Validity of anthropometric equation-based estimators of fat mass in Samoan adults

Abstract

Introduction:

In 1999, a set of highly accurate Polynesian-specific equations to estimate adult body fat from non-invasive field measures of age, sex and (Eq. 1) height and weight, (Eq. 2) height, weight, and bioelectrical impedance analysis (BIA) resistance, and (Eq. 3) height, weight, and the sum of two skinfold thicknesses were published. The purpose of this study was to evaluate the performance of the equation-based estimators in a sample of Samoan adults recruited 20 years later between 2017 and 2019.

Methods:

Age, sex, height, weight, BIA resistance, skinfold thickness, and fat mass as measured using dual energy x-ray absorptiometry (DXA) were available for 432 Samoan adults (mean age 50.9 years, 56% female) seen in 2017/19. We compared equation-derived fat mass and DXA-derived fat mass using scatterplots and Pearson correlation coefficients. We then updated the equation coefficient estimates in a training set (2/3 of the sample) and evaluated the performance of the updated equations in a testing set (the remaining 1/3 of the sample).

Results:

Equation-derived fat mass was strongly correlated with DXA-derived fat mass for Eq. 1 (r²=0.95, n=432), Eq. 2 (r²=0.97, n=425), and Eq. 3 (r²=0.95, n=426). Updating the equation coefficient estimates resulted in mostly similar coefficients and nearly identical testing set performance for Eq. 1 (r²=0.96, n=153), Eq. 2 (r²=0.98, n=150), and Eq. 3 (r²=0.96, n=150).

Conclusions:

The Polynesian-specific body fat estimation equations remained stable despite changing social and environmental factors and marked increase in obesity prevalence in Samoa.

INTRODUCTION

As well as being an important individual health indicator, monitoring population-level changes in fat mass provides insight into processes of modernization and nutritional transitions. While multi-compartment modeling, magnetic resonance imaging (MRI), dual energy x-ray absorptiometry (DXA), underwater weighing, and air displacement plethysmography are accepted as some of the best practices for estimating body fat (Blue et al., 2021; Borga et al., 2018), these approaches are prohibitively costly and challenging to implement in large population-based studies, especially in low-resource settings. Equation-based estimates of body fat based on more affordable, accessible, and low participant-burden measures (e.g., weight, height, skinfold thicknesses, bioelectrical impedance analysis [BIA]) are important tools for research and clinical practice.

Over the past several decades, an increasing number of population-specific equations have been developed, reflecting differences in body composition by ancestry/ethnicity (Heymsfield et al., 2016). This is particularly important for Polynesians, who have greater lean mass per kilogram of total body weight than Europeans (Swinburn et al., 1999). Few studies have, however, explored the performance of these equations over time, specifically in the context of rapidly increasing population-level adiposity.

Here we evaluated the performance of Polynesian-specific equations developed by Swinburn et al. (1999) in Samoan adults recruited between 2017–19 and compared the performances of the original to updated equations with coefficients estimated from our measurements. The original Swinburn equations, using age, sex, weight, height, BIA, and skinfold thicknesses, showed excellent agreement with DXA-derived fat mass. While we did not expect the relationship between BIA measures and fat mass to change, we hypothesized that sex- and age-specific temporal changes in adiposity (i.e., greater increases in obesity prevalence among females than males and younger versus older adults in Samoa over the past 20 years (Lin et al., 2017)) could impact the equations and reduce their predictive performance compared to DXA measurement.

MATERIALS AND METHODS

Study design, setting, and sample

This was a secondary analysis of data from the 2017/19 Soifua Manuia (“Good Health”) observational study (Hawley et al., 2020) which was aimed at understanding the effects of a genetic variant (rs373863828, CREBRF:c.1370G>A p.[R457Q]) on cardiometabolic health in adults from Samoa (Hawley et al., 2014, 2020; Minster et al., 2016). The overall sample consisted of 519 adults (n=286 female) recruited from ‘Upolu, Samoa. The study was approved by Institutional Review Boards at Yale University, Brown University, and the University of Pittsburgh, and by the Health Research Committee of the Samoa Ministry of Health. All participants gave written informed consent.

Measurements

Age and sex were participant-reported. Height, weight, and skinfold thicknesses (subscapular, triceps) were measured to the nearest 0.1 kg, 0.1 cm, and 0.1 mm, respectively (Hawley et al., 2020). Measurements that exceeded the 65 mm maximum capacity of the skinfold calipers were set to missing (n=6). In individuals without metal implants or pacemakers, resistance measures were obtained via BIA (RJL BIA-101Q device, RJL Systems, MI, USA). CREBRF rs373863828 data (considered only in post hoc analyses) were generated using TaqMan real-time PCR (Applied Biosystems) (Minster et al., 2016). Total body fat mass was measured in kg using DXA (Lunar iDXA, version Encore 17, GE Healthcare Medicine, WI, USA). The Lunar iDXA machine was chosen because it had the largest scan area and weight limit (204 kg) at the time the study was conducted. When an individual’s width exceeded the scan area, a right-side scan was “mirrored” to estimate total body fat.

Swinburn Equations

We examined three of the four equations derived by Swinburn et al. (1999)—with a correction to units for the height variable (Keighley et al., 2006). All equations included age, sex, height, and weight, with two equations containing additional variables. For conceptual simplicity, the equations are described here as: the ‘height and weight equation’ (Eq. 1); ‘bioelectrical impedance equation’ (Eq. 2); and the ‘sum of two skinfolds (triceps and subscapular) equation’ (Eq. 3). We could not examine Swinburn’s fourth ‘sum of four skinfolds (triceps, biceps, subscapular, and suprailiac) equation’, as biceps skinfold data were not available in our sample.

Statistical analyses

We performed statistical analyses in R 4.1.2. First, we used standard descriptive statistics to evaluate participant characteristics, understand missing data patterns, and identify/remove extreme outliers. We then estimated fat mass in our sample using the original “Swinburn equations” and compared equation-derived fat mass and DXA-derived fat mass using scatterplots and Pearson correlation coefficients. We then randomly split our 2017/19 sample into a ‘training set’ (2/3 of the sample) and ‘testing set’ (1/3 of the sample). Using the training set, we created “updated equations” by re-calculating the intercept and equation coefficient estimates using linear regression. We then compared our versions of the equations with updated coefficients to Swinburn’s original equations; coefficients were determined to be “similar” if Swinburn’s coefficient point estimates fell within the 95% confidence intervals in our updated versions. Finally, we evaluated the performance of the updated equations by comparing the correlation between equation-derived fat mass and DXA-derived fat mass in the testing set with Bland–Altman plots (Bland & Altman, 1986).

RESULTS

Participant characteristics

Participant characteristics are presented in Table 1 for the 2017/19 overall sample, sex-stratified sample, and testing/training sets, as well as the Swinburn et al. (1999) Samoan sample for comparison. A total of 432 participants recruited in 2017/19 were eligible for this study given the availability of both DXA data and complete data for at least one equation (Figures S1–S2). The overall sample had a mean age of 50.9 years, was 56% female, and had a mean BMI of 35.7 kg/m². The training and testing sets consisted of n=279 (64.6%) and n=153 (35.4%) participants, respectively; there were no statistically significant differences between groups. A single BIA resistance outlier with an implausible value of <100 Ω was set to missing.

Table 1.

Participant characteristics of the 2017/19 sample and Swinburn et al. (1999)’s Samoan sample.

	2017/19 Samoan sample1						Swinburn (1999) Samoan sample2
Characteristic3	Overall N=432	Female n=241	Male n=191	Training Set n=279	Testing Set n=153	p-value4	Female n=97	Male n=88
Age (years)	50.9 (9.8)	50.1 (9.4)	52.0 (10.2)	50.8 (10.0)	51.3 (9.4)	0.61	43.6 (14.5)	44.0 (15.1)
Sex, n (%)						0.94
Female, n (%)	241 (56.0)			156 (56%)	85 (56%)
Male, n (%)	191 (44.0)			123 (44%)	68 (44%)
Height (cm)	166.6 (7.8)	162.1 (5.7)	172.3 (6.2)	166.5 (7.4)	166.8 (8.5)	0.63	161 (6.0)	173 (6.3)
Weight (kg)	99.2 (22.0)	99.2 (22.2)	99.2 (21.7)	98.6 (21.4)	100.3 (22.9)	0.45	85.7 (17.2)	94.7 (13.9)
BMI (kg/m2)	35.7 (7.7)	37.7 (7.9)	33.3 (6.6)	35.6 (7.5)	36.1 (8.0)	0.51	33.3 (6.3)	31.8 (4.6)
Fat Mass (kg)5	37.7 (15.6)	43.8 (14.5)	30.0 (13.5)	37.5 (14.9)	38.1 (16.9)	0.74	35.7 (11.4)	25.4 (9.2)
Body Fat (%)5	37.1 (9.7)	43.5 (5.7)	29.0 (7.5)	37.2 (9.1)	36.9 (10.9)	0.75	40.8 (6.8)	26.0 (7.2)
Resistance (Ω)6	423.0 (69.1)	449.0 (67.2)	389.8 (56.2)	426.6 (70.9)	416.4 (65.5)	0.14	476.7 (65.4)	389.6 (40.4)
Missing, n	7	3	4	4	3
Reactance (Ω)6	46.9 (10.3)	46.8 (11.1)	47.0 (9.1)	46.8 (9.0)	47.0 (12.3)	0.89	49.1 (9.0)	44.5 (7.3)
Missing, n	6	2	4	4	2
Triceps Skinfold (mm)1	32.5 (12.0)	35.4 (10.9)	28.9 (12.3)	32.4 (11.8)	32.8 (12.2)	0.68	32 (11.8)	17.3 (9.8)
Subscapular Skinfold (mm)1	36.5 (12.5)	38.9 (10.9)	33.5 (13.7)	36.9 (12.6)	35.8 (12.3)	0.37	31.8 (10.5)	25.4 (9.6)
Missing, n	6	4	2	3	3

¹Our sample used to evaluate the performance of the Swinburn equations and update the intercept/coefficient estimates;

²Swinburn et al (1999) Samoan sample that the original equations were derived from;

³Mean (SD) unless otherwise denoted;

⁴Comparison of participant differences in the training and testing set using Welch’s two sample t-test;

⁵DXA-derived;

⁶BIA-derived.

Swinburn Equations

As shown in Table 2 and Figure S3, Swinburn equation–estimated fat mass was strongly correlated with DXA-derived fat mass for all three equations: Eq. 1 (r²=0.95, n=432), Eq. 2 (r²=0.97, n=425), and Eq. 3 (r²=0.95, n=426).

Table 2.

Performance of Swinburn equations and updated equations in Samoan sample recruited in 2017/19.

	Eq. 1: Height and Weight		Eq 2: Bioimpedance		Eq. 3: Sum of Two Skinfolds
Swinburn’s original equations	$\mathit{\text{Fat mass}}=35.98+0.05\left(age\right)-10.51\left(sex\right)-0.35\left(\mathit{\text{height}}\right)+0.64\left(\mathit{\text{weight}}\right)$		$\mathit{\text{Fat mass}}=11.58+0.04\left(age\right)-6.00\left(sex\right)-0.15\left(\mathit{\text{height}}\right)+0.79\left(\mathit{\text{weight}}\right)-0.39\left(\frac{{\mathit{\text{height}}}^2}{\mathit{\text{resistance}}}\right)$		$\mathit{\text{Fat mass}}=31.66+0.05\left(age\right)-9.05\left(sex\right)-0.32\left(\mathit{\text{height}}\right)+0.59\left(\mathit{\text{weight}}\right)+0.06\left(\mathit{\text{sum of two skinfolds}}\right)$
Updated equations1	$\mathit{\text{Fat mass}}=35.35+0.05\left(age\right)-9.67\left(sex\right)-0.36\left(\mathit{\text{height}}\right)+0.65\left(\mathit{\text{weight}}\right)$		$\mathit{\text{Fat mass}}=18.73+0.06\left(age\right)-6.4\left(sex\right)-0.22\left(\mathit{\text{height}}\right)+0.76\left(\mathit{\text{weight}}\right)-0.28\left(\frac{{\mathit{\text{height}}}^2}{\mathit{\text{resistance}}}\right)$		$\mathit{\text{Fat mass}}=32.85+0.05\left(age\right)-9.65\left(sex\right)-0.34\left(\mathit{\text{height}}\right)+0.64\left(\mathit{\text{weight}}\right)+0.013\left(\mathit{\text{sum of two skinfolds}}\right)$
Performance in 2017/19 Samoa data	n	r2 (95% CI)2	n	r2 (95% CI)2	n	r2 (95% CI)2
Swinburn equations in total sample	432	0.95 (0.94 to 0.96)	425	0.97 (0.96 to 0.98)	426	0.95 (0.94 to 0.96)
Updated equations in training data	279 of 432 (64.6%)	0.95 (0.94 to 0.96)	275 of 425 (64.7%)	0.97 (0.96 to 0.98)	276 of 426 (64.8%)	0.95 (0.93 to 0.96)
Updated equations in testing data	153 of 432 (35.4%)	0.96 (0.94 to 0.97)	150 of 425 (35.3%)	0.98 (0.97 to 0.99)	150 of 426 (35.2%)	0.96 (0.94 to 0.97)

¹Updated intercept and coefficient estimates calculated using training data;

²Square of the Pearson correlation coefficient (r²) and 95% confidence intervals comparing equation-derived (estimated) and DXA-derived (best practice comparison) fat mass; age, years; sex, 0=female, 1=male; height, cm; weight, kg; resistance, Ω; skinfold thickness, mm.

Updated Equations

Our versions of the equations with updated intercept/coefficient estimates were largely similar to the Swinburn equations. Specifically, all Swinburn coefficient point estimates fell within the 95% confidence intervals for our estimates except the height, weight, and height²/BIA resistance coefficients for Eq. 2, and the weight coefficient for Eq. 3 (Table S1). In the testing set, estimated fat mass was again strongly correlated with DXA-derived fat mass for updated versions of Eq. 1 (r²=0.96, n=153), Eq. 2 (r²=0.98, n=150), and Eq. 3 (r²=0.96, n=150) (Table 2). Performance plots are presented (Figure S4). Bland–Altman plots indicated no consistent bias between approaches (Figures S5–S6). In the entire 2017/19 sample, comparison of fat mass estimated using the Swinburn equations and our updated equations resulted in near perfect correlation (r²=1, Figure S7).

DISCUSSION

Our study demonstrates that the Swinburn et al. (1999) equations remain useful for estimating fat mass more than 20 years after their publication despite marked increases in BMI among Samoan adults over the same period (Fu et al., 2022; Lin et al., 2017). Compared to the New Zealand-based Samoans who were included in the sample used to derive Swinburn’s equations, the mean BMI in our sample was greater, with differences accounted for largely by fat mass (Table 1). While updated Eq. 1 (height and weight) was nearly identical to the original, we observed a change in coefficients for the height, weight, and height²/resistance terms in Eq. 2 (bioelectrical impedance) and the weight term in Eq. 3 (sum of two skinfolds) (Table S1); unfortunately, we do not have confidence intervals for Swinburn’s point estimates for further comparison. We hypothesize that the more pronounced differences observed for Eq. 2 could be due to the differences in the BIA resistance between our sample and the Swinburn sample in women but not men (Table 1), which we suspect resulted from differences in fasting status, hydration, exercise, body shape, environmental factors, or medical conditions (Dehghan & Merchant, 2008).

Despite these differences, all equations (Swinburn and our updated versions) were excellent predictors of DXA-derived fat mass (r²≥0.95). Eq. 1 (height and weight) and Eq. 3 (sum of two skinfolds) had identical performance. This suggests that, to estimate fat mass among our sample, there is no need for additional skinfold measurements, which have been criticized for the level of training required to ensure inter- and intra-observer reliability (Stomfai et al., 2011). The fact that the correlations between equation- and DXA-derived fat mass were strongest for Eq. 2 (bioelectrical impedance), but only negligibly so compared with the other equations, indicates that BIA may also not be necessary in large population-based studies focused on total adiposity.

Strengths of this study include the availability of a large sample of individuals from a historically understudied group at high risk for obesity as well as unique DXA data from a low-resource setting. This study was limited in that multiple BIA measurements were not taken, which prevented us from assessing measurement precision and technical error. Further, the basic body composition methods applied here, including skinfold thickness estimation, BIA, and DXA, are to some degree all impacted by hydration status (Fosbøl & Zerahn, 2015). Despite this, equation-derived and DXA-measured fat mass had excellent agreement. Finally, this study was potentially limited in that the sample was enriched for the CREBRF obesity-risk variant, though post hoc exploration showed no influence on the performance of the equations (Figure S8). While it is possible that the equations might not work as well for individuals with more extreme measures of height, weight, BMI, or other participant factors, we have demonstrated that the equations are highly accurate within the range of values in our sample.

CONCLUSION

Given the high accuracy and impressive performance of both the Swinburn and updated equations in estimating fat mass (r²≥0.95), these simple, inexpensive, and less burdensome equation-based fat mass estimators remain important tools, particularly in low resource settings.

Data availability:

dbGAP accession #phs000914.v1.p1