Optimized predictions of absolute and relative amounts of body fat from weight, height, other anthropometric predictors, and age
the Sahlgrenska Academy at Gteborg University, Department of Body Composition and Metabolism, Gteborg, Sweden (IL, BH, AKL, CDS, and LS), and the University Hospital of rebro, Department of Surgery, rebro, Sweden (IN)
ABSTRACT
Background: Body mass index (BMI) is the dominating weight-for-height index, but its validity as a body fat (BF) index has not been properly examined.
Objectives: Our aims were to establish and validate optimal weight-for-height indexes for predicting absolute and relative (percentage) amounts of BF, to examine whether other commonly available anthropometric variables or age could add to the predictive power, and to explore the upper limit for percentage BF.
Design: One thousand one hundred twelve randomly selected subjects, and an additional 149 obese subjects, were included in the study. The subjects were randomly allocated to either a primary study group or a validation group. BF was measured with dual-energy X-ray absorptiometry. The relations between weight/heightx (W/Hx) and BF (absolute or percentage) were examined for values of the exponent x that ranged from 0.0 to 3.0. The predictive power of equations that were based on optimal weight-for-height indexes was compared with equations based on weight, height, other anthropometric variables, and age.
Results: Absolute BF was optimally and linearly predicted by W/H1, whereas the percentage BF was optimally and nonlinearly predicted by W/H2. The percentage BF asymptotically approached 52% in women and 56% in men. The percentage BF increased only marginally from BMI (in kg/m2) values of >35 in women and >60 in men. Predictions of absolute BF were associated with smaller errors (8.5% for men and 5.7% for women) than were predictions of percentage BF (8.7% for men and 7.9% for women). The addition of other anthropometric measurements for both men and women, and the addition of age for women only, in the regression analyses moderately reduced these errors.
Conclusion: Our data suggest that W/H may be a more optimal weight-for-height index than is BMI, particularly at high body weights.
Key Words: Body fat indexes maximum relative fatness prediction of body fat weight-for-height
INTRODUCTION
By 1835, the Belgian mathematician Lambert Adolphe Jacques Quetelet observed that the weight of normal adults was proportional to their height squared; ie, that weight/height2 (W/H2) was constant for people of normal build (1). Today, Quetelet's index is better known as the body mass index (BMI), which is the most widely used measure to describe degrees of underweight and overweight in the literature. Compelling reasons must thus be provided for proposing an alternative weight-for-height index.
Benn (2) suggested that the exponent (p) of height should be chosen in such a way that W/Hp results in a correlation with height of zero. However, Benn never examined the correlation between measured body fat (BF) and height (2), and study groups with positive and negative correlations between height and BF have been reported (3).
BMI has been used both as a risk index and as a body fat index (4, 5). The exponent of height will not necessarily be the same in an optimal risk index as in an optimal body fat index that is based on weight-for-height. Also, the exponent of height in an optimal risk index may be different in different study groups and for different endpoints (3, 6).
In the present study, we focus on weight-for-height indexes as BF indicators. BMI is usually used as an indicator of percentage BF (7), but sometimes it is used as an index of the absolute amount of BF (8). The optimal exponent of height may be different when estimating percentage and absolute BF, but this has not been properly examined. Furthermore, it is obvious that the human body cannot contain 100% fat. The relation between percentage BF and any weight-for-height index must thus be curvilinear. The level at which the percentage BF asymptotically approaches an upper maximal percentage of body weight has not previously been examined. At a given body weight, height is negatively related to BF. This cannot be reflected by BMI or other weight-for-height ratios, and, therefore, an examination into whether BF is better predicted by weight, height, other anthropometric measurements, and age as separate independent variables seems warranted. For the reasons outlined above, our aims were to examine the following in a randomly selected sample of persons, which had an added number of obese persons: 1) to establish optimal weight-for-height indexes for the prediction of absolute and percentage BF in men and women; 2) to examine if multivariate equations based on weight, height, and other anthropometric variables can predict BF with higher precision than the optimal weight-for-height index; and 3) to examine if the percentage BF asymptotically approaches an upper maximal value.
SUBJECTS AND METHODS
Subjects
One hundred forty-nine obese persons from 2 Swedish cities (Mlndal and rebro) who were part of the Xenical for the prevention of of diabetes in obese study (XENDOS; 9) were added to a randomly selected sample of persons (n = 1112) from the general population from the same 2 cities (10). Thus, a total of 1261 subjects (548 men and 713 women) were examined. All subjects were white, except for 4 women of Asian origin. Participation rates were 53.7% for the men and 57.6% for the women in the population-based sample. A nonparticipation analysis indicated similar characteristics between participants and nonparticipants (10).
The men and women in the total sample were each randomly allocated to either a primary study group or a validation group. The primary study groups were used for developing optimal weight-for-height indexes and anthropometric equations for predicting absolute BF (in kg) and percentage BF. These indexes and equations were then tested in the validation groups.
The Ethics Review Boards at Gteborg and rebro University hospitals approved all examinations of the randomly selected subjects. Similarly, the examinations of the obese subjects [ie, the baseline examination of the XENDOS subgroup (9)] were approved by the same boards. Informed consent was obtained from all subjects before the examinations.
Anthropometric measurements
After an overnight fast, the subjects' anthropometric measurements were taken while they were dressed in underwear. The subjects' height was measured to the nearest 0.01 m while the subjects were standing barefoot with their backs to a wall-mounted stadiometer. The subjects' weight was measured to the nearest 0.1 kg with calibrated scales.
Two trunk circumferences were measured while the subjects were in a recumbent position. The waist circumference was measured in cm at the end of a normal expiration at the point midway between the most caudal part of the lateral costal arch and the iliac crest. The hip circumference was measured in cm at the symphysis-trochanter femoris level. The sagittal trunk diameter was measured in cm with the use of a carpenter's spirit level and a ruler (11) while the subjects were in a recumbent position on an examination table that had a firm surface. The spirit level was placed 90 degrees to the length axis of the body over the abdomen at the level of the iliac crest. The sagittal trunk diameter was the vertical distance from the examination table up to the horizontal level as measured with the ruler (11).
Dual-energy X-ray absorptiometry
Body composition was assessed with dual-energy X-ray absorptiometry (DXA), which results in a 3-compartment model that consists of BF, lean tissue mass (LTM), and bone mineral content (BMC) (12). The 2 DXA scanners used for the Mlndal and rebro samples were LUNAR DPX-L machines (LUNAR Radiation, Madison WI) with identical software (version 1.31) and with the extended analysis program for total body analysis (13). The LUNAR DPX-L scanner uses a constant potential X-ray source and a K-edge filter to achieve a congruent beam of stable dual-energy radiation. A quality assurance test was conducted on a daily basis, as recommended by the manufacturer. According to the manufacturer recommendations, persons with body weights 35 or 120 kg cannot be reliably examined with the DPX-L scanner (13). None of the subjects weighed <43 kg. In the present study, the upper body weight limit was 110.0 kg.
The precision of our Mlndal scanner was estimated in a comparison of 2 separate examinations of 10 healthy, nonobese subjects. The within-subject CVs were 1.7% for BF, 0.7% for LTM, 1.9% for BMC, and 1.5% for bone mineral density (BMD). The precision was also examined in 50 obese subjects who were measured twice on the 2 DXA scanners. The within-subject CVs for the machine used in the Mlndal sample were 1.6% for BF, 0.7% for LTM, 0.9% for BMC, and 0.8% for BMD. The within-subject CVs for the rebro machine were 1.4% for BF, 1.0% for LTM, 1.4% for BMC, and 0.6% for BMD.
Statistics
Age, anthropometric measurements, and DXA-measured body components are presented as means (±SDs). Equations obtained from the primary study groups were tested in the validation groups, and errors between the measured and predicted BF were calculated as the within-subject CVs.
To establish optimal weight-for-height indexes, correlation coefficients (r) for measured BF (absolute or percentage) compared with W/Hx were plotted against the exponent of height (x), where x ranged from 0.0 to 3.0. Measured BF (absolute or percentage) was regressed by the optimal power type indexes in the primary study groups, and the resulting equations were used to predict absolute or percentage BF in the validation groups. Differences in absolute residuals and in absolute changes between the measured and predicted BF, as obtained by the equations, were tested with paired t tests.
In the primary groups, multiple regression analyses were performed to develop anthropometry-based multivariate equations predicting absolute BF. Body height, weight, waist and hip circumferences, sagittal diameter, and age were included in the regression model. Backward elimination of the variables was then undertaken until all remaining terms in the equation were significant. Finally, the equations were refined by examining whether any previously removed variable could be added back into the model with a maintained significance.
To predict percentage BF from BMI (or other power-type weight-height indexes), nonlinear least-square fits were performed with the use of an exponential equation in the primary study groups. The best fits of percentage BF (y) were achieved by adjusting 3 coefficients, which represented the asymptote; ie, y value at high BMIs (a), the BMI at 0% BF (x0), and the "bending" of the curve (b) in the equation:
(1)
To illustrate the parameters (a) and (x0), the nonlinear curves were extrapolated outside the range of observations.
All tests were two-tailed. The statistical analyses and the random allocation of subjects to primary and validation groups were conducted with JMP statistical software package, version 5.1.1 (SAS Institute Inc, Cary, NC) and IGOR PRO version 4.09A (WaveMetrics Inc, Portland, OR).
RESULTS
Sample characteristics
The age, anthropometric measures, and DXA-measured body compositions for the primary groups and the validation groups are shown in Table 1. No statistically significant differences were observed between the primary group and the validation group, either for the men or women. In both the primary and validation groups, the men and women were of similar age and had similar BMIs. Compared with the men, the women were shorter, had lower body weights, waist circumferences, sagittal trunk diameters, lean tissue masses, and bone mineral contents and higher hip circumferences and absolute and percentage BF (P < 0.01 for all) (Table 1).
Optimal weight-for-height indexes
The optimal weight-for-height index for the prediction of absolute BF was close to W/H1.0 in both the men (optimal exponent of height 1.1) and the women (optimal exponent 0.9) in the primary study groups (Figure 1). W/H seemed to be more closely correlated with BF in the women (rmax = 0.97) than in the men (rmax = 0.91).
In contrast, the percentage BF was more optimally predicted by weight-for-height indexes close to BMI (W/H1.8 for men and W/H1.9 for women). The optimal correlation coefficients were lower for the prediction of percentage BF (rmax = 0.78 for men and 0.85 for women) than for the prediction of absolute BF.
The DXA-measured absolute BF in the primary group was regressed by either W/H or W/H2 in both the men and women (Figure 2). Compared with W/H2, W/H resulted in higher r values and significantly lower mean absolute residuals (2.8 compared with 3.1 kg in the men, P = 0.003; 2.1 compared with 2.5 kg in the women, P < 0.001). In the women, the relation between absolute BF and BMI was nonlinear (ie, BMI2 contributed significantly to the explained variance). The linear relations between absolute BF and W/H are described by the equations:
(2)
(3)
Measured absolute body fat compared with body fat predicted from weight-for-height indexes
The 4 equations of Figure 2 were used to predict BF in the validation groups (Figure 3). In a plot of measured versus predicted absolute BF, the intercepts were close to zero and regression coefficients close to 1.0 (Figure 3). However, the absolute differences between the measured and predicted absolute BF were significantly lower (P < 0.01) when W/H rather than BMI was used in the predictive equations, and the corresponding errors were lower (8.5% compared with 9.4% for men and 5.7% compared with 6.8% for women) (Figure 3).
Univariate and multivariate prediction of absolute body fat
In the men in the primary study group, R2 values for absolute BF compared with selected single variables were 0.86 for waist circumference, 0.82 for W/H, 0.78 for W/H2, 0.76 for weight, and 0.00 for height. In the women, the corresponding values were 0.94, 0.92, 0.91, 0.86, and 0.01. The same rankings and similar R2 values were observed in the validation group.
Next, we examined if the predictions of absolute BF that were based on W/H could be improved in the primary study group by using weight and height separately and by adding age and additional anthropometric measurements (waist circumference, hip circumference, and sagittal trunk diameter) to the regression analysis (Table 2).
In the men, a regression analysis with backward elimination (see Statistics) resulted in 3 significant predictors: weight, height, and waist circumference. Compared with the equation based on W/H, this equation resulted in significantly lower absolute residuals and higher explained variances (Table 2, upper part). In the women, weight, height, waist circumference, hip circumference, and age all remained significant after backward elimination, and the corresponding equation resulted in lower absolute residuals than did the equation based on W/H (absolute BF: 1.8 compared with 2.1 kg; P < 0.001). An equation based only on weight, height, and waist circumference also resulted in lower absolute residuals in the women in the primary study group (absolute BF: 2.0 compared with 2.1 kg; P < 0.001) (Table 2, upper part).
The anthropometric, multivariate equations that were developed in the primary study group were used to estimate absolute BF in the validation group (Table 2, lower part). In the men, the equation based on weight, height, and waist circumference resulted in significantly lower absolute differences between the measured and estimated absolute BF than did the equation based on W/H (absolute BF: 2.3 compared with 2.6 kg; P = 0.02). The corresponding percentage errors were 7.7% and 8.5%. In the women, the complete anthropometric equation reduced the absolute differences, whereas the equation based on weight, height, and waist circumference did not (Table 2, lower part).
Nonlinear relations between percentage body fat and weight-for-height indexes
As illustrated in Figure 1, weight-for-height indexes close to BMI seem to be optimal for predicting the percentage BF. The nonlinear relations between percentage BF and W/H2 in the men and women in the primary study group, when analyzed with an exponential model, are shown in Figure 4. 3In the women (Figure 4B), BF asymptotically approached 51.6% (95% CI: 49.4%, 53.9%) of body weight. Interestingly, similar asymptotic values were obtained when the percentage BF was regressed by weight (59.3%), W/H (53.7%), and W/H3 (51.8%). As illustrated by the curve shape in Figure 4B, the percentage BF in the women increased only marginally at BMI values > 35.
In the men in the primary study group, the BMI range covered was smaller than in the women, and the relation between percentage BF and BMI was less curvilinear (smaller b in the exponential equation; Figure 4A). Nevertheless, the percentage BF asymptotes were similar in the men (56.0%; 95% CI: 31.9%, 80.1%) and women (51.6%). Similar asymptotic values were obtained when the percentage BF of the men was regressed by weight (58.3%), W/H (54.6%), and W/H3 (53.7%). In the men, the percentage BF increased only marginally at BMI values > 60. With the same exponential function, 0% body fat was achieved at a BMI of 13.1 in the men (Figure 4A) and 13.5 kg/m2 in the women (Figure 4B).
The exponential equations of Figures 4A and 4B were used to predict the percentage BF in the validation group (Figures 4C and 4D). The absolute difference between the measured percentage BF and the percentage BF that was predicted from the exponential equations was 3% for both the men and women. The corresponding CVs were 8.7% for the men and 7.9% for the women.
DISCUSSION
The optimal exponent x of height in the equation W/Hx was 1.1 in the men and 0.9 in the women when estimating the absolute amount of BF from weight-for-height indexes in our study groups. When estimating the percentage BF, the optimal exponents were 1.8 and 1.9, respectively. However, the change in predictive power by approximating these exponents to 1.0 and 2.0, respectively, was marginal (flat top of curves in Figure 1). We therefore recommend W/H when predicting the absolute amount of BF and BMI when predicting the percentage BF. The relation between W/H and absolute BF was linear, whereas the one between BMI and the percentage BF was nonlinear.
Several publications have specified criteria for an optimal obesity index (2, 5, 14–19). Some of the suggested criteria are the following: 1) the index should be highly correlated with body weight, 2) the index should be highly correlated with body fat expressed in absolute terms or as a percentage, and 3) the index should have as low a correlation as possible with height. The first criterion is correct, but insufficient. Several studies have tested weight-for-height indexes only in relation to weight (15, 16, 20), and evidently such procedures are not sufficient for establishing an optimal BF index. The second criterion is correct, and weight-for-height indexes have been correlated with skinfold-thickness (21) or with both absolute and percentage BF, as measured with underwater weighing (22–24). Several studies have suggested that percentage BF is optimally related to BMI (14, 18, 19, 22, 25), which agrees with our study. However, it has also been claimed that absolute BF is optimally predicted by BMI (8, 22), which clearly contrasts with our findings. Garrow and Webster (8) claimed that BMI was the optimal weight-for-height index for predicting BF mass because BF/H2 was closely related to W/H2 (r = 0.943). Evidently, the same denominator in both expressions may contribute to the high correlation. The last criterion, which was suggested by Benn (2), can be questioned because the correlation coefficients between height and BF can range from negative to positive values depending on the study groups examined (3). Thus, it seems reasonable that weight-for-height indexes should ideally be related to height in the same way as measured BF (3).
The percentage BF was nonlinearly related to BMI and other weight-for-height indexes. In the clinic, the percentage BF is intuitively considered to be proportionally related to BMI. Although this is approximately true in the normal BMI range, the percentage BF was only marginally increased between high and very high BMIs. Our exponential model indicated that the relative amount of BF may not exceed 50–60%. With the same model, a 0% BF was estimated to occur at a BMI of 13 kg/m2. However, we did not examine sigmoidal curves due to a lack of observations at low BMIs.
In a comparatively small study by Lean et al (26), the percentage BF that was calculated with densitometry was more closely related to waist circumference than to BMI, particularly in men. We observed the same ranking of predictors in men; however, in our women, body weight, W/H, and BMI were more closely related to BF than was waist circumference. In our study, the addition of waist circumference to weight and height improved the precision of absolute BF predictions to a moderate extent.
We chose to predict BF from various weight-for-height based equations to calculate errors of predicted compared with measured BF. However, it must be stressed that such equations are, to a certain degree, population-specific, whereas a given weight-for-height ratio is population-independent. For example, Gallagher et al (24) used 6 equations from the literature to predict percentage BF from BMI; the derived values ranged from 24.8% to 28.0% BF in 312 men and from 34.0% to 37.7% BF in 394 women. We agree with Gallagher et al (24) that this represents a remarkable concordance between predictive equations.
BMI has been used extensively to study the relations between body build and incidence of cardiovascular disease. Because weight is positively related and height negatively related both to cardiovascular disease risk factors (27) and to hard endpoints (ie, deaths) (28), whether BMI is an optimal risk index remains in question. For instance, in a previous congress report, we found that myocardial infarction was optimally predicted by W/H4.8 in 1462 women, whereas W/H2.2 predicted myocardial infarction optimally in men in 2 separate study groups (n = 784 and n = 10 004) (3). Optimal risk indexes need to be additionally evaluated in separate studies, particularly because the exponent of height (x) influences the ranking of persons by weight-for-heightx.
The present study was limited in some respects. Only persons aged 30–61 y were examined. Due to limitations of the DXA technology, subjects with body weights >110 kg were excluded. Therefore, our statements are correct only to the extent that DXA is a valid technique. The subjects were mainly white, and our optimal indexes and equations were based on study groups of limited size (274 men and 357 women). On the other hand, most of our study subjects were randomly selected, and we validated our results in separate, but equally large, study groups. Although similar procedures have been used in other studies (26), independent validations of weight-for-height indexes and BF equations are unusual (29).
In conclusion, the present study showed that absolute BF was best predicted by W/H, whereas the percentage BF was optimally predicted by W/H2. The relative amount of BF did not seem to exceed 50–60% of body weight. Although BMI was approximately proportional to the percentage BF in the normal-weight range, this was not the case in severely obese subjects. In contrast, W/H was linearly related to the absolute amount of BF over the examined weight ranges. These circumstances, as well as the fact that absolute BF was predicted with a greater precision than was percentage BF, suggest that W/H may be a more optimal weight-for-height index than BMI, particularly at high body weights.
ACKNOWLEDGMENTS
We thank Hoffmann-La Roche Ltd for generously providing the data from the Swedish XENDOS-study.
IL, CDS, and LS contributed to the study design. IL, BH, and LS contributed to the data analysis. IL, AKL, IN, and LS were responsible for different parts of data collection. All authors contributed to the manuscript writing. None of the authors had any conflicts of interest.
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ABSTRACT
Background: Body mass index (BMI) is the dominating weight-for-height index, but its validity as a body fat (BF) index has not been properly examined.
Objectives: Our aims were to establish and validate optimal weight-for-height indexes for predicting absolute and relative (percentage) amounts of BF, to examine whether other commonly available anthropometric variables or age could add to the predictive power, and to explore the upper limit for percentage BF.
Design: One thousand one hundred twelve randomly selected subjects, and an additional 149 obese subjects, were included in the study. The subjects were randomly allocated to either a primary study group or a validation group. BF was measured with dual-energy X-ray absorptiometry. The relations between weight/heightx (W/Hx) and BF (absolute or percentage) were examined for values of the exponent x that ranged from 0.0 to 3.0. The predictive power of equations that were based on optimal weight-for-height indexes was compared with equations based on weight, height, other anthropometric variables, and age.
Results: Absolute BF was optimally and linearly predicted by W/H1, whereas the percentage BF was optimally and nonlinearly predicted by W/H2. The percentage BF asymptotically approached 52% in women and 56% in men. The percentage BF increased only marginally from BMI (in kg/m2) values of >35 in women and >60 in men. Predictions of absolute BF were associated with smaller errors (8.5% for men and 5.7% for women) than were predictions of percentage BF (8.7% for men and 7.9% for women). The addition of other anthropometric measurements for both men and women, and the addition of age for women only, in the regression analyses moderately reduced these errors.
Conclusion: Our data suggest that W/H may be a more optimal weight-for-height index than is BMI, particularly at high body weights.
Key Words: Body fat indexes maximum relative fatness prediction of body fat weight-for-height
INTRODUCTION
By 1835, the Belgian mathematician Lambert Adolphe Jacques Quetelet observed that the weight of normal adults was proportional to their height squared; ie, that weight/height2 (W/H2) was constant for people of normal build (1). Today, Quetelet's index is better known as the body mass index (BMI), which is the most widely used measure to describe degrees of underweight and overweight in the literature. Compelling reasons must thus be provided for proposing an alternative weight-for-height index.
Benn (2) suggested that the exponent (p) of height should be chosen in such a way that W/Hp results in a correlation with height of zero. However, Benn never examined the correlation between measured body fat (BF) and height (2), and study groups with positive and negative correlations between height and BF have been reported (3).
BMI has been used both as a risk index and as a body fat index (4, 5). The exponent of height will not necessarily be the same in an optimal risk index as in an optimal body fat index that is based on weight-for-height. Also, the exponent of height in an optimal risk index may be different in different study groups and for different endpoints (3, 6).
In the present study, we focus on weight-for-height indexes as BF indicators. BMI is usually used as an indicator of percentage BF (7), but sometimes it is used as an index of the absolute amount of BF (8). The optimal exponent of height may be different when estimating percentage and absolute BF, but this has not been properly examined. Furthermore, it is obvious that the human body cannot contain 100% fat. The relation between percentage BF and any weight-for-height index must thus be curvilinear. The level at which the percentage BF asymptotically approaches an upper maximal percentage of body weight has not previously been examined. At a given body weight, height is negatively related to BF. This cannot be reflected by BMI or other weight-for-height ratios, and, therefore, an examination into whether BF is better predicted by weight, height, other anthropometric measurements, and age as separate independent variables seems warranted. For the reasons outlined above, our aims were to examine the following in a randomly selected sample of persons, which had an added number of obese persons: 1) to establish optimal weight-for-height indexes for the prediction of absolute and percentage BF in men and women; 2) to examine if multivariate equations based on weight, height, and other anthropometric variables can predict BF with higher precision than the optimal weight-for-height index; and 3) to examine if the percentage BF asymptotically approaches an upper maximal value.
SUBJECTS AND METHODS
Subjects
One hundred forty-nine obese persons from 2 Swedish cities (Mlndal and rebro) who were part of the Xenical for the prevention of of diabetes in obese study (XENDOS; 9) were added to a randomly selected sample of persons (n = 1112) from the general population from the same 2 cities (10). Thus, a total of 1261 subjects (548 men and 713 women) were examined. All subjects were white, except for 4 women of Asian origin. Participation rates were 53.7% for the men and 57.6% for the women in the population-based sample. A nonparticipation analysis indicated similar characteristics between participants and nonparticipants (10).
The men and women in the total sample were each randomly allocated to either a primary study group or a validation group. The primary study groups were used for developing optimal weight-for-height indexes and anthropometric equations for predicting absolute BF (in kg) and percentage BF. These indexes and equations were then tested in the validation groups.
The Ethics Review Boards at Gteborg and rebro University hospitals approved all examinations of the randomly selected subjects. Similarly, the examinations of the obese subjects [ie, the baseline examination of the XENDOS subgroup (9)] were approved by the same boards. Informed consent was obtained from all subjects before the examinations.
Anthropometric measurements
After an overnight fast, the subjects' anthropometric measurements were taken while they were dressed in underwear. The subjects' height was measured to the nearest 0.01 m while the subjects were standing barefoot with their backs to a wall-mounted stadiometer. The subjects' weight was measured to the nearest 0.1 kg with calibrated scales.
Two trunk circumferences were measured while the subjects were in a recumbent position. The waist circumference was measured in cm at the end of a normal expiration at the point midway between the most caudal part of the lateral costal arch and the iliac crest. The hip circumference was measured in cm at the symphysis-trochanter femoris level. The sagittal trunk diameter was measured in cm with the use of a carpenter's spirit level and a ruler (11) while the subjects were in a recumbent position on an examination table that had a firm surface. The spirit level was placed 90 degrees to the length axis of the body over the abdomen at the level of the iliac crest. The sagittal trunk diameter was the vertical distance from the examination table up to the horizontal level as measured with the ruler (11).
Dual-energy X-ray absorptiometry
Body composition was assessed with dual-energy X-ray absorptiometry (DXA), which results in a 3-compartment model that consists of BF, lean tissue mass (LTM), and bone mineral content (BMC) (12). The 2 DXA scanners used for the Mlndal and rebro samples were LUNAR DPX-L machines (LUNAR Radiation, Madison WI) with identical software (version 1.31) and with the extended analysis program for total body analysis (13). The LUNAR DPX-L scanner uses a constant potential X-ray source and a K-edge filter to achieve a congruent beam of stable dual-energy radiation. A quality assurance test was conducted on a daily basis, as recommended by the manufacturer. According to the manufacturer recommendations, persons with body weights 35 or 120 kg cannot be reliably examined with the DPX-L scanner (13). None of the subjects weighed <43 kg. In the present study, the upper body weight limit was 110.0 kg.
The precision of our Mlndal scanner was estimated in a comparison of 2 separate examinations of 10 healthy, nonobese subjects. The within-subject CVs were 1.7% for BF, 0.7% for LTM, 1.9% for BMC, and 1.5% for bone mineral density (BMD). The precision was also examined in 50 obese subjects who were measured twice on the 2 DXA scanners. The within-subject CVs for the machine used in the Mlndal sample were 1.6% for BF, 0.7% for LTM, 0.9% for BMC, and 0.8% for BMD. The within-subject CVs for the rebro machine were 1.4% for BF, 1.0% for LTM, 1.4% for BMC, and 0.6% for BMD.
Statistics
Age, anthropometric measurements, and DXA-measured body components are presented as means (±SDs). Equations obtained from the primary study groups were tested in the validation groups, and errors between the measured and predicted BF were calculated as the within-subject CVs.
To establish optimal weight-for-height indexes, correlation coefficients (r) for measured BF (absolute or percentage) compared with W/Hx were plotted against the exponent of height (x), where x ranged from 0.0 to 3.0. Measured BF (absolute or percentage) was regressed by the optimal power type indexes in the primary study groups, and the resulting equations were used to predict absolute or percentage BF in the validation groups. Differences in absolute residuals and in absolute changes between the measured and predicted BF, as obtained by the equations, were tested with paired t tests.
In the primary groups, multiple regression analyses were performed to develop anthropometry-based multivariate equations predicting absolute BF. Body height, weight, waist and hip circumferences, sagittal diameter, and age were included in the regression model. Backward elimination of the variables was then undertaken until all remaining terms in the equation were significant. Finally, the equations were refined by examining whether any previously removed variable could be added back into the model with a maintained significance.
To predict percentage BF from BMI (or other power-type weight-height indexes), nonlinear least-square fits were performed with the use of an exponential equation in the primary study groups. The best fits of percentage BF (y) were achieved by adjusting 3 coefficients, which represented the asymptote; ie, y value at high BMIs (a), the BMI at 0% BF (x0), and the "bending" of the curve (b) in the equation:
(1)
To illustrate the parameters (a) and (x0), the nonlinear curves were extrapolated outside the range of observations.
All tests were two-tailed. The statistical analyses and the random allocation of subjects to primary and validation groups were conducted with JMP statistical software package, version 5.1.1 (SAS Institute Inc, Cary, NC) and IGOR PRO version 4.09A (WaveMetrics Inc, Portland, OR).
RESULTS
Sample characteristics
The age, anthropometric measures, and DXA-measured body compositions for the primary groups and the validation groups are shown in Table 1. No statistically significant differences were observed between the primary group and the validation group, either for the men or women. In both the primary and validation groups, the men and women were of similar age and had similar BMIs. Compared with the men, the women were shorter, had lower body weights, waist circumferences, sagittal trunk diameters, lean tissue masses, and bone mineral contents and higher hip circumferences and absolute and percentage BF (P < 0.01 for all) (Table 1).
Optimal weight-for-height indexes
The optimal weight-for-height index for the prediction of absolute BF was close to W/H1.0 in both the men (optimal exponent of height 1.1) and the women (optimal exponent 0.9) in the primary study groups (Figure 1). W/H seemed to be more closely correlated with BF in the women (rmax = 0.97) than in the men (rmax = 0.91).
In contrast, the percentage BF was more optimally predicted by weight-for-height indexes close to BMI (W/H1.8 for men and W/H1.9 for women). The optimal correlation coefficients were lower for the prediction of percentage BF (rmax = 0.78 for men and 0.85 for women) than for the prediction of absolute BF.
The DXA-measured absolute BF in the primary group was regressed by either W/H or W/H2 in both the men and women (Figure 2). Compared with W/H2, W/H resulted in higher r values and significantly lower mean absolute residuals (2.8 compared with 3.1 kg in the men, P = 0.003; 2.1 compared with 2.5 kg in the women, P < 0.001). In the women, the relation between absolute BF and BMI was nonlinear (ie, BMI2 contributed significantly to the explained variance). The linear relations between absolute BF and W/H are described by the equations:
(2)
(3)
Measured absolute body fat compared with body fat predicted from weight-for-height indexes
The 4 equations of Figure 2 were used to predict BF in the validation groups (Figure 3). In a plot of measured versus predicted absolute BF, the intercepts were close to zero and regression coefficients close to 1.0 (Figure 3). However, the absolute differences between the measured and predicted absolute BF were significantly lower (P < 0.01) when W/H rather than BMI was used in the predictive equations, and the corresponding errors were lower (8.5% compared with 9.4% for men and 5.7% compared with 6.8% for women) (Figure 3).
Univariate and multivariate prediction of absolute body fat
In the men in the primary study group, R2 values for absolute BF compared with selected single variables were 0.86 for waist circumference, 0.82 for W/H, 0.78 for W/H2, 0.76 for weight, and 0.00 for height. In the women, the corresponding values were 0.94, 0.92, 0.91, 0.86, and 0.01. The same rankings and similar R2 values were observed in the validation group.
Next, we examined if the predictions of absolute BF that were based on W/H could be improved in the primary study group by using weight and height separately and by adding age and additional anthropometric measurements (waist circumference, hip circumference, and sagittal trunk diameter) to the regression analysis (Table 2).
In the men, a regression analysis with backward elimination (see Statistics) resulted in 3 significant predictors: weight, height, and waist circumference. Compared with the equation based on W/H, this equation resulted in significantly lower absolute residuals and higher explained variances (Table 2, upper part). In the women, weight, height, waist circumference, hip circumference, and age all remained significant after backward elimination, and the corresponding equation resulted in lower absolute residuals than did the equation based on W/H (absolute BF: 1.8 compared with 2.1 kg; P < 0.001). An equation based only on weight, height, and waist circumference also resulted in lower absolute residuals in the women in the primary study group (absolute BF: 2.0 compared with 2.1 kg; P < 0.001) (Table 2, upper part).
The anthropometric, multivariate equations that were developed in the primary study group were used to estimate absolute BF in the validation group (Table 2, lower part). In the men, the equation based on weight, height, and waist circumference resulted in significantly lower absolute differences between the measured and estimated absolute BF than did the equation based on W/H (absolute BF: 2.3 compared with 2.6 kg; P = 0.02). The corresponding percentage errors were 7.7% and 8.5%. In the women, the complete anthropometric equation reduced the absolute differences, whereas the equation based on weight, height, and waist circumference did not (Table 2, lower part).
Nonlinear relations between percentage body fat and weight-for-height indexes
As illustrated in Figure 1, weight-for-height indexes close to BMI seem to be optimal for predicting the percentage BF. The nonlinear relations between percentage BF and W/H2 in the men and women in the primary study group, when analyzed with an exponential model, are shown in Figure 4. 3In the women (Figure 4B), BF asymptotically approached 51.6% (95% CI: 49.4%, 53.9%) of body weight. Interestingly, similar asymptotic values were obtained when the percentage BF was regressed by weight (59.3%), W/H (53.7%), and W/H3 (51.8%). As illustrated by the curve shape in Figure 4B, the percentage BF in the women increased only marginally at BMI values > 35.
In the men in the primary study group, the BMI range covered was smaller than in the women, and the relation between percentage BF and BMI was less curvilinear (smaller b in the exponential equation; Figure 4A). Nevertheless, the percentage BF asymptotes were similar in the men (56.0%; 95% CI: 31.9%, 80.1%) and women (51.6%). Similar asymptotic values were obtained when the percentage BF of the men was regressed by weight (58.3%), W/H (54.6%), and W/H3 (53.7%). In the men, the percentage BF increased only marginally at BMI values > 60. With the same exponential function, 0% body fat was achieved at a BMI of 13.1 in the men (Figure 4A) and 13.5 kg/m2 in the women (Figure 4B).
The exponential equations of Figures 4A and 4B were used to predict the percentage BF in the validation group (Figures 4C and 4D). The absolute difference between the measured percentage BF and the percentage BF that was predicted from the exponential equations was 3% for both the men and women. The corresponding CVs were 8.7% for the men and 7.9% for the women.
DISCUSSION
The optimal exponent x of height in the equation W/Hx was 1.1 in the men and 0.9 in the women when estimating the absolute amount of BF from weight-for-height indexes in our study groups. When estimating the percentage BF, the optimal exponents were 1.8 and 1.9, respectively. However, the change in predictive power by approximating these exponents to 1.0 and 2.0, respectively, was marginal (flat top of curves in Figure 1). We therefore recommend W/H when predicting the absolute amount of BF and BMI when predicting the percentage BF. The relation between W/H and absolute BF was linear, whereas the one between BMI and the percentage BF was nonlinear.
Several publications have specified criteria for an optimal obesity index (2, 5, 14–19). Some of the suggested criteria are the following: 1) the index should be highly correlated with body weight, 2) the index should be highly correlated with body fat expressed in absolute terms or as a percentage, and 3) the index should have as low a correlation as possible with height. The first criterion is correct, but insufficient. Several studies have tested weight-for-height indexes only in relation to weight (15, 16, 20), and evidently such procedures are not sufficient for establishing an optimal BF index. The second criterion is correct, and weight-for-height indexes have been correlated with skinfold-thickness (21) or with both absolute and percentage BF, as measured with underwater weighing (22–24). Several studies have suggested that percentage BF is optimally related to BMI (14, 18, 19, 22, 25), which agrees with our study. However, it has also been claimed that absolute BF is optimally predicted by BMI (8, 22), which clearly contrasts with our findings. Garrow and Webster (8) claimed that BMI was the optimal weight-for-height index for predicting BF mass because BF/H2 was closely related to W/H2 (r = 0.943). Evidently, the same denominator in both expressions may contribute to the high correlation. The last criterion, which was suggested by Benn (2), can be questioned because the correlation coefficients between height and BF can range from negative to positive values depending on the study groups examined (3). Thus, it seems reasonable that weight-for-height indexes should ideally be related to height in the same way as measured BF (3).
The percentage BF was nonlinearly related to BMI and other weight-for-height indexes. In the clinic, the percentage BF is intuitively considered to be proportionally related to BMI. Although this is approximately true in the normal BMI range, the percentage BF was only marginally increased between high and very high BMIs. Our exponential model indicated that the relative amount of BF may not exceed 50–60%. With the same model, a 0% BF was estimated to occur at a BMI of 13 kg/m2. However, we did not examine sigmoidal curves due to a lack of observations at low BMIs.
In a comparatively small study by Lean et al (26), the percentage BF that was calculated with densitometry was more closely related to waist circumference than to BMI, particularly in men. We observed the same ranking of predictors in men; however, in our women, body weight, W/H, and BMI were more closely related to BF than was waist circumference. In our study, the addition of waist circumference to weight and height improved the precision of absolute BF predictions to a moderate extent.
We chose to predict BF from various weight-for-height based equations to calculate errors of predicted compared with measured BF. However, it must be stressed that such equations are, to a certain degree, population-specific, whereas a given weight-for-height ratio is population-independent. For example, Gallagher et al (24) used 6 equations from the literature to predict percentage BF from BMI; the derived values ranged from 24.8% to 28.0% BF in 312 men and from 34.0% to 37.7% BF in 394 women. We agree with Gallagher et al (24) that this represents a remarkable concordance between predictive equations.
BMI has been used extensively to study the relations between body build and incidence of cardiovascular disease. Because weight is positively related and height negatively related both to cardiovascular disease risk factors (27) and to hard endpoints (ie, deaths) (28), whether BMI is an optimal risk index remains in question. For instance, in a previous congress report, we found that myocardial infarction was optimally predicted by W/H4.8 in 1462 women, whereas W/H2.2 predicted myocardial infarction optimally in men in 2 separate study groups (n = 784 and n = 10 004) (3). Optimal risk indexes need to be additionally evaluated in separate studies, particularly because the exponent of height (x) influences the ranking of persons by weight-for-heightx.
The present study was limited in some respects. Only persons aged 30–61 y were examined. Due to limitations of the DXA technology, subjects with body weights >110 kg were excluded. Therefore, our statements are correct only to the extent that DXA is a valid technique. The subjects were mainly white, and our optimal indexes and equations were based on study groups of limited size (274 men and 357 women). On the other hand, most of our study subjects were randomly selected, and we validated our results in separate, but equally large, study groups. Although similar procedures have been used in other studies (26), independent validations of weight-for-height indexes and BF equations are unusual (29).
In conclusion, the present study showed that absolute BF was best predicted by W/H, whereas the percentage BF was optimally predicted by W/H2. The relative amount of BF did not seem to exceed 50–60% of body weight. Although BMI was approximately proportional to the percentage BF in the normal-weight range, this was not the case in severely obese subjects. In contrast, W/H was linearly related to the absolute amount of BF over the examined weight ranges. These circumstances, as well as the fact that absolute BF was predicted with a greater precision than was percentage BF, suggest that W/H may be a more optimal weight-for-height index than BMI, particularly at high body weights.
ACKNOWLEDGMENTS
We thank Hoffmann-La Roche Ltd for generously providing the data from the Swedish XENDOS-study.
IL, CDS, and LS contributed to the study design. IL, BH, and LS contributed to the data analysis. IL, AKL, IN, and LS were responsible for different parts of data collection. All authors contributed to the manuscript writing. None of the authors had any conflicts of interest.
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