Development and validation of skinfold-thickness prediction equations with a 4-compartment model

¹ From the VA Medical Center, Geriatric Research, Education and Clinical Center, Durham, NC (MJP); Wright State University School of Medicine, Lifespan Health Research Center, Kettering, OH (SAC and RMS); and the Center for the Study of Aging and Human Development, Duke University Medical Center, Durham, NC (MJP).

² Supported by the National Institutes of Health, National Institute of Child Health and Human Development, grant no. R01HD12252.

³ Address reprint requests to MJ Peterson, Durham VAMC (182), Geriatric Research, Education and Clinical Center, 508 Fulton Street, Durham, NC 27705. E-mail: peter076{at}mc.duke.edu.

ABSTRACT  
Background: Skinfold-thickness measurements are commonly obtained for the indirect assessment of body composition.

Objective: We developed new skinfold-thickness equations by using a 4-compartment model as the reference. Additionally, we compared our new equations with the Durnin and Womersley and Jackson and Pollock skinfold-thickness equations to evaluate each equation’s validity and precision.

Design: Data from 681 healthy, white adults were used. Percentage body fat (%BF) values were calculated by using the 4-compartment model. The cohort was then divided into validation and cross-validation groups. Equations were developed by using regression analyses and the 4-compartment model. All equations were then tested by using the cross-validation group. Tests for accuracy included mean differences, R², and Bland-Altman plots. Precision was evaluated by comparing root mean squared errors.

Results: Our new equations’ estimated means for %BF in men and women (22.7% and 32.6%, respectively) were closest to the corresponding 4-compartment values (22.8% and 32.8%). The Durnin and Womersley equation means in men and women (20.0% and 31.0%, respectively) and the Jackson and Pollock mean in women (26.2%) underestimated %BF. All equations showed a tendency toward underestimation in subjects with higher %BF. Bland-Altman plots showed limited agreement between Durnin and Wormersley, Jackson and Pollock, and the 4-compartment model. Precision was similar among all the equations.

Conclusions: We developed accurate and precise skinfold-thickness equations by using a 4-compartment model as the method of reference. Additionally, we found that the skinfold-thickness equations frequently used by clinicians and practitioners underestimate %BF.

Key Words: Body composition • skinfold thickness • body compartments • anthropometry • adipose tissue • nutritional assessment • body fat • obesity

INTRODUCTION  
Higher amounts of body fat and obesity are associated with increased risks of adverse health events and greater mortality (1, 2). Skinfold thicknesses are commonly measured in clinical and field settings for the assessment of percentage body fat (%BF) because this method is simple to perform and low in cost (3). Two of the most widely used skinfold-thickness equations are those developed by Durnin and Womersley and Jackson and Pollock (4–6).

The Durnin and Wormersley equation and the Jackson and Pollock equation were developed and validated by using a 2-compartment (2C) model. The 2C model separates the composition of the body into fat mass and fat-free mass. Using Siri’s equation (7), the 2C model is written as:

SUBJECTS AND METHODS  
Subjects
The subjects in the present study are a subset of the participants in the Fels Longitudinal Study. They were enrolled in the Fels Longitudinal Study between 1929 and the present, typically soon after their birth. Most of the Fels participants are white, resided in southwestern Ohio at the time of their enrollment, and were selected for enrollment because their parents were willing to allow them to participate in a long-term, serial study. To date, there have been > 1200 participants in the study; they are examined at regular intervals throughout their life span. Of these 1200, a total of 900 are participating in the currently funded National Institutes of Health study. All subjects provided written informed consent.

The Fels Longitudinal Study and its participants have been described in detail previously (19). The standard body-composition exam consists of the anthropometric assessment of weight, stature, and several skinfold thicknesses (chest and abdomen skinfold thicknesses are not currently measured). Many other measures of body composition, including DXA, hydrodensitometry, and bioelectrical impedance, are also obtained. The protocol for this study is reviewed and approved annually by the Wright State University Institutional Review Board. The study sample is representative of the national population in terms of its socioeconomic composition, except for a slight underrepresentation of the lowest socioeconomic group in recent decades. After excluding participants without all of the data needed to derive a %BF reference from the 4C model (see below), there were a total of 681 healthy, white male (n = 360) and female (n = 321) participants available for derivation of the %BF_4C individual values. This larger sample was then randomly divided into a validation sample (274 men and 230 women) to develop the %BF_new equations and a cross-validation sample (86 men and 91 women) used to compare all the equations.

Development of %BF_4C values
DXA scans were performed with a Lunar DPX (Lunar Co, Madison, WI) with total body scan software version 3.6z. The Lunar DPX uses a constant X-ray source and a K-edge filter to achieve a congruent beam of dual-energy radiation. Tissue mass and bone mass are calculated, and tissue mass is further divided into fat-free nonskeletal mass and fat mass. Total body bone mineral content is calculated relative to DXA-determined fat-free mass.

Deuterium oxide dilution methods were used to determine TBW according to the procedures described by Schoeller et al (20). Briefly, this method involves measuring the degree of dilution of a known dose of deuterium after it has equilibrated with TBW. Participants emptied their bladders before the collection of a 6-mL baseline saliva sample and then drank 15 mL deuterium oxide (99.9% purity; Cambridge Isotope Laboratories, Woburn, MA) in a solution of 75 mL deionized water. A second saliva sample was collected exactly 2 h later. The 2 samples were centrifuged and the supernate was collected, sealed, frozen, and transported to the Kettering-Scott Magnetic Resonance Laboratory (Kettering, OH) for analysis. Nuclear magnetic resonance spectrometry was used to determine the TBW from each sample. These values were then divided by 1.04 to account for the estimated 4% H⁺ nonaqueous exchange (21).

The hydrodensitometry method was used to measure BD according to the method described by Siri (7). This method determines BD by using standardized hydrostatic weighing with correction for residual volume. Residual volume was measured twice on land to the nearest 0.1 L by nitrogen washout, using a computerized spirometer (Solatron, Dayton, OH). Underwater weight was determined with the participant sitting in a chair suspended from 4 load cells in a tank of water at 35 °C. When the participant was completely submerged and at maximal exhalation, underwater weights were recorded to the nearest 0.002 kg from a digital display. Ten repeated underwater weights were completed, and the average of the highest 3 weights (because these are indicative of maximal exhalation) was used to calculate BD corrected for residual volume.

The methods described above can be combined to estimate %BF by using the equation for the %BF_4C model (11):

RESULTS  
%BF_new equations
The physical characteristics of subjects in the validation and cross-validation groups are shown in Table 1. In both groups, men and women differed significantly in height, weight, and BMI, but age was not significantly different between the sexes. Men in the validation group were heavier than were men in the cross-validation group. Physical characteristics did not differ significantly between women in the validation and cross-validation groups.

View this table:
TABLE 1 . Descriptive characteristics of the validation and cross-validation groups¹  
Regression analyses in the validation group (Table 2) revealed that the sum of the triceps, subscapular, suprailiac, and midthigh skinfold thicknesses (sum4) explained 56% (partial R² = 0.56) of the variance of %BF in men and 65% (partial R² = 0.64) of the variance of %BF in women. In men, age, height, and sum4² were also significant contributors to the model, but to a lesser degree, with no remaining variable’s partial R² being > 0.027. In women, in addition to the same set of variables that were significant in the model for men, BMI was also a significant predictor of %BF, although its effect size was relatively small (partial R² = 0.024). Interestingly, sum3, sum3², circumferential measures, and weight were not significant predictors of %BF in either model. The final equations, which were used in subsequent analyses, are as follows for men and women:

View this table:
TABLE 2 . Regression coefficients, partial explanation of variance (partial R²), and significance of independent variables in the new percentage body fat (%BF_new) equations (validation group)  

DISCUSSION  
We developed new skinfold-thickness prediction equations and compared them with the equations of Durnin and Wormersley and Jackson and Pollock, and with a 4C model, which we used as the reference equation. To our knowledge, no previous study has used a 4C model to cross-validate several skinfold-thickness prediction equations. We chose the Durnin and Wormersley and Jackson and Pollock equations because of their popularity in the field and in research settings (18, 24–31). Previous studies have explored the predictive accuracy and precision of the Jackson and Pollock and Durnin and Wormersley equations in different populations (18, 24–31). Our study is also unique in that we present data from healthy, white men and women who had characteristics comparable to those of the groups used by Durnin and Wormersley and Jackson and Pollock.

The skinfold-thickness equations developed in our laboratory had no significant mean differences with the %BF_4C model in men or women in the cross-validation group. In this cohort, %BF_DW and %BF_JP means were significantly lower than the %BF_4C mean, which may need to be considered when using the Durnin and Wormersley and Jackson and Pollock equations to predict %BF in groups similar to the one presented here. Bland-Altman plots provided additional information regarding the underestimation of %BF by the Durnin and Wormersley and Jackson and Pollock equations. With the Durnin and Wormersley equations, the lower limits of agreement (mean differences - 2 SD) were -12.9% and -11.4% in men and women, respectively. These lower limits of agreement are considerably larger than the upper limit values, at 7.2% and 7.9% in men and women, respectively. On the basis of these data, a man or woman is more likely to have their %BF underestimated using the Durnin and Wormersley equations. This tendency to have the limits of agreement shifted toward underestimations is even more pronounced in women using the Jackson and Pollock equation, with upper and lower limits of agreement of 3.3% and -16.5%, respectively. This indicates that a woman could have her %BF underestimated by as much as 16.5%. These underestimations are most likely a result of systematic overestimations of BD. For example, the mean BD value with the Durnin and Wormersley equation was higher, at 1.032 g/mL, than the value of 1.028 g/mL that was measured by hydrodensitometry. Although 0.004 g/mL may initially appear to be a small difference in BD estimates, when using these 2 values to predict %BF, the differences in mean predicted %BF values are almost 2%. A relatively small under- or overestimation of BD can result in considerable errors in predicted %BF values.

%BF_new, %BF_JP, and %BF_DW all had similar estimates of precision, as shown by the similar RMSE values. A prediction equation’s RMSE is certainly important, however, it should not be considered the only criterion when choosing a proper equation. Although %BF_DW and %BF_JP values were similar in terms of RMSE values and precision, we showed that accuracy was less than desirable in the Durnin and Wormersley and Jackson and Pollock equations in a cohort similar in age and physical characteristics to their derivation samples.

Providing precise and accurate body-composition information is of great importance. The comparisons provided in this paper should aid in making a more informed decision, considering precision and accuracy, when choosing among popular equations for predicting %BF. In summary, we have shown that our newly developed generalized equations, which use the 4C model as a reference, can accurately predict %BF in healthy, white adults. Our newly developed skinfold-thickness equations are important for 2 reasons. First, the %BF_new equations were validated and cross-validated with large samples of men and women spanning a wide age range (18–55 y). The validation sample used by Durnin and Wormersley was similar to ours in size, but they did not cross-validate their equations. Jackson and Pollock did cross-validate, but their cross-validation did not provide an analysis of their equations’ potential to over- or underestimate %BF. Second, the %BF_new equations were developed and validated by using a 4C model as a reference. The 4C model has been shown to be more accurate in measuring %BF than the 2C method, which was the criterion method for Durnin and Wormersley and Jackson and Pollock. When validated against the 4C model, the Durnin and Wormersley equations underestimated %BF in men and women and the Jackson and Pollock generalized equations underestimated %BF in women to a relatively high degree. We recommend considering an equation’s accuracy and precision to fully understand its strengths and weaknesses. This may require finding the original source for the derivation of the equation and objectively analyzing the information presented to find the best equation for a specific population.

ACKNOWLEDGMENTS  
We thank the participants of the Fels Longitudinal Study and the data collection staff, without whom this work would not have been possible. We also thank Miriam Morey for her thoughtful review of drafts and for her support of MJP throughout the writing and revision of this work.

MJP, SAC, and RMS were all involved in the study design and writing of the manuscript. Data analyses were performed by MJP. The authors had no financial or personal interests in the sponsoring organization.

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