing a systematic error in the estimation of %BF (28). Research has shown that BM lost during hemodialysis or 0.82.4 L water ingestion did not greatly affect estimates of fat or lean tissue measured by DXA (29). Dehydration was correctly identified by DXA as lean tissue with no change in fat or bone loss (30). Theoretical calculations (31) and other data (32) indicate that a 5% change in the water fraction of FFM would result in an error in FMDXA of
0.40.5 kg, which corresponded to a difference between %BFDXA and %BFd,w,m of
2.7% of BM (32).
In the present study, the relation between the water fraction of FFM and the discrepancy between estimates of change in %BF with the 4-component model and with DXA were evaluated by using FFMDXA instead of the 4-component model because the FFM estimate with the 4-component model is heavily influenced by the water estimate, thereby affecting both the numerator and denominator, possibly resulting in a spurious association. Indeed, a significant relation existed between the difference between changes in %BFd,w,m and %BFDXA, and changes in FFM estimated with the 4-component model (r = -0.43, P < 0.05), whereas this relation did not exist when FFMDXA was used as the dependent measure (r = 0.15, P > 0.05). A change in hydration of FFMDXA was significantly related to the difference between change in %BFDXA and change in %BFd,w,m. Regression analysis determined that a 5% change in the water fraction of FFM (
3.6%) resulted in a difference in BM of 2.2% between changes in %BFDXA and changes in %BFd,w,m. Although our findings should be interpreted cautiously because of the use of FFMDXA to calculate the change in the water fraction of FFM, it suggests that changes in lean tissue mass hydration may have accounted for some of the difference between estimates of change in %BFDXA and the criterion method.
Another error in %BFDXA estimates results from changes in body tissue thickness. An increase in object thickness causes preferential loss of lower-energy photons relative to high-energy photons, termed "beam hardening," resulting in altered attenuation constants for the various tissues, which may lead to error in body-composition estimates (33). In the present study, changes in BMI or body depth were not related to the difference between estimates of change in %BF by the 4-component model and DXA. These findings may be related to the homogeneous subject pool used and the restricted range of change in BMI and body depth.
It is important to note that the conclusions regarding DXA's ability to correctly assess %BFd,w,m apply to the equipment used (Hologic QDR 1000W with enhanced software version 5.71) and that significant differences exist between manufacturers and software that could result in different findings (3436).
The magnitude of error for the estimation of change in %BFd,w,m was nearly identical for BIA, SFT, and BMI, and there were no systematic differences between methods. These findings do not agree with those of Fogelhom et al (5), who found that BIA and SFT measurements underestimated the change in FM compared with the estimates made with a 4-component model. Regarding BIA, the authors speculated that their refeeding, weight-stabilization period after weight loss may have resulted in an expansion of intracellular water caused by glycogen resynthesis. Single-frequency BIA at a frequency of 50-kHz is more dependent on extracellular water than on total body water (37). Therefore, the change in total body water may not have been detected accurately by BIA. The findings of the present study also may have been influenced by the small change in %BF induced as a result of the weight-loss protocol.
Although BMI provided the least accurate assessment of %BFd,w,m before the intervention, on average, BMI estimated the change in %BFd,w,m as well as or better than did DXA, BIA, and SFT. This finding is important considering the relatively low cost of the method and the minimal skill needed to use it. These findings agree with those of Fogelholm et al (5). The accuracy of BMI in predicting the change in %BFd,w,m is largely dependent on the composition of the weight lost. Deviations from a typical weight-loss composition of 1525% FFM and 7585% FM result in greater errors in prediction of the change in %BFd,w,m. Our findings suggest that BMI is comparable with DXA, BIA, and SFT measurement in predicting changes in %BFd,w,m.
Although the above findings are based on the assumption that differences between clinical estimates of %BF and %BFd,w,m resulted from error in the clinical estimate of %BF, estimates of %BF with a 4-component model are not without error. It has been suggested that increased error associated with the greater number of measurements contributing to %BFd,w,m may negate its greater theoretic accuracy (38). We and others (39) found, however, that the within-subjects SD for replicate measurements of %BFd,w,m is low (
0.6% of BM) and similar to that derived with other indirect methods based on fewer measurements (eg, within-subjects SD for replicate measurements of %BFd of
0.6% of BM), indicating that propagation of measurement error is not a significant problem. Furthermore, it must be recognized that measurements of %BFd,w,m are not completely independent of %BFDXA or %BFd because density and bone mineral are used in the calculation of %BFd,w,m. The effect of this lack of independence is not known.
Data from this study highlight the difficulty in accurately assessing small changes in body composition with clinical methods. For example, the SEEs for predicting changes in %BFd,w,m from changes in %BFDXA, %BFBIA, %BFSFT, and %BFBMI were 1.9%, 2.1%, 2.0%, and 2.1% of BM, respectively, for an average SEE of
2.0% of BM for the clinical methods. With use of the law of propagation of errors and assuming that the criterion measure is not error free (within-subjects SD of %BFd,w,m: 0.6% of BM), the portion of the SEE attributable to the clinical method is reduced to 1.9% of BM. To detect a true change in %BF from a weight loss in 95% of individuals, %BF would have to change by
3.8%.
In conclusion, the results suggest that errors in estimation of the change in %BF by DXA, BIA, SFT measurement, and BMI are similar when compared with a 4-component model. The associations between estimates of change in %BF with the clinical methods and changes in %BFd,w,m were stronger than the associations between changes in the clinical methods and changes in %BF estimated by densitometry. Furthermore, the magnitude of error in the clinical assessment methods was not affected by type of weight-loss intervention (diet or diet plus aerobic exercise). Although BIA, SFT, and BMI estimates of mean changes in %BF were unbiased, DXA overestimated the loss in %BF in the intervention groups. Because the average error of prediction with the clinical methods used in this study was
2% of BM, small physiologic changes in %BF with weight loss may not be quantified accurately with these clinical assessment methods.
| FOOTNOTES |
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3 Address reprint requests to EM Evans, Washington University, School of Medicine, 660 South Euclid Avenue, Campus Box 8113, St Louis, MO 63110. E-mail: eevans{at}imgate.wustl.edu.
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