Relative fat mass (RFM) as a new estimator of whole-body fat percentage ─ A cross-sectional study in American adult individuals

Abstract

High whole-body fat percentage is independently associated with increased mortality. We aimed to identify a simple anthropometric linear equation that is more accurate than the body mass index (BMI) to estimate whole-body fat percentage among adult individuals. National Health and Nutrition Examination Survey (NHANES) 1999-2004 data (n = 12,581) were used for model development and NHANES 2005-2006 data (n = 3,456) were used for model validation. From the 365 anthropometric indices generated, the final selected equation was as follows: 64 - (20 × height/waist circumference) + (12 × sex), named as the relative fat mass (RFM); sex = 0 for men and 1 for women. In the validation dataset, compared with BMI, RFM better predicted whole-body fat percentage, measured by dual energy X-ray absorptiometry (DXA), among women and men. RFM showed better accuracy than the BMI and had fewer false negative cases of body fat-defined obesity among women and men. RFM reduced total obesity misclassification among all women and all men and, overall, among Mexican-Americans, European-Americans and African-Americans. In the population studied, the suggested RFM was more accurate than BMI to estimate whole-body fat percentage among women and men and improved body fat-defined obesity misclassification among American adult individuals of Mexican, European or African ethnicity.

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SCientifiC REPORtS | (2018) 8:10980 | DOI:10.1038/s41598-018-29362-1
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Relative fat mass (RFM) as a new
estimator of whole-body fat
percentage ─ A cross-sectional
study in American adult individuals
Orison O. Woolcott & Richard N. Bergman
High whole-body fat percentage is independently associated with increased mortality. We aimed
to identify a simple anthropometric linear equation that is more accurate than the body mass
index (BMI) to estimate whole-body fat percentage among adult individuals. National Health
and Nutrition Examination Survey (NHANES) 1999–2004 data (n = 12,581) were used for model
development and NHANES 2005–2006 data (n = 3,456) were used for model validation. From the 365
anthropometric indices generated, the nal selected equation was as follows: 64 − (20 × height/waist
circumference) + (12 × sex), named as the relative fat mass (RFM); sex = 0 for men and 1 for women.
In the validation dataset, compared with BMI, RFM better predicted whole-body fat percentage,
measured by dual energy X-ray absorptiometry (DXA), among women and men. RFM showed better
accuracy than the BMI and had fewer false negative cases of body fat-dened obesity among women
and men. RFM reduced total obesity misclassication among all women and all men and, overall,
among Mexican-Americans, European-Americans and African-Americans. In the population studied,
the suggested RFM was more accurate than BMI to estimate whole-body fat percentage among women
and men and improved body fat-dened obesity misclassication among American adult individuals of
Mexican, European or African ethnicity.
High body fat percentage (adipose tissue mass relative to total body weight) is associated with mortality1,2.
Recently, a large cohort study in adult individuals with a follow-up of 14 years reported that low baseline body
mass index (BMI, weight in kilograms divided by the square of the height in meters) and high body fat percentage
are independently associated with increased mortality3.us, accurate estimation of body fat percentage is highly
relevant from a clinical and public health perspective, an aspect that has been endorsed by the American Heart
Association Obesity Committee4.
Obesity, a state of excessive accumulation of body fat, is an important risk factor for multiple chronic pathol-
ogies including diabetes, coronary artery disease, hypertension and certain types of cancer5–7. Interestingly, the
denition of obesity has changed over the last century. For example, early reports have dened obesity as the 20%
to 40% excess of weight over the normal of 300 grams per centimeter of height8. Others have arbitrarily proposed
body fat-dened obesity as a body fat percentage >35% for women and >25% for men9. To date, there is no
consensus for the denition of obesity based on body fat percentage10,11. A BMI ≥30 is currently used to dene
obesity12. In fact, BMI is widely used to assess body fatness12,13, despite its limited accuracy to estimate body fat
percentage9,14,15. An inherent problem of BMI due to its limited accuracy to estimate body fat percentage is mis-
classication of body fat-dened obesity. For example, a BMI ≥30 would overlook nearly 50% of women who
had a body fat percentage higher than 35%9. Among the participants of the ird National Health and Nutrition
Examination Survey, the diagnostic accuracy of BMI for body fat-dened obesity was estimated at 94% among
women compared with 82% among men9. us, simple and low-cost alternatives to BMI with better diagnostic
accuracy for obesity in both sexes would be of considerable importance.
Although several sophisticated techniques are available to obtain accurate estimates of whole-body fat per-
centage16; these methods are unsuitable for routine clinical purposes and large population studies. Consequently,
Sports Spectacular Diabetes and Obesity Wellness and Research Center, Cedars-Sinai Medical Center, Los Angeles,
CA, 90048, USA. Correspondence and requests for materials should be addressed to O.O.W. (email: Orison.
Woolcott@cshs.org)
Received: 3 May 2018
Accepted: 9 July 2018
Published: xx xx xxxx
OPEN
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numerous equations based on anthropometrics have been proposed as alternatives to BMI to better estimate
whole-body fat percentage17–25. Some published equations require more than 10 dierent anthropometric meas-
urements19, others require up to four dierent skinfold measurements21; some are relatively complex equations
with numerous terms20,25. us, one common problem among existing equations is the lack of simplicity, showing
limited potential for their use in routine clinical practice or public health.
In the present study, we systematically explored more than 350 anthropometric indices aiming to identify
a simple anthropometric linear equation that is more accurate than the BMI as a potential alternative tool for
clinical and epidemiological purposes to estimate whole-body fat percentage among female and male adult indi-
viduals. e second aim of the study was to evaluate its clinical utility.
Results
Study population. We included for analysis data from adult individuals 20 years of age and older who
participated in the National Health and Nutrition Examination Survey (NHANES) 1999–2006. NHANES
1999–2004 data (n = 12,581) were used for model development and NHANES 2005–2006 data (n = 3,456) were
used for model validation. Participants selection for the development and validation datasets is shown in Fig.1.
Characteristics of the participants studied are described in Table1. Mean valuesof whole-body fat percentage
measured by dual energy X-ray absorptiometry (DXA) in the development and validation datasets were 39.9%
and 39.4% in women, and 28.0% and 27.8% in men, respectively. e frequencies of DXA multiply imputed data
in the development and validation datasets are described in Supplementary Tables1 and 2, respectively.
Model development, performance, and selection. Supplementary Table3 shows correlation matrix
among the commonly used anthropometrics including body weight, height, BMI, triceps and subscapular skin-
folds, arm and leg lengths, and waist, calf, arm and thigh circumferences. Since arm and leg lengths showed poor
correlation with body fat percentage, they were excluded from further analysis. In total, 365 anthropometric
indices were empirically generated and tested for correlation with body fat percentage (see Supplementary Table4
for a full list of all indices generated).
Equations were derived using linear regression. Our selected regression models included those based on
the simplest indices with the highest correlation with body fat percentage among women and among men.
Among the 365 generated indices, height3/(waist × weight) showed the highest correlation with whole-body
fat percentage among women (r = −0.81; P < 0.001). (√Height)/waist equation showed the highest correlation
with whole-body fat percentage among men (r = −0.85; P < 0.001). Height3/(waist × weight) showed slightly
stronger correlation than the simple 1/BMI (r = −0.79; P < 0.001) among women. Among men, (√height)/waist
showed slightly stronger correlation than the simpler index height/waist (r = −0.84; P < 0.001). Height2/(waist ×
√weight) showed high correlations both among women and men. us, we nally selected the ve aforemen-
tioned indices to evaluate model performance.
Given height/waist is the reciprocal of the widely used waist-to-height ratio, we also examined the predicting
ability of waist/height index. Height/waist better predicted whole-body fat percentage and showed lower root
mean squared error (RMSE) than waist/height among men and women, andacross ethnic groups (Supplementary
Table5) and age categories (Supplementary Table6). us, we dropped waist/height from further analysis.
Supplementary Fig.1 shows improved linear relationship between whole-body fat percentage and height/waist
by sex and ethnicity. All selected models showed lower prediction of body fat percentage in older individuals
(Supplementary Table6). We found a progressive decline in body weight, height and fat-free mass aer 50 years
of age, and a steeper decline in fat mass and waist circumference aer 70 years of age among women and men
(Supplementary Fig.5), which coincided with the lower predicting ability of all models in older individuals.
For practical reasons, performance analyses of all selected models presented here were tested using their
rounded and simplest expression (details are provided in the Supplementary material). Raw equations are shown
in Supplementary Table7. Concordance coecients between DXA-measured whole-body fat percentage and
nal selected models are shown in Supplementary Table8.
Figure 1. Flow diagram of participant selection for the development and validation datasets. DXA, dual energy
X-ray absorptiometry.
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All selected models showed higher accuracy than BMI among women, whereas precision was improved only
in models based on three anthropometrics and 1/BMI (Supplementary Table9). Among men, height/waist equa-
tion showed the highest accuracy, and was also superior to BMI. Models based on three anthropometrics but not
1/BMI were also more accurate than BMI. All models but not 1/BMI were more precise than BMI among men
(Supplementary Table9).
Height/waist equation, named as the relative fat mass (RFM), was the nal model selected because of its sim-
plicity (it requires only two common anthropometrics), it was superior to BMI in predicting body fat percentage
among men, had similar predicting ability relative to BMI among women and had overall better performance
than BMI among women and men, independently.
Final equations are as follows:
−×Equation forwomen:76(20 (height/waist))(1)
−×Equation formen:64(20 (height/waist))(2)
or
−× +×RFM: 64 (20(height/waist)) (12sex)(3)
In equations (1–3), height and waist (circumference) are expressed in meters. In (3), sex = 0 for male and 1 for
female. e coecients for equations (1) and (2) were rounded for practical purposes.
Supplementary Fig.3 shows good agreement between RFM and DXA.
Although we found a signicant interaction between age and RFM among women (P < 0.001), that was not
case among men (P = 0.088). However, inclusion of age in the nal model did not improve R2 among women
(RFM model: R2 = 0.66; RFM and AGE model: R2 = 0.66) or among men (RFM model: R2 = 0.75; RFM and AGE
model: R2 = 0.75). Likewise, inclusion of ethnicity in the nal model did not substantially increased R2 among
men (RFM and ethnicity model: R2 = 0.76). Among women, inclusion of ethnicity in the model did not improve
body fat prediction (R2 = 0.66). us, age and ethnicity were not included in our nal model selected.
NHANES 1999–2004 NHANES 2005–2006
P value(Development dataset) (Validation dataset)
Wom en Men Wom en Men For Women For Men
N = 6,261
(51%) N = 6,320
(49%) N = 1,700
(50.3%) N = 1,756
(49.7%)
Age, yr 47.2 ± 0.3 45.0 ± 0.3 43.3 ± 0.4 42.1 ± 0.6 <0.001 <0.001
Ethnicity 0.23 0.54
Mexican-American, % 6.4 ± 0.9 8.0 ± 0.9 7.3 ± 0.9 9.5 ± 1.3
European-American, % 71.7 ± 1.8 72.2 ± 1.6 69.7 ± 3.1 71.2 ± 2.8
African-American, % 11.3 ± 1.1 9.9 ± 0.9 12.4 ± 2.2 10.8 ± 1.7
Age category <0.001 <0.001
20–39 years old, % 36.6 ± 1.0 41.3 ± 1.0 39.7 ± 1.3 44.1 ± 1.9
40–59 years old, % 39.1 ± 0.9 39.1 ± 0.7 46.9 ± 1.4 43.9 ± 1.4
≥60 years old, % 24.2 ± 0.7 19.7 ± 0.6 13.4 ± 1.1 12.1 ± 1.3
BMI category 0.10 0.02
<18.5, % 2.5 ± 0.3 1.2 ± 0.2 2.2 ± 0.5 1.2 ± 0.3
18.5–24.9, % 35.8 ± 1.1 30.0 ± 0.7 36.6 ± 1.9 25.4 ± 1.8
25–29.9, % 28.8 ± 0.9 40.9 ± 0.8 24.8 ± 1.2 39.6 ± 1.4
≥30, % 32.9 ± 1.0 28.0 ± 0.7 36.4 ± 1.7 33.8 ± 2.3
Anthropometry
Body weight, kg 74.1 ± 0.4 86.8 ± 0.3 75.8 ± 0.9 89.5 ± 0.9 0.08 0.005
Height, cm 162.2 ± 0.1 176.2 ± 0.1 162.6 ± 0.2 176.6 ± 0.2 0.05 0.08
BMI, kg/m228.2 ± 0.1 27.9 ± 0.1 28.7 ± 0.3 28.6 ± 0.3 0.17 0.01
Waist circumference, cm 93.1 ± 0.4 99.5 ± 0.3 93.9 ± 0.8 100.8 ± 0.8 0.37 0.12
Whole-body fat mass, kg 30.8 ± 0.3 25.3 ± 0.2 31.2 ± 0.6 26.0 ± 0.5 0.47 0.23
Whole-body fat free mass, kg 41.9 ± 0.2 59.5 ± 0.2 43.1 ± 0.3 61.6 ± 0.4 0.002 <0.001
Whole-body fat percentage 39.9 ± 0.2 28.0 ± 0.1 39.4 ± 0.3 27.8 ± 0.3 0.17 0.48
Trunk fat percentage 38.2 ± 0.2 29.1 ± 0.1 37.5 ± 0.3 28.8 ± 0.4 0.13 0.38
Table 1. Characteristics of adult individuals (≥20 years old) included in the study*. *Values represent pooled
weighted mean estimates (or percentages, as indicated) ± standard errors. Percentages may not total 100 due to
rounding. BMI, body mass index (weight in kilograms divided by the square of the height in meters). P values
were calculated using the Wald test.
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Model validation and performance. In the validation dataset, compared with BMI, RFM had a more
linear relationship with DXA whole-body fat percentage among women (adjusted coecient of determination,
R2: 0.69; 95% CI, 0.67–0.72; vs. 0.65; 95% CI, 0.63–0.67) and men (R2: 0.75; 95% CI, 0.72–0.77 vs. 0.61; 95%
CI, 0.59–0.63) (Fig.2 and Supplementary Table10). RFM had less bias than BMI among women (0.9%; 95%
CI, 0.6% to 1.1% vs. −10.9%; 95% CI, −11.2% to −10.5%) and a similar low bias among men (RFM: 0.5%;
BMI: 0.7%) (Table2). Among women, RFM showed higher accuracy than BMI (91.5% vs. 21.6%; P < 0.001).
RFM was also more precise than BMI (4.9%; 95% CI, 4.6–5.2% vs. 5.8%; 95% CI, 5.5–6.2%). Among men,
RFM showed higher accuracy than BMI (88.9% vs. 81.9%; P < 0.001) and better precision (RFM: 4.2%; 95%
CI, 3.9–4.6% vs. BMI: 5.1%; 95% CI, 4.9–5.4%) (Table2 and Supplementary Fig.4). Among women, RFM was
more accurate than BMI across ethnic groups (P < 0.001 for all comparisons). Among men, RFM was also more
accurate among European-Americans (P < 0.001) and African-Americans (P < 0.001) (Table2). RFM also
showed better performance than BMI across age categories (Supplementary Fig.5) and across body fat quintiles
(Supplementary Fig.6). Among men, RFM also showed better performance than CUN-BAE (Clinica Universidad
de Navarra-body adiposity estimator), Gallagher, Deurenberg and Kagawa equations, including across ethnic
groups. Among women, RFM was superior to Deurenberg and Kagawa equations (Table2).
Internal validation with bootstrapping conrmed RFM was a better predictor of body fat percentage than BMI
among women and men (Supplementary Table11). RFM predicting ability decreased with age (Supplementary
Table12). RFM was more accurate and more precise than BMI (Supplementary Table13) and had superior accu-
racy than BMI across age categories (Supplementary Fig.7 and Supplementary Table14) and body fat ranges;
however, accuracy was lower in leaner individuals (Supplementary Fig.8).
RFM was a better predictor of trunk fat percentage than of whole-body fat percentage or whole-body fat mass
(Supplementary Table15).
Obesity misclassication. To compare the rates of obesity misclassication between BMI and our nal
model, we arbitrarily dened obesity as DXA-measured body fat percentage ≥33.9% for women and ≥22.8% for
men, based on the corresponding cut-points between the rst and second quintiles for each sex. ese cut-points
were calculated using combined datasets (NHANES 1999–2006). In the validation dataset, when using same DXA
Figure 2. Prediction of whole-body fat percentage by RFM using linear regression in NHANES 2005–2006
(validation dataset). RFM, relative fat mass, which is based on height/waist. R2, coecient of determination;
RMSE, root mean squared error. Data plots correspond to DXA imputation 1.
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All Mexican-American European-American African-American
Women (n = 1,700)
Bias (95% CI)
BMI −10.9 (−11.2 to −10.5) −11.0 (−11.5 to −10.5) −11.0 (−11.3 to −10.6) −9.3 (−10.0 to −8.6)
RFM†0.9 (0.6 to 1.1) 1.5 (1.1 to 2.0) 0.6 (0.4 to 0.9) 1.5 (0.6 to 2.3)
CUN-BAE equation‡−0.2 (−0.5 to 0.1) −0.4 (–1.4 to 0.7) −0.4 (−0.7 to 0.0) 1.6 (0.9 to 2.4)
Gallagher equation§−2.8 (−3.1 to −2.6) −2.9 (−3.9 to −2.0) −2.9 (−3.1 to −2.6) −1.4 (−2.2 to −0.6)
Deurenberg equation¶−2.3 (−2.7 to −2.0) −2.9 (−3.8 to −2.1) −2.3 (−2.7 to −1.8) −0.3 (−1.2 to 0.6)
Kagawa equation#1.9 (1.5 to 2.4) 3.6 (2.7 to 4.5) 1.6 (1.2 to 2.0) 3.9 (3.0 to 4.8)
Accuracy (95% CI)
BMI 21.6 (18.9 to 24.4) 17.8 (13.4 to 22.2) 20.4 (17.5 to 23.3) 36.3 (30.8 to 41.8)
RFM 91.5 (89.9 to 93.0) 91.7 (88.2 to 95.3) 92.1 (90.1 to 94.2) 89.4 (86.2 to 92.5)
CUN-BAE equation 92.0 (90.3 to 93.7) 91.0 (86.7 to 95.2) 93.0 (90.9 to 95.2) 92.1 (88.4 to 95.9)
Gallagher equation 88.4 (86.1 to 90.8) 87.5 (82.5 to 92.4) 88.9 (85.7 to 92.1) 91.8 (88.2 to 95.4
Deurenberg equation 79.0 (76.9 to 81.1) 76.5 (69.3 to 83.6) 80.4 (77.8 to 83.0) 79.8 (75.7 to 83.8)
Kagawa equation 82.8 (80.9 to 84.8) 76.1 (69.7 to 82.6) 84.8 (82.5 to 87.1) 75.1 (70.7 to 79.5)
Precision (95% CI)
BMI 5.8 (5.5 to 6.2) 4.7 (4.0 to 5.4) 5.7 (5.3 to 6.1) 5.7 (5.1 to 6.2)
RFM 4.9 (4.6 to 5.2) 4.6 (4.0 to 5.3) 4.9 (4.5 to 5.2) 5.3 (4.7 to 5.9)
CUN-BAE equation 6.0 (5.7 to 6.3) 6.0 (5.4 to 6.5) 5.9 (5.5 to 6.3) 5.6 (4.8 to 6.5)
Gallagher equation 5.2 (4.9 to 5.5) 5.0 (4.4 to 5.7) 5.1 (4.7 to 5.5) 5.1 (4.5 to 5.7)
Deurenberg equation 7.5 (7.1 to 8.0) 7.5 (6.6 to 8.5) 7.3 (6.6 to 7.9) 8.3 (7.5 to 9.1)
Kagawa equation 7.3 (6.9 to 7.7) 7.2 (6.2 to 8.2) 7.2 (6.8 to 7.7) 7.7 (6.8 to 8.6)
Men (n = 1,756)
Bias (95% CI)
BMI 0.7 (0.5 to 0.9) 0.6 (0.1 to 1.0) 0.5 (0.3 to 0.8) 2.8 (2.1 to 3.5)
RFM 0.5 (0.3 to 0.8) 1.0 (0.5 to 1.5) 0.5 (0.2 to 0.7) 0.9 (0.3 to 1.4)
CUN-BAE equation −0.1 (−0.4 to 0.2) −0.9 (−1.4 to −0.33) −0.24 (−0.7 to 0.2) 2.0 (1.3 to 2.7)
Gallagher equation −3.7 (−3.8 to −3.5) −4.4 (−4.8 to −4.1) −3.7 (−3.9 to −3.5) −1.7 (−2.3 to −1.1)
Deurenberg equation −1.9 (−2.3 to −1.6) −3.7 (−4.2 to −3.1) −1.9 (−2.4 to −1.4) −0.3 (−1.3 to 0.8)
Kagawa equation 2.3 (2.0 to 2.6) 3.1 (2.9 to 3.3) 2.1 (1.8 to 2.5) 2.3 (1.5 to 3.2)
Accuracy (95% CI)
BMI 81.9 (79.6 to 84.3) 88.9 (87.0 to 90.7) 82.6 (79.7 to 85.4) 67.1 (57.8 to 76.5)
RFM 88.9 (86.8 to 91.1) 91.3 (88.9 to 93.7) 88.7 (86.0 to 91.3) 86.7 (81.3 to 92.1)
CUN-BAE equation 79.1 (76.6 to 81.7) 83.3 (78.6 to 88.1) 79.7 (76.9 to 82.6) 70.0 (61.1 to 78.8)
Gallagher equation 71.0 (68.4 to 73.7) 64.6 (58.5 to 70.6) 71.2 (67.7 to 74.7) 80.4 (76.8 to 84.0)
Deurenberg equation 69.4 (66.8 to 72.0) 64.4 (58.8 to 69.9) 69.8 (66.4 to 73.2) 71.9 (67.2 to 76.5)
Kagawa equation 76.1 (73.4 to 78.8) 74.8 (69.0 to 80.5) 76.3 (73.4 to 79.3) 71.5 (64.6 to 78.3)
Precision (95% CI)
BMI 5.1 (4.9 to 5.4) 4.1 (3.6 to 4.7) 5.2 (4.8 to 5.6) 5.2 (4.5 to 5.8)
RFM 4.2 (3.9 to 4.6) 3.8 (3.3 to 4.3) 4.4 (4.0 to 4.8) 3.9 (3.5 to 4.3)
CUN-BAE equation 5.7 (5.3 to 6.2) 5.3 (4.6 to 5.9) 5.8 (5.2 to 6.3) 5.7 (5.1 to 6.4)
Gallagher equation 5.0 (4.4 to 5.5) 4.3 (3.8 to 4.8) 5.0 (4.4 to 5.6) 4.9 (4.3 to 5.5)
Deurenberg equation 6.2 (5.8 to 6.6) 5.6 (4.7 to 6.5) 6.1 (5.5 to 6.8) 5.7 (5.0 to 6.5)
Kagawa equation 5.0 (4.6 to 5.4) 4.1 (3.5 to 4.7) 5.1 (4.7 to 5.5) 5.3 (4.7 to 5.8)
Table 2. Comparison of performance between RFM and published equations based on BMI or waist-to-
height ratio for prediction of body fat percentage among adult participants (n = 3,456) in the validation
dataset (NHANES 2005–2006)*. *Values represent weighted estimates with 95% condence intervals (95%
CI) from DXA imputed data. Model performance was evaluated as follows: Bias was calculated as the
median dierence between estimated and measured body fat percentage. Accuracy was calculated as the
proportion of cases with <20% dierence between estimated and measured body fat percentage. Precision
was calculated as the condence interval of the interquartile range of the dierence between estimated
and measured body fat percentage. †RFM equation: 64 − (20 × height/waist) + (12 × sex). ‡CUN-BAE
equation: −44.988 + (0.503 × age) + (10.689 × sex) + (3.172 × BMI) − (0.026 × BMI2) + (0.181 × BMI ×
sex) − (0.02 × BMI × age) − (0.005 × BMI2 × sex) + (0.0002 × BMI2 × age). §Gallagher equation: 64.5 −
(848 × (1/BMI)) + (0.079 × age) − (16.4 × sex) + (0.05 × sex × age) + (39.0 × sex × (1/BMI)). ¶Deurenberg
equation: − (11.4 × sex) + (0.20 × age) + (1.294 × BMI) − 8. #Kagawa equation: − 8.339 + (92.701 × waist/
height) − (0.078 × age) − (11.062 × sex). For RFM and CUN-BAE equations, sex = 0 for male and 1 for
female. For Gallagher, Deurenberg and Kagawa equations, sex = 1 for male and 0 for female. For CUN-BAE,
Gallagher, Deurenberg and Kagawa equations, age in years. For RFM and Kagawa equations, height and waist
(circumference) in meters. BMI, body mass index (body weight in kilograms divided by squared height in
meters); CUN-BAE, Clinica Universidad de Navarra-body adiposity estimator; RFM, relative fat mass.
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cut-points for obesity diagnosis (≥33.9% for women and ≥22.8% for men), RFM had higher sensitivity than
BMI. Table3 shows total positive and negative cases of obesity identied using either BMI or RFM. RFM resulted
in fewer false negatives among women (5.0%; 95% CI, 3.1–6.8% vs. 72.0%; 95% CI, 67.3–76.6%; P < 0.001) and
men (3.8%; 95% CI, 1.8–5.8% vs. 4.1%; 95% CI, 2.1–6.1%; P < 0.001). ere were fewer false positives with RFM
among men (32.3%; 95% CI, 25.8–38.8% vs. 49.7%; 95% CI, 44.2–55.3%; P < 0.001) but more false positives
among women (41.0%; 95% CI, 32.2–49.9% vs. 0%; P < 0.001).
Obesity total misclassication was also lower with RFM than with BMI among all women (12.7% vs. 56.5%; P < 0.001)
and all men (9.4% vs. 13.0%; P < 0.001) (Fig.3), and among all Mexican-Americans (8.2% vs. 35.4%; P < 0.001),
all European-Americans (11.3% vs. 35.2%; P < 0.001) and all African-Americans (9.9% vs. 37.2%; P < 0.001).
In the internal validation dataset, compared with BMI, obesity total misclassication was lower with RFM
among women (P < 0.001) and men (P < 0.001), among all Mexican-Americans, all European-Americans and all
African-Americans (P < 0.001 for all three ethnic groups), and across age categories (P < 0.001 for all compari-
sons). Although we found a lower total misclassication rate with RFM among other ethnicities (Non-Hispanic
Asians, Native Americans, and those who self-reported multiple ethnicity) (RFM: 12.9%, BMI: 41.9%; P < 0.001),
these ndings should be interpreted with caution as NHANES 1999–2006 did not oversample to get reliable esti-
mates on these minority American ethnic groups.
Diagnostic accuracy for obesity and diabetes. In the validation dataset, compared with BMI, RFM
showed better diagnostic accuracy for body fat-dened obesity among men (area under curve [AUC]: 0.94 vs.
0.91; P < 0.001) and similar diagnostic accuracy among women (AUC: 0.929 vs. 0.933; P = 0.52). RFM was also
better than BMI in identifying diabetes cases among women (AUC: 0.79 vs 0.73; P = 0.002) and men (AUC: 0.80
vs. 0.76; P = 0.001).
Sensitivity analysis of the combined datasets showed RFM had a better diagnostic accuracy than BMI for high
body-fat percentage among men (P < 0.001) regardless the DXA cut-point used to dene obesity (Supplementary
Fig.9). RFM also showed a signicant improvement over BMI and Gallagher, CUN-BAE and Deurenberg equa-
tions among men (Supplementary Table16).
RFM was superior to DXA-measured trunk fat percentage in discriminating diabetes among women
(P < 0.001) but not among men (P = 0.548) (Supplementary Fig.10).
Discussion
In the present study, we identified the relative fat mass (RFM), which is a simple linear equation based on
height-to-waist ratio, as a potential alternative tool to estimate whole-body fat percentage in women and men 20
years of age and older. Our analyses were performed using nationally representative samples of the US adult pop-
ulation which allowed us to evaluate the performance of RFM among Mexican-Americans, European Americans,
and Africans-Americans.
In the validation dataset, the performance of RFM to estimate DXA-measured body fat percentage was overall
more consistent than that of BMI among women and men, across ethnic groups, young, middle-age and older
adults, and across quintiles of body fat percentage, although the accuracy of RFM was lower among individ-
uals with lower body fatness. RFM also showed overall better performance (accuracy and precision) than the
CUN-BAE, Gallagher, Deurenberg and Kagawa equations to estimate whole-body fat percentage among women
and men.
e selection of our nal model deserves some comment. e main aim of the present study was to identify
a simple anthropometric equation, that could potentially be used for clinical and epidemiological purposes, as
an alternative to BMI to better assess body fatness among adult individuals. No attempt was made to generate
non-linear equations or complex linear equations based on a high number of anthropometrics. Previous studies
have addressed this point19,22. Although our selected models based on three anthropometrics showed the highest
adjusted R-squared than those based on two anthropometrics among women, we believe they would unlikely
represent a practical alternative to BMI. Although the equations based on 1/BMI and height/waist showed a good
predicting value among women and men, respectively, a dierent index for each sex would also result in low
practicality when compared with BMI. us, we nally selected the height/waist equation (RFM) because it was
DXA-Negative DXA-Positive Total DXA-Negative DXA-Positive Total
Wom en
BMI-Negative 622 1,960 2,582 RFM-Negative 362 110 472
BMI-Positive 0 818 818 RFM-Positive 260 2,668 2,928
Tot al 622 2,778 3,400 To tal 622 2,778 3,400
Men
BMI-Negative 366 70 436 RFM-Negative 468 74 542
BMI-Positive 386 2,690 3,076 RFM-Positive 284 2,686 2,970
Tot al 752 2,760 3,512 To tal 752 2,760 3,512
Table 3. Positive and negative cases of DXA-diagnosed obesity* identied using either BMI or RFM among
adult participants (n = 3,456) in the validation dataset (NHANES 2005–2006). *Obesity was dened as a DXA
body fat percentage ≥33.9% for women and ≥22.8% for men based on the cut-points between the rst and
second quintiles for each sex. DXA, dual energy X-ray absorptiometry.
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the simplest equation among all selected models that better estimated whole-body fat percentage than the BMI
among women and men, independently. Although waist-to-height ratio is widely used in epidemiology as a pre-
dictor of cardiovascular risk factors26,27, our results from the development dataset showed better linear relation-
ship between whole-body fat percentage and height-to-waist ratio (the foundation of RFM) versus waist-to-height
ratio among women, men, across ethnic groups, and age categories (Supplementary Tables5 and 6).
It should be noted that for body fat estimation purposes, the useful waist-to-height ratio is not an intuitive surro-
gate of whole-body fat percentage.
In our validation dataset, we found a high rate of false negative cases (low sensitivity) of body fat-dened obe-
sity when using BMI at the cut-points arbitrarily chosen, both among women and men. ese ndings are con-
sistent with those from previous studies, regardless the DXA body fat cut-points used to dene obesity9,28,29. An
RFM ≥33.9 for women and ≥22.8 for men showed a high sensitivity to identify individuals with obesity, 95.0%
and 96.2%, respectively. Likewise, using same cut-points, RFM had lower rates of obesity total misclassication
than BMI among all women and all men and among Mexican-Americans (8.2%), European-Americans (11.3%)
and African-Americans (~9.9%), indicating a consistent and relatively low rate of obesity misclassication with
RFM across these ethnic groups.
e lower rates of obesity misclassication with RFM compared with BMI (among women: ~13% vs. ~57%,
respectively; among men: ~9% vs. ~13%), supports the clinical utility of RFM to identify individuals with high
body fat percentage, a condition that has been associated with increased mortality1–3. Overall, our data show
that the lower rates of obesity total misclassication with RFM are largely due to the higher sensitivity (lower
false negatives) of RFM for body fat-dened obesity among women and men, supporting the potential of RFM
as a screening tool for obesity. Compelling evidence indicates lifestyle intervention in adult individuals with
overweight or obesity may reduce morbidity and all-cause mortality29,30. us, one important aspect will be to
evaluate whether early lifestyle intervention in individuals with high body fat percentage assessed by RFM could
oer clinical benets to reduce morbidity and mortality in the short and long term.
One limitation of previous studies proposing predicting equations of body fat percentage is the lack of infor-
mation on the diagnostic accuracy for high body fatness19,20,25. In the present study, RFM showed better diag-
nostic accuracy for body fat-dened obesity among men compared with BMI and the CUN-BAE, Gallagher
and Deurenberg equations. Among women, RFM had similar diagnostic accuracy for obesity than BMI and
CUN-BAE, Gallagher, Deurenberg and Kagawa equations. us, one benet of using RFM over BMI is its rel-
atively high diagnostic accuracy for obesity in both sexes (AUC ≥ 0.93). An additional advantage of RFM over
Figure 3. Obesity total misclassication error in NHANES 2005–2006. Bars show comparison of total
misclassication of obesity diagnosed by DXA-whole-body fat percentage (≥33.9% for women and ≥22.8% for
men, based on the corresponding cut-points between the rst and second quintiles for each sex) when using
RFM and BMI at same DXA cut-points and a BMI of 30. Error bars are standard error.
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BMI was its superior diagnostic accuracy for diabetes, a well-established cardiovascular risk factor31. RFM also
showed superior diagnostic accuracy for diabetes relative to CUN-BAE and Gallagher equations among women.
Our ndings are consistent with meta-analyses of numerous cross-sectional studies, concluding waist-to-height
ratio is superior to BMI to identify cardiovascular risk factors, including diabetes26,27.
Measurement of waist circumference is unstandardized and subject to variability. However, measurement
error due to the anatomical placement of measuring tape appears to have little eect on the association between
waist circumference and cardiovascular risk factors, including diabetes32. Moreover, the reproducibility between
measurements is very high33. Nevertheless, if waist circumference measurements become part of routine clinical
evaluation, it should be implemented with adequate tools and professional training.
e present study has some limitations. (1) We used DXA as the reference method. Compared with the
four-compartment method, DXA underestimates fat percentage in the lower ranges and in men, and overesti-
mates fat percentage in the higher ranges and in women34,35. us, the performance of RFM could well be slightly
superior or inferior to the actual estimates depending on the relative fat mass and sex. (2) NHANES data analysis
by ethnicity was limited to Mexican-American, European-American, and African-American adult individuals.
erefore, our results cannot be extrapolated to other ethnic groups. Future studies will be required to evaluate
the performance of RFM in other ethnicities (e.g. Asians and Native-American populations) as well as in chil-
dren, athletes, and in individuals with specic diseases. (3) Our study was cross-sectional and used a single-point
measurement of each anthropometric. us, our study was not designed to propose RFM cut-points for the diag-
nosis of obesity. We dened obesity using arbitrary cut-points of DXA-measured body fat percentage to compare
obesity misclassication by RFM and BMI. Sensitivity analysis showed RFM had better diagnostic accuracy for
obesity than BMI among men regardless the cut-point used to dene obesity. (4) RFM validation was limited to a
nationally representative sample of the US population. External validation of the RFM performance and obesity
misclassication with RFM in populations from other countries are warranted.
Our findings showed RFM equation, which is based on height/waist, had superior performance (accu-
racy and precision) to BMI and the CUN-BAE, Gallagher, Deurenberg and Kagawa equations to estimate
whole-body fat percentage in women and men. Overall, total misclassication of body fat-dened obesity with
RFM was lower than with BMI among women and men, across ethnic groups, including Mexican-Americans,
European-Americans and African-Americans. We conclude that, in the population studied, RFM was more accu-
rate than BMI to estimate whole-body fat percentage among women and men and improved body fat-dened
obesity misclassication among American adult individuals of Mexican, European or African ethnicity.
Methods
Study population. NHANES is a program designed to study the health and nutritional status of the non-in-
stitutionalized population of the United States. NHANES is conducted annually and released in two-year cycles
using a nationally representative sample across the country, selected using a multistage, probability sampling
design. NHANES 1999–2004 and NHANES 2005–2006 oversampled Mexican-American and African-American
populations to obtain representative samples of these ethnic groups for reliable estimates36. us, analysis by eth-
nic groups were limited to Mexican-American, European-American (White) and African-American individuals.
e present study did not require approval or exemption from the Cedars-Sinai Medical Center Institutional
Review Board as it involved the analysis of publicly available de-identied data only.
Data. An advantage of using NHANES for the present study is that it constitutes the largest database contain-
ing information on whole-body composition for the US population, which was collected between 1999 and 2006
using the well accepted method DXA37,38. us, DXA was used as the reference method to measure whole-body
fat percentage.
NHANES 1999–2004 was used as the development dataset. Multiple imputation was applied to replace miss-
ing DXA data39. Details are provided in the Supplementary Material. Model development included individuals 20
to 85 years of age. In total, 12,581 observations were included for model development (Fig.1).
NHANES 2005–2006 was used as the validation dataset. Multiple imputation was also used to account for
missing data (see Supplementary Material). Model validation included individuals 20 to 69 years of age, as DXA
was performed only on individuals 69 years old and younger in this sample. In total, 3,456 observations were
included for model validation (Fig.1).
Anthropometric measurements. Waist circumference was measured placing the measuring tape around
the trunk (unclothed waist) in a horizontal plane at the level of the uppermost lateral border of the right ilium
during standing position at the end of the expiration. e measurement was recorded to the nearest 0.1 cm. Body
weight was measured with an electronic scale (examinee wearing underwear only). Height was measured with an
electronic stadiometer40. Other anthropometrics were measured using standard procedures40.
DXA scans. DXA scans were acquired using a Hologic QDR 4500A fan-beam densitometer (Hologic, Inc.,
Bedford, Massachusetts) and Hologic DOS soware version 8.26:a3*. Scans were reviewed and analyzed by the
University of California, San Francisco, using Hologic Discovery soware, version 12.1 for NHANES 1999–2004
and version 12.4 for NHANES 2005–200639. Body fat percentage was calculated as the ratio of DXA whole-body
fat mass (g) to DXA whole-body total mass (g), multiplied by 100.
Model development and selection. Common anthropometrics including body weight, height, triceps
and subscapular skinfolds, arm and leg lengths, and waist, calf, arm and thigh circumferences were tested for
correlation with DXA-measured whole-body fat percentage in men and women, independently. Simple and
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combined anthropometrics that had the highest correlation with body fat percentage among women and men,
independently, were the foundation for our model development using linear regression for survey data. We also
explored the eect of adding age and ethnicity in the regression models. Two- and three-way anthropometric
indices were generated, including combination of integer powers, square root, and reciprocal transformations.
Model selection was based on the ability to predict whole-body fat percentage (R2) in both women and men and
sex-ethnicity subgroups, the lowest RMSE, the lowest Akaike information criterion41, the overall performance
in terms of accuracy and precision, and the simplicity to estimate body fat percentage in both women and men.
Further details are provided in the Supplementary Material.
Model validation. Validation of the nal model was performed in NHANES 2005–2006. RFM performance
was validated in the participants of the NHANES 2005–2006, a large nationally representative sample of the US
adult population but dierent sample from the development dataset. Development and validation datasets were
combined into one dataset (NHANES 1999–2006, n = 16,037 adult individuals) to perform internal validation
using the most accepted technique, the bootstrapping, to obtain bootstrapped standard errors and verify the sta-
tistical dierences between selected models and BMI42.
Model performance. We used concordance correlation coecient and Bland-Altman plots to examine the
agreement between estimated and DXA-measured body fat percentage43. Bias was calculated as the median dif-
ference between estimated and measured body fat percentage. For the purpose of the present study, accuracy
(how closely an individual estimate agrees with the “true” or reference value) was calculated as the proportion of
cases with <20% dierence between estimated and DXA-measured whole-body fat percentage44. Precision was
calculated as the interquartile range of the dierence between estimated and measured body fat percentage44.
e performance of our nal model was compared with four published equations that are based on age and BMI
or waist-to-height ratio reported to have a high prediction for body fat percentage: Gallagher25, CUN-BAE20,
Deurenberg45 and Kagawa equations46.
Obesity misclassication. To date, there is no consensus on the diagnosis of obesity based on body fat
percentage. us, to dene obesity based on body fat percentage we used arbitrary cut-points of DXA-measured
body fat percentage: ≥33.9% for women and ≥22.8% for men (corresponding cut-points between the rst and
second quintiles for each sex). Misclassication of body fat-dened obesity was expressed as false negative rate
(1–sensitivity), false positive rate (1–specicity), and total misclassication error (the proportion of false positives
and false negatives together among all women, all men, and among both sexes combined).
Diagnostic accuracy for obesity and diabetes. Diabetes was dened if an individual had a measured
glycated hemoglobin ≥6.5% or a fasting plasma glucose ≥126 mg/dL or self-reported diagnosed diabetes47.
Diagnostic accuracy for obesity and diabetes were estimated using the receiver-operating-characteristic curve
analysis, expressed as the AUC48.
Statistical analysis. We used clusters and strata information and probability weights for all analyses to
account for the complex design of the NHANES49. Estimates of the Akaike information criterion and concordance
correlation coecient were adjusted for probability weights only. Initial examination of the association between
body fat percentage and anthropometrics, including those generated in the present study, were performed using
unweighted data. Listwise deletion was used to handle missing data for correlation analyses. Pooled data estimates
(and their 95% condence intervals) were obtained using Rubin’s equations50 implemented in STATA for analysis
of multiple imputation in complex survey data. Variance estimates for development and validation datasets were
obtained using Taylor series linearization. Bootstrapping with 1000 replicates was used to obtain condence
intervals for adjusted R-squared and RMSE in the development and validation datasets and to perform internal
validation. Wald test was used to test for interaction of ethnicity and age category with selected indices on the
prediction of body fat and to calculate P values to evaluate the accuracy and diagnostic accuracy (AUC) between
models51. Bonferroni correction was applied for multiple comparisons. All analyses were performed using Stata
14 for Windows (StataCorp LP, College Station, TX). P values were set to a two-tailed alpha level of 0.05.
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Acknowledgements
We are indebted to Dr. Francesca Piccinini, Dr. Morvarid Kabir and Dr. Paul Zimmet for their very helpful
comments on the manuscript, and to Dr. William F. Woolcott for his valuable discussion on the clinical
application of our nal model equation. We also thank the Centers for Disease Control and Prevention (CDC)
and the National Center for Health Statistics (NCHS) for providing access to the NHANES datasets. ese studies
were supported by the National Institutes of Health (Grants DK29867 and DK27619 to RNB). e funders had no
role in the study design, collection, analysis or interpretation of the data, writing the manuscript, or the decision
to submit the paper for publication.
Author Contributions
e authors’ responsibilities were as follows: O.O.W. and R.N.B.: designed the research; O.O.W.: conducted
the research; O.O.W.: performed the statistical analysis; O.O.W. and R.N.B.: wrote the paper; O.O.W.: takes full
responsibility for the work as a whole, including the study design, access to data, and the decision to submit and
publish the manuscript; and all authors: read and approved the nal manuscript.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-018-29362-1.
Competing Interests: e authors declare no competing interests.
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