# Development and validation of anthropometric equations to estimate body composition in adult women

### Translated title (es): Desarrollo y validación de ecuaciones antropométricas para estimar la composición corporal en mujeres adultas

#### Abstract

#### Resumen

## Introduction

Colombian adult women (age range 18 to 64 years) had a high prevalence of overweight (35.0%) and obesity (20.1%) that coexists with less proportion of underweight people (3.0%)
^{1}
. These prevalences are based on the body mass index (BMI) application
^{1}
. The BMI is a body weight-height index that does not differentiate the fat mass from the fat free mass
^{2}
^{,}
^{3}
. This is relevant since it is the excess of fat mass, nor necessarily the excess of body weight, that represents higher risk of developing cardiovascular diseases and type 2 diabetes
^{2}
^{,}
^{4}
. Correspondingly, is the deficit of fat free mass, frequently observed in underweight, but also in normal weight and overweight people, that associates with negative clinical outcomes, lower functional capacities, and impairment of overall health
^{3}
. Therefore, in sceneries looking to prevent, diagnose, and treat underweight, overweight, and obesity, the application of methods to assess body composition (i.e. fat mass and fat free mass) are preferred than the body weight-height indices like BMI
^{2}
^{,}
^{3}
.

Anthropometric equations are widely used to estimate body composition and recently new equations have been developed for specific populations
^{5}
^{-}
^{9}
. The equations are developed following three general steps
^{10}
. First, body composition is determined in a group of people by a reference method (i.e. a highly acute laboratory method). Second, in the same group of people measurements such as body weight, height, skinfold thickness and circumferences are collected. Third, the collected body measurements are used as predictors to obtain the best equation estimating the quantities of fat mass or fat free mass
^{10}
. In general, anthropometric equations are population specific, given that the relation between body measurements and body components (i.e. fat mass and fat free mass calculated from body density) are modified by age, sex, and ethnicity
^{2}
^{,}
^{11}
. Therefore, an anthropometric equation should not be applied to a population different from it was derivate without a previous validation
^{2}
^{,}
^{11}
. Durning-Womersly
^{12}
and Jackson-Pollock
^{13}
are traditional equations commonly used to evaluate body composition worldwide. These equations and the more recently published by Ramirez-Torun
^{14}
have shown poor validity to estimate body composition in Colombian women
^{15}
.

This study aimed to develop and validate practical anthropometric equations to estimate body composition in women living in Medellín-Colombia. The study hypothesized the new equations will perform better in Colombian women than the equations developed in foreign countries.

## Materials and Methods

### Study design and participants

This is a cross-sectional study with a convenience sample of 151 women with ages between 18 to 59 years. Participants were students, teachers and volunteers attending the outreach programs from the University of Antioquia, Medellín-Colombia. No athletes were included in the study or women with implants (e.g. silicon, plastic, metal), in pregnancy or having any other physiological conditions that might have altered the results. The study was approved by the Bioethics Committee of the Faculty of Medicine from the University of Antioquia and was performed according to the Helsinki Declaration. Written consent was obtained from each participant.

Hydrodensitometry and anthropometric measurements were done in the Human Body Composition Laboratory, at the School of Nutrition and Dietetics from the University of Antioquia, Medellín-Colombia. Participants were scheduled to attend the laboratory a day that did not include five days before or after menses. Volunteers were asked to avoid intense physical activity and food that produces gases (e.g. beans, broccoli, and cabbage) the day before the test. Participants arrived at the laboratory between 7:00 am and 9:00 am after a fast period of at least four hours. After urinating/defecating volunteers removed garments, jewels, and wore a bathing suit for anthropometric and hydrodensitometry measurements.

### Anthropometry

Measurements were carried out by two trained anthropometrists following the standard techniques described by Lohman, *et al*
^{16}
. Body weight was measured to the nearest 0.05 kg using a digital scale (Detecto CN20LS, USA). Height was measured to the nearest 0.1 cm using an anthropometer (GPM 101, Switzerland). Arm, waist, abdominal, hip, thigh, and calf circumferences were measured to the nearest 0.1 cm using a metal tape (Lufkin W606PM, USA). Skinfold thickness was measured to the nearest 0.2 mm with a caliper (Harpenden CE0120, England) including biceps, triceps, subscapular, midaxillary, suprailiac, abdominal, medium thigh, and medial calf. Anthropometric measurements were done at least by duplicate or by triplicate when the difference between the first and the second values were higher than 0.05 kg in body weight, 0.5 cm in height, 1% in circumferences, and 5% in skinfold thickness. Body composition was calculated using Durning-Womersly
^{12}
, Jackson-Pollock
^{13}
, and Ramirez-Torun
^{14}
equations.

### Hydrodensitometry

Body density was determined by underwater weighing with simultaneous measurement of residual lung volume. Volunteers entered to a tank filled with water at 36 ±0.2^{º}C and sat on a plastic chair suspended from a scale with 0.02 kg of sensitivity (Chatillon, C-103616, USA). Participants submerged completely in water using a nose clip and breathing through a mouthpiece connected to a spirometer (Sensor Medics, VMAX 22, USA). Residual lung volume and underwater weight were recorded simultaneously at the end of a maximal exhalation. Body volume was calculated by subtracting underwater body weight (UBW) from body weight, and dividing the difference by water density at 36^{º} C [i.e. body volume = (body weight - UBW) / water density]. Then, body volume was adjusted by subtraction of the residual lung volume and 0.1 L of estimated intestinal gas, as recommended
^{17}
. Body density was calculated dividing body weight by the adjusted body volume. The whole procedure was repeated at least twice or up to obtain two body densities with a difference ≤ 0.002 g/mL in each participant. The selected body densities were averaged and the BF% was calculated with the Siri equation, BF% = 4.95 / body density - 4.50
^{17}
.

### Statistical analysis

Normal distribution of data was tested with the Kolmogorov-Smirnov test. Means, standard deviation and range were calculated for all variables. Participants´ data were randomly divided in two groups; equation-building group (n=106) and validation group (n= 45). Multiple linear regression models were ran using anthropometric data in the equation-building group as predictors, to identify the best prediction equations of the BF%. The equations were ascertained by identifying the models that meet the normality, collinearity, variance homogeneity and the Durbin Watson´s criterion. The Akaike information criterion (AIC) that estimates the quality of the statistical models was also calculated for each equation. Two selected equations using two skinfold thickness, one circumference, height, and age, showed a good adjusted determination coefficient (adjusted r^{2}) and a low standard error of the estimate (SEE). Using the same criteria, a third equation that did not include skinfold thickness among the predictors was also selected. These equations were used to estimate the BF% in the validation group and the adjusted r^{2} and the SEE were obtained. Averages of BF%, fat mass, and fat free mass estimated by the new equations and those of Durning-Womersley, Jackson-Pollock and Ramirez-Torun were compared with hydrodensitometry using paired t-test. Pearson correlation coefficient and Intraclass correlation coefficient (ICC) for BF% were also calculated. Data analyses were made using The Statistical Package for Social Sciences for Windows (SPSS. 22.0, 2013, SPSS, Inc, Chicago, IL).

## Results

Twelve subjects did not successfully complete the underwater weighing test, mainly for being unable to breathe underwater through the mouthpiece. These subjects were excluded from the analysis and did no differ in any anthropometric measurements from the participants used to develop and validate the equations. Complete anthropometric measurements and underweight weighing were obtained in 151 women, ranging from 18 to 59 years old. Participants´ data were randomly divided in two groups, equation-building group (n=106) and validation group (n=45). There were not significant differences between groups in age (33.5 ±12.9; 35.0 ±11.9 y, *p* =0.656), BMI (23.6 ±3.0; 23.7 ±3.4 kg/m^{2}, *p* =0.833), BF% (31.2 ±5.9; 31.3 ±6.1, *p* =0.975) or any anthropometric measurement (Table 1). The BF% ranged between 19% to 44% in the equation-building group, and between 21% to 44% in the validation group (Table 1).

Characteristics | Equation-building group (n= 106) | Validation group (n= 45) | |||
---|---|---|---|---|---|

Mean ± SD | Range | Mean ± SD | Range | ||

Age (yrs)* | 33.5 ± 12.9 | 18-59 | 35.0 ± 11.9 | 19-59 | 0.656 |

Body weight (kg)* | 58.6 ± 8.0 | 42-83 | 59.6 ± 8.2 | 43-72 | 0.669 |

Height (cm) | 157.6 ± 6.5 | 143-175 | 158.5 ± 6.4 | 143-174 | 0.309 |

Body mass index (kg/m^{2})* |
23.6 ± 3.0 | 18-31 | 23.7 ± 3.4 | 19-32 | 0.833 |

Arm circumference (cm)* | 27.7 ± 2.6 | 22-34 | 28.2 ± 3.1 | 23-36 | 0.333 |

Waist circumference (cm) |
59-93 | 74.5 ± 8.4 | 61-89 | 0.851 | |

Abdominal circumference (cm)* | 84.2 ± 7.6 | 69-105 | 85.4 ± 6.9 | 69-101 | 0.528 |

Hip circumference (cm) | 97.5 ± 5.6 | 84-105 | 97.9 ± 5.7 | 84-112 | 0.726 |

Medium-thigh circumference (cm) | 49.4 ± 4.0 | 41-60 | 49.9 ± 3.6 | 41-58 | 0.456 |

Calf circumference (cm) | 35.3 ± 2.5 | 30-44 | 35.8 ± 2.5 | 31-42 | 0.391 |

Bicipital skinfold (mm)* | 10.2 ± 3.4 | 4-25 | 10.5 ± 4.7 | 4-17 | 0.372 |

Tricipital skinfold (mm) | 19.5 ± 4.9 | 11-32 | 21.3 ± 5.7 | 9-30 | 0.072 |

Subscapular skinfold (mm)* | 22.5 ± 8.8 | 8-47 | 22.9 ± 9.1 | 8-50 | 0.085 |

Midaxillary skinfold (mm)* | 17.7 ± 7.0 | 7-38 | 18.5 ± 7.6 | 7-36 | 0.801 |

Suprailiac skinfold (mm) | 34.0 ± 8.0 | 18-52 | 34.8 ± 7.6 | 12-52 | 0.187 |

Abdominal skinfold (mm)* | 28.2 ± 7.8 | 14-59 | 27.4 ± 7.1 | 14-51 | 0.723 |

Medium-thigh skinfold (mm) | 27.1 ± 7.9 | 11-48 | 29.7 ± 9.8 | 13-51 | 0.092 |

Medial-calf skinfold (mm) | 19.5 ± 6.4 | 6-33 | 19.8 ± 7.9 | 5-43 | 0.866 |

Body density (g/mL) | 1.028 ± 0.012 | 1,003-1,055 | 1.029 ± 0.013 | 1,005-1,055 | 0.820 |

Body Fat (%) | 31.2 ± 5.9 | 19-44 | 31.3 ± 6.1 | 21-44 | 0.975 |

Differences between groups were calculated by T-test *In non-normally distributed variables the Mann-Whitney U test was used |

The selected anthropometric equations for estimating BF% are showed in Table 2. Equation 1 includes the measurements of body height, abdominal circumference, triceps- and calf- skinfold thickness plus age. Equation 2 includes the same measurements than Equation 1 except for the calf skinfold that was replaced by the midaxillary skinfold. Equation-3 included body weight, height and abdominal circumference measurements. Equations 1 and 2 had similar determination coefficients and SEE in the equation-building group (Table 2). Equation 1 showed a slightly better performance than Equation 2 during the validation process with a higher determination coefficient (0.71 Vs 0.67) and lower SEE (2.84 Vs 3.06). Equation 3 had lower determination coefficient and higher SEE than Equations 1 and 2, in both, equation-building and validation group (Table 2). The Akaike information criterion was similar between Equation 1 and 2 (549 vs 547). The Equation 3 had higher AIC than Equations 1 and 2 (AIC=569; *p* <0.001) presenting a lower quality statistical model (Table 2).

Equations | Equation-building group ^{§} |
Validation group | |||
---|---|---|---|---|---|

Adjusted r^{2} |
SEE | AIC | r^{2
} |
SEE | |

0.72 | 3.12 | 549 | 0.71 | 2.84 | |

0.72 | 3.08 | 547 | 0.67 | 3.06 | |

0.66 | 3.44 | 569* | 0.55 | 3.55 | |

SEE: Standard error of estimate. AIC: Akaike Information Criterium. r^{2}: determination coefficient. ST: skinfold thickness in mm, CI: circumference in cm*Different from Equation 1 and Equation 2 ( § Assumption models (p value) Equation 1: Shapiro Wilk test= 0.9543; Durbin-Watson test= 0.9023; Homogeneity of variances test= 0.4803; Variance Inflate Factor <2.8 Equation 2: Shapiro Wilk test= 0.1318; Durbin-Watson test= 0.9535; Homogeneity of variances test=0.8445; Variance Inflate Factor <3.4 Equation 3: Shapiro Wilk test= 0.1489; Durbin-Watson test= 0.8721; Homogeneity of variances test= 0.5135; Variance Inflate Factor <4.5 |

The BF% obtained by hydrodensitometry and anthropometric equations in the validation group are shown in Table 3. There were not significant differences (*p* >0.05) between the BF% assessed by hydrodensitometry (31.5 ±5.3) and the estimated by Equation 1 (31.0 ±4.0), Equation 2 (31.2 ±4.0) and Equation 3 (31.0 ±4.6). The BF% was over estimated by the equations of Durning-Womerley (+4.26; *p* <0.001) and Ramirez-Torun (+1.10; *p* <0.05) and underestimated by the equation of Jackson-Pollock (-5.03; *p* <0.001) (Table 3). The BF% estimated by the anthropometric equations significantly correlated (*p* <0.001) with the hydrodensitometry results, the higher correlations were observed for Equation 1 (r= 0.81; *p* <0.001, ICC= 0.77; *p* <0.001) and Equation 2 (r= 0.79; *p* <0.001, ICC= 0.76; *p* <0.001) (Table 3).

Validation group (n= 45) | Body fat (%) | Differences from Hydro† | Pearson correlation | Intraclass correlation |
---|---|---|---|---|

Hydrodensitometry | 31.5 ± 5.3 | --- | --- | --- |

Equation 1 | 31.0 ± 4.0 | 0.50 | 0.81** | 0.77** |

Equation 2 | 31.2 ± 4.0 | 0.31 | 0.79** | 0.76** |

Equation 3 | 31.0 ± 4.6 | 0.49 | 0.74** | 0.73** |

Durnin-Womersley | 35.8 ± 4.0 | 4.26** | 0.75** | 0.51** |

Jackson-Pollock | 26.5 ± 5.4 | -5.03** | 0.77** | 0.53** |

Ramirez-Torun | 32.6 ± 4.8 | 1.10* | 0.77** | 0.75** |

* |

Body composition obtained by hydrodensitometry and anthropometric equations in the validation group are shown in Table 4. There were not significant differences (*p* >0.05) between the kilograms of fat mass and fat free mass obtained by hydrodensitometry (19.0 ±4.9; 40.5 ±4.2, respectively) and those estimated by Equation 1 (18.7 ±4.4; 40.8 ±3.7, respectively), Equation 2 (18.8 ±4.4; 40.7 ±3.6, respectively) and Equation 3 (18.7 ±4.8; 40.7±3.4, respectively). The equations of Durning-Womerley, Jackson-Pollock and Ramirez-Torun estimated quantities of fat mass and fat free mass significantly different (*p* <0.05) from those obtained by the reference method (Table 4).

Validation group (n= 45) | Fat Mass (kg) | Fat Free Mass (kg) | ||
---|---|---|---|---|

Mean (±SD) | Diff. from Hydro† | Mean (±SD) | Diff. from Hydro† | |

Hydrodensitometry | 19.0 ± 4.9 | --- | 40.5 ± 4.2 | --- |

Equation 1 | 18.7 ± 4.4 | -0.30 | 40.8 ± 3.7 | 0.30 |

Equation 2 | 18.8 ± 4.4 | -0.18 | 40.7 ± 3.6 | 0.18 |

Equation 3 | 18.7 ± 4.8 | -0.24 | 40.7 ± 3.4 | 0.23 |

Durnin-Womersley | 21.5 ± 4.5 | 2.50** | 38.0 ± 3.7 | -2.50** |

Jackson-Pollock | 16.0 ± 4.8 | -2.96** | 43.4 ± 4.2 | 2.96** |

Ramirez-Torun | 19.7 ± 5.1 | 0.72* | 39.7 ± 3.1 | -0.73* |

* |