Validation of Predictive Equations for Estimating Lean Soft Tissue and Fat-Free Mass in Class II–V Obesity: A Multicenter Observational Study with Implications for Bariatric Surgery Monitoring

Abstract

Background

Preoperative analysis of body composition is critical for anticipating metabolic changes and optimizing outcomes after bariatric surgery (BS). This study assessed agreement between dual-energy X-ray absorptiometry (DXA)-derived fat-free mass (FFM) and lean soft tissue (LST) and estimates from anthropometric equations in individuals with class-II obesity or greater.

Methods

FFM and LST were measured by DXA in 123 participants with class-II obesity or greater before and approximately 1 month after BS. Six equations were used to estimate FFM and five to estimate LST. The estimates were calculated at both time points, and changes from pre- to post-BS were compared with the DXA-derived values. Paired t-tests were used to evaluate differences between the predicted and measured values.

Results

At the group level, the Li et al. equation for higher body mass index (BMI) values demonstrated the highest agreement with DXA-FFM before surgery (mean-difference, 0.01 kg; 95% confidence interval [CI], –0.74 to 0.74), whereas the Li et al. equation for normal BMI values showed the greatest agreement at follow-up (mean-difference, 1.71 kg; 95% CI, 1.30 to 2.13). For LST estimation, the Salamat et al. equation provided the greatest accuracy before BS (mean-difference, 0.03 kg; 95% CI, –1.35 to 1.40), and the Kulkarni et al. equation achieved the best performance in capturing group-level changes during follow-up (mean-difference, 0.48 kg; 95% CI, 0.05 to 0.92).

Conclusion

Although certain predictive equations yielded acceptable group-level agreement with DXA, their individual-level performance was inconsistent, limiting their clinical utility. Further research is warranted to develop predictive models with enhanced precision and reliability.

INTRODUCTION

Obesity is a chronic disease caused by multiple factors, and it constitutes a major public health concern.¹ The prevalence of this disease ranges from 20% to 31% in European women and 23% to 29% in European men, and data from the United States of America (USA) are even more alarming, with 38% of men and 40% of women classified as obese.² Furthermore, it is expected that obesity will reach its maximum levels between 2026 and 2054, with the USA and United Kingdom (UK) reaching those levels first.² Data on type III obesity (body mass index [BMI] above 40 kg/m²) are also concerning, with studies developed in the UK and USA predicting significant increases in its prevalence.^3,4 Although conservative treatments such as psychological support, diet, and exercise can have a moderate efficacy in managing obesity,⁵ once the BMI exceeds 35 kg/m², the effectiveness of those treatments is much lower than that of invasive treatments such as bariatric surgery (BS).⁶

BS is currently the most effective treatment option for severe obesity.⁷ Its effects are, in most cases, markedly beneficial, encompassing weight loss, reduction of cancer risk, and remission of type 2 diabetes mellitus, among other positive outcomes.⁸ Nevertheless, it is notable that 15% to 35% of the patients who undergo this type of surgery do not achieve the desired weight loss.⁹ Furthermore, only 2 years after surgery, a significant proportion of patients have regained a substantial amount of the weight they initially lost. In Europe, 64% of patients who undergo BS regain weight.¹⁰ In terms of body composition, body weight loss comprises the loss of fat mass and fat-free mass (FFM). FFM encompasses all non-fat molecules in the body, regardless of where they occur.¹¹ Although the scientific literature has used FFM and lean body mass as interchangeable terms, a recent critical perspective on this topic stated that the term FFM should be used.¹¹ Moreover, the term lean soft tissue (LST) should be used when referring to the FFM while excluding bone mineral content and when measuring body composition with an accurate device such as dual-energy X-ray absorptiometry (DXA).

Patients undergoing BS experience a drastic loss of FFM following surgery.¹² Changes in FFM and LST can explain inadequate weight loss or subsequent weight regain because they have a critical effect on the basal metabolic rate,¹³ which in turn affects total energy expenditure¹⁴ and therefore weight loss and regain. Monitoring FFM and LST in these patients is therefore essential. Moreover, some authors have suggested that FFM or LST can be a better predictor of drug dosage than weight or BMI in patients with obesity¹⁵ because most of the physiological parameters that affect drug pharmacokinetics do not increase linearly with total body weight, but they do appear to correlate with FFM.¹⁶ However, accurate measurement of LST and FFM requires technology that is not usually available in clinical practice, such as DXA, which is primarily reserved for osteoporosis screening, costly, and often unavailable for routine clinical use. In addition to financial constraints, other practical factors, including portability, operational complexity, and time requirements,¹⁷ limit the widespread implementation of such techniques. Those considerations underscore the continued relevance of anthropometric methods, which offer a more accessible, rapid, and feasible approach for evaluating body composition in clinical and research settings.

Differences in body composition among patients with varying weights can result in the overestimation of FFM or LST when applying prediction equations to patients with obesity types II, III, or IV. It is therefore essential to validate those equations in this patient population. This approach could identify the most accurate predictive equation for this population. Moreover, it is plausible that some equations will perform well in individuals with class III or IV obesity, but their predictive accuracy could diminish following the weight loss induced by BS, posing a challenge for follow-up studies of patients undergoing BS, who are typically classified as having type III obesity preoperatively and reclassified as type I or II 6 to 12 months post-surgery due to the substantial weight reduction that results from the procedure.

Our aims in this study were: (1) to determine the accuracy of predictive equations for estimating FFM or LST in patients with type II obesity or higher by directly comparing them with DXA measurements and (2) to assess whether any existing equations can accurately detect the drastic changes in FFM and LST that result from rapid, BS-induced weight loss.

METHODS

Research centers and study protocols

Three research centers participated in this study: the Growth, Exercise, NUtrition and Development (GENUD) research group from the University of Zaragoza (UNIZAR; Spain), the Research Center in Physical Activity, Health and Leisure (CIAFEL) research group from the University of Porto (UPORTO; Portugal), and the Comprehensive Health Research Center, University of Evora (UEVORA; Portugal).

A randomized controlled trial (RCT) with 28 participants was conducted by researchers from UNIZAR.¹⁸ That study was approved by the Ethics Committee of Clinical Research of Aragón (CEICA, Spain) with reference number C.I. PI22/380 and registered at Clinicaltrials.gov (NCT05695599). For this study, DXA assessments made 1 week pre-surgery and 45 days post-surgery were selected.

Researchers from UPORTO developed the Bariatric Surgery and Exercise Intervention Bone (BASEIB) project¹⁹ (ClinicalTrials. gov NCT02843048), which was approved by the São João Medical Center ethics committee (CES 192–14). For this project, data from 61 participants with a BMI above 35 kg/m² were collected pre-surgery and 1 month post-surgery.

The Exercise Post Bariatric Surgery (EXPOBAR) RCT was performed by UEVORA²⁰ (Clinicaltrials.gov NCT03497546) and approved by the Hospital Espírito Santo de Évora Ethics Committee (HESE_CE_1917/21). Participants in the EXPOBAR RCT were assessed at multiple time points. For this study, 36 DXA assessments from baseline (pre-surgery) and 1 month after surgery were selected.

Independently of the research center, all participants signed an informed consent form before any measurements took place.

Sample

The three studies included participants with a baseline BMI above 35 kg/m² who were scheduled for BS. Two participants presented a BMI above 55 kg/m² and were ultimately excluded from this study (one participant from UNIZAR and one from UEVORA). Participants in the RCT conducted in Spain had to be between 18 and 50 years old, and those in the Portuguese samples ranged from 18 to 65 years of age. The main characteristics of the study population are presented in Table 1. Participant characteristics for each research center are presented in Supplementary Table 1.

Table 1.

Characteristics of the participants before and after bariatric surgery

Characteristic	Whole sample (n = 123)
	T1	T2
Sex (male:female)	29 (23.58):94 (76.42)
Age (yr)	43.74 ± 10.43
Height (cm)	161.97 ± 9.67
Weight (kg)	114.04 ± 17.61	100.93 ± 15.45
BMI (kg/m2)	43.33 ± 4.38	38.51 ± 4.29
Type of obesity
Type I	0	29 (23.58)
Type II	33 (26.83)	50 (40.65)
Type III	44 (35.77)	36 (29.27)
Type IV	38 (30.89)	7 (5.69)
Type V	8 (6.50)	1 (0.81)
Waist circumference (cm)	123.71 ± 11.88	112.99 ± 11.08
Hip circumference (cm)	133.95 ± 10.05	125.82 ± 9.19
Waist to hip ratio	0.93 ± 0.10	0.91 ± 0.09
Lean soft tissue (kg)	56.62 ± 11.74	50.36 ± 10.52
Fat-free mass (kg)	59.01 ± 12.07	52.84 ± 10.90

Values are presented as number (%) or mean±standard deviation.

T1, pre-surgery assessment; T2, post-surgery assessment; BMI, body mass index.

Anthropometric measurements

Height was measured using the same stadiometer (SECA 225; SECA; accuracy to the nearest 0.1 cm) at both UNIZAR and UEVORA, and a portable stadiometer (SECA 213; SECA) was used at UPORTO. Body weight was measured without shoes and in minimal clothing using a bioelectrical impedance device (TANITA MC780MAN; Tanita) at UNIZAR, a digital scale (SECA 791; SECA; Selecta Classic Line) at UEVORA, and another digital scale (SECA 899; SECA) at UPORTO, all with a precision of 0.1 kg. BMI was calculated as body weight in kilograms divided by height in meters squared (kg/m²).

Body composition terms: FFM, lean body mass, and LST

It is important to clarify that in this study we follow the terminology described by Heymsfield et al.¹¹ in their recent critical perspective. The prediction equations that estimate body fat and subtract it from total body weight to obtain FFM are presented in Table 2. These equations are called ‘FFM prediction equations,’ regardless of the name given to them by the original authors. Equations that subtract bone mineral content from FFM are also presented in Table 2 and are called ‘LST prediction equations’ regardless of the original authors’ terminology.

Table 2.

Equations used to predict fat-free mass and lean soft tissue

Author (year)	Number, sex (age)–BMI	Estimated component	Equation	Development
				R2	SEE (kg)
Equations used to estimate FFM
Equations only using weight, age, sex, or BMI
Gallagher et al.(2000)27*	613, M (48 yr)–24.9 kg/m2† 1,013, F (44 yr)–24.9 kg/m2†	BF (%)	76.0–1,097.8 × (1/BMI)–20.6 × sex (M:1/F:0)+0.053 × age (yr)+154 × sex (M:1/F:0) × (1/BMI)+0.034 × sex (M:1/F:0) × age (yr)	0.9‡	4.31‡
Janmahasatian et al. (2005)29	146, M (18–82 yr)–34.5 kg/m2	FFM (kg) (M)	(9,270 ×weight [kg])/(6,680+216 × BMI)	0.75	RMSE: 3.52
	157, F (19–79 yr)–34.7 kg/m2	FFM (kg) (F)	(9,270 ×weight [kg])/(8,780+244 × BMI)	0.76	RMSE: 3.13
Larsson et al. (2006)24*	274, M (31–61.8 yr)-26.2 kg/m2	BF (kg) (M)	–30.84+1.120 ×weight (kg)/height (m)	0.82	2.8
	357, F (30.0–61.0 yr)–26.6 kg/m2	BF (kg) (F)	–24.18+1.181 ×weight (kg)/height (m)	0.88	2.1
Li et al. (2019)23	2,987, M (53.9 yr)–23.1 kg/m2	FFM (kg) (M)	−25.498−0.051 × age (yr)+0.312 × height (cm)+0.263 ×weight (kg)+0.373 × BMI	0.78	3.1
	7,696, F (55.8 yr)–22.4 kg/m2	FFM (kg) (M) For higher BMI	−74.474−0.025 × age (yr)+0.602 × height (cm)+1.077 × BMI	0.74	3.3
		FFM (kg) (F)	8.032+0.534 ×weight (kg)+0.070 × height (cm)−0.533 × BMI	0.70	2.4
		FFM (kg) (F) For higher BMI	21.024+0.587 ×weight (kg)−0.019 × age (yr)−0.697 × BMI	0.69	2.7
Equations using the above parameters plus hip or WC
Larsson et al. (2006)24*	274, M (31–61.8 yr)–26.2 kg/m2	BF (kg) (M)	18.38–13.49 × height (m)+0.2572 ×weight (kg)+ 0.4567 × WC (cm)	0.94	2.1
	357, F (30.0–61.0 yr)–26.6 kg/m2	BF (kg) (F)	15.20–25.69 × height (m)+0.6276 ×weight (kg)+ 0.1069 × WC (cm)	0.95	2.0
Equations used to estimate lean soft tissue
Equations only using weight, age, sex, or BMI
Lee et al. (2017)28§	5,239, M (42.7 yr)–26.6 kg/m2	LST (kg) (M)	–14.729–0.071 × age (yr)+0.210 × height (cm)+ 0.468 ×weight (kg)–0.441 ×Mexican+0.320 ×Hispanic+ 1.821 × Black–0.784 × other ethnicity	0.88	2.96
	4,519, F (45.3 yr)–25.8 kg/m2	LST (kg) (F)	–14.292–0.046 × age (yr)+0.201 × height (cm)+0.347 × weight (kg)–0.448 ×Mexican – 0.047 ×Hispanic+ 1.128 × Black–0.384 × other ethnicity	0.85	2.39
Yu et al. (2013)31	188, Both (18–83 yr)–26.7 kg/m2	LST (kg)	22.93+0.68 ×weight (kg)–1.14 × BMI–0.01 × age (yr)+ 9.94 × sex (M:1/F:0)	0.91	3.61
Kulkarni et al. (2013)30	851, M (30.1 yr)–21.2 kg/m2	LST (kg) (M)	–15.605–(0.032 × age [yr])+(0.192 × height [cm])+ (0.502 ×weight [kg])	0.90	1.92
	481, F (34.7 yr)–23.2 kg/m2	LST (kg) (F)	–13.034–(0.018 × age [yr])+(0.165 × height [cm])+ (0.409 ×weight [kg])	0.91	1.84
Equations using the above parameters plus hip or waist circumference
Lee et al. (2017)28§,ǁ	5,239, M (42.7 yr)–26.6 kg/m2	LST (kg) (M)	19.363+0.001 × age (yr)+0.064 × height (cm)+ 0.756 ×weight (kg)–0.366 × WC (cm)–0.066 ×Mexican+ 0.231 ×Hispanic+0.432 × Black–1.007 × other ethnicity	0.91	2.55
	4,519, F (45.3 yr)–25.8 kg/m2	LST (kg) (F)	–10.683–0.039 × age (yr)+0.186 × height (cm)+ 0.383 ×weight (kg)–0.043 × WC (cm)–0.359 ×Mexican– 0.059 ×Hispanic+1.085 × Black–0.34 × other ethnicity	0.85	2.38
Salamat et al. (2015)25	100, Both (47 yr)–28 kg/m2	LST (kg)	14.966+0.588 × BMI+18.694 × sex (M:1/F:0)+0.137 × HC (cm)–0.138 × age (yr)	0.77	1.84

*For these equations, total body fat is calculated, and FFM is then estimated by subtracting fat mass from the total body mass; ^†Mean average age and BMI from three presented groups (three different ethnicities); ^‡Gallagher et al.²⁷ presented multiple R, and the SEE is presented for body fat %; ^§Authors call it lean body mass, but they explain that they subtracted bone from the lean value obtained from dual-energy X-ray absorptiometry and are therefore reporting lean soft tissue; ^ǁRace variables are binary (1 if yes, 0 if no), and white is the reference group.

BMI, body mass index; SEE, standard error of the estimate; FFM, fat-free mass; BF, body fat; RMSE, root mean square error; WC, waist circumference; LST, lean soft tissue; HC, hip circumference.

Body composition measurements

All three universities used Hologic densitometers in their studies and followed the same measurement protocols. The CIAFEL (UPORTO) research group and the Comprehensive Health Research Center (UEVORA) used an Hologic Explorer QDR DXA scanner (Hologic Inc.), and the GENUD (UNIZAR) research group used an Hologic Horizon QDR DXA scanner (Hologic Inc.). All patients were measured while wearing light clothing, with all metal items removed prior to scanning. Patient positioning followed standard recommendations, and device calibration was performed daily before each round of scans. For participants whose body width exceeded the scanning area limits during whole body assessments, one of the upper or lower limbs was positioned outside the scanning area. The software then performed a posterior replication of the scanned limb to estimate the measurements of both limbs.

Equations used

Two systematic reviews served as a reference to compile existing prediction equations.^21,22 Only equations developed using DXA as the reference method are included in this study. Additionally, we included only equations that can be applied using routine clinical variables: weight, height, waist and hip circumference, BMI, sex, and age. Race was also included because it can improve the prediction estimates in some formulas. From the article by Li et al.,²³ we selected the general formula (including all participants) and the formula for higher BMIs (henceforth referred to as ‘Li et al. higher BMI’). If an article presented a formula for only one sex, it was not included (Larsson et al.²⁴ presents formulas for both sexes, but also gives a formula for females, using height, weight, and waist and hip circumferences, that is not available for males). Hip circumference was not measured in the UEVORA participants, and therefore estimations for the Salamat et al.²⁵ equation include only participants from UNIZAR and UPORTO. The selected equations for predicting FFM and LST are presented in Table 2.

Experimental design

This study was conducted in two phases to address the main aims.

1. Assessment of previous anthropometric equations. FFM and LST were estimated using the equations in Table 2. These estimates were calculated at two time points (before BS and approximately 1 month after).

2. Assessment of changes. The differences between the pre- to post-surgery changes estimated from the equations and the DXA results were calculated.

Statistical analyses

Demographic characteristics in both groups are expressed as the mean±standard deviation (SD). Analyses of variance were used to compare sample characteristics among the different research centers. Paired t-tests were conducted to compare pre- and post-surgery results and analyze differences between the results obtained from the equations and those from DXA. The constant error (CE) was calculated as the mean difference between the FFM or LST according to DXA and each anthropometric equation. The 95% limits of agreement (CE±1.96 SD) were also calculated for each equation, along with the mean absolute error (MAE). Linear regression analyses between the FFM or LST measured by DXA and estimated by the anthropometric equations were applied to determine Pearson correlation coefficient (r), coefficient of determination (r²), and standard error of the estimate (SEE). Cohen’s d was used as a measure of effect size, with values lower or equal to around 0.2 interpreted as small, near 0.5 to 0.8 as medium, and equal to or above 0.8 as large. According to the cutoffs established by Hopkins et al.,²⁶ Pearson correlation coefficients can be trivial (0.0–0.1), small (0.1–0.3), moderate (0.30–0.49), large (0.50–0.69), very large (0.70–0.89), or nearly perfect (0.90–1.00). Additionally, agreement between DXA-derived values and anthropometric equation-derived estimates was evaluated using the intraclass correlation coefficient (ICC), specifically the two-way random effects model with absolute agreement for single measures (ICC [2−1]), which is appropriate for assessing concordance between fixed methods applied across a random sample of participants. The ICC ranges from −1 to 1, with higher values indicating better agreement.

RESULTS

Characteristics of the study population are presented in Table 1. Weight, BMI, waist circumference, hip circumference, waist to hip ratio, LST, and FFM all decreased significantly after surgery (all P<0.05). When the research centers were compared (Supplementary Table 1), participants from UNIZAR were found to be younger than those from UEVORA (P<0.05). Furthermore, participants from UNIZAR were taller and had a higher weight, LST, and FFM than those from UEVORA and UPORTO at both the pre- and post-surgery time points (all P<0.05). Participants from UNIZAR also had a higher hip circumference at the pre-surgery stage and a higher waist to hip ratio both pre- and post-surgery compared with those from UPORTO (all P<0.05).

Tables 3 and 4 present the FFM and LST predicted by the different anthropometric equations, along with the Pearson correlation coefficients, coefficients of determination, MAEs, SEEs, CEs, and 95% limits of agreement. For the estimation of FFM, the equations developed by Gallagher et al.²⁷ (mean difference of 0.6 kg, P=0.206, and MAE=4.15 kg) and Li et al.²³ (mean difference of −0.5 kg for the normal BMI equation and 0.01 kg for the higher BMI equation, with corresponding MAEs of 3.35 kg and 3.42 kg, respectively) provided the most accurate estimations. With the exception of the Larsson et al.²⁴ equation that used waist circumference (r=0.086), all of the correlation coefficients were nearly perfect (r=0.935–0.944) and demonstrated excellent agreement with DXA, with ICC values exceeding 0.90. When the FFM measurements obtained via DXA were compared with individual-level estimates derived from the predictive equations, all equations demonstrated limited accuracy (Fig. 1). Among them, the equations by Gallagher et al.²⁷ and Larsson et al.²⁴ yielded the most favorable results. Specifically, the Gallagher et al.²⁷ equation estimated FFM within ±1 kg of the DXA measurement for 15% of the participants, compared with 16% for the Larsson et al.²⁴ equation. When the threshold for agreement was broadened to ±3 kg, both equations showed concordance in 44% of participants. At a threshold of ±5 kg, the Gallagher et al.²⁷ equation aligned with 69% of participants, and the Larsson et al.²⁴ equation aligned with 76%.

Table 3.

Estimations of FFM and LST obtained with different equations and mean differences compared with DXA

Equation	FFM or LST estimation	Mean difference and 95% CI (DXA-prediction)	P	Effect size	r/r2	SEE/MAE (kg)	ICC (95% CI)
Equations used to estimate FFM
FFM from DXA: 59.01 ± 12.07 kg
Equations only using weight, age, sex, or BMI
Gallagher et al. (2000)27	58.42 ± 14.23	0.60 (–0.33 to 1.52)	0.206	0.110	0.935*/0.874	4.30/4.15	0.92 (0.90 to 0.94)
Janmahasatian et al. (2005)29	57.55 ± 11.37	1.46 (0.73 to 2.19)	< 0.001	0.360	0.940*/0.884	4.12/3.50	0.93 (0.90 to 0.95)
Larsson et al. (2006)24	57.99 ± 12.89	1.02 (0.25 to 1.80)	0.010	0.230	0.941*/0.886	4.09/3.69	0.94 (0.91 to 0.95)
Li et al. (2019)23	59.51 ± 11.84	–0.50 (–1.21 to 0.21)	0.167	–0.130	0.944*/0.890	3.99/3.35	0.92 (0.78 to 0.96)
Li et al. (2019)23 (higher BMI)	59.01 ± 11.45	0.01 (–0.74 to 0.74)	0.998	0.001	0.940*/0.883	4.14/3.42	0.94 (0.92 to 0.95)
Equations using the above parameters plus hip or waist circumference
Larsson et al. (2006)24	50.05 ± 9.22	9.01 (6.17 to 11.85)	< 0.001	0.570	0.086/0.007	12.11/11.12	0.00 (–0.11 to 0.12)
Equations used to estimate LST
LST from DXA: 56.62 ± 11.74 kg
Equations only using weight, age, sex, or BMI
Lee et al. (2017)28	59.55 ± 13.07	–2.93 (–3.68 to –2.17)	< 0.001	–0.690	0.948*/0.898	3.77/4.09	0.92 (0.89 to 0.94)
Yu et al. (2013)31	52.98 ± 12.89	3.64 (2.80 to 4.48)	< 0.001	0.770	0.931*/0.867	4.31/4.87	0.89 (0.70 to 0.94)
Kulkarni et al. (2013)30	62.76 ± 12.88	–6.14 (–6.87 to –5.41)	< 0.001	–1.500	0.949*/0.900	3.72/6.30	0.84 (0.16 to 0.94)
Equations using the above parameters plus hip or waist circumference
Lee et al. (2017)28	59.78 ± 13.18	–3.11 (–3.85 to –2.37)	< 0.001	–0.750	0.951*/0.904	3.65/4.16	0.92 (0.78 to 0.96)
Salamat et al. (2015)25†	57.70 ± 8.47	0.03 (–1.35 to 1.40)	0.971	0.001	0.877*/0.769	6.00/5.11	0.81 (0.76 to 0.86)

Values are presented as mean±standard deviation unless otherwise indicated.

*P<0.05 for the correlation coefficients; ^†For this equation (n=88).

FFM, fat-free mass; LST, lean soft tissue; DXA, dual-energy X-ray absorptiometry; CI, confidence interval; r, Pearson correlation coefficient; r², coefficient of determination; SEE, standard error of the estimate; MAE, mean absolute error; ICC, intraclass correlation coefficient; BMI, body mass index.

Table 4.

Changes in FFM and LST from equations and DXA

Equation	Change in FFM or LST estimation	Mean difference and 95% CI (DXA-prediction)	P	Effect size	r/r2	SEE/MAE (kg)	ICC (95% CI)
Equations used to estimate FFM
Change in FFM from DXA: 6.25 ± 2.77 kg
Equations only using weight, age, sex, or BMI
Gallagher et al. (2000)27	3.69 ± 2.20	2.56 (2.13 to 2.99)	< 0.001	1.070	0.558*/0.312	2.31/2.98	0.35 (0.00 to 0.58)
Janmahasatian et al. (2005)29	3.25 ± 1.31	3.00 (2.58 to 3.43)	< 0.001	1.280	0.535*/0.287	2.35/3.28	0.21 (–0.05 to 0.43)
Larsson et al. (2006)24	3.86 ± 1.90	2.39 (1.97 to 2.80)	< 0.001	1.030	0.562*/0.315	2.31/2.83	0.35 (0.01 to 0.57)
Li et al. (2019)23	4.54 ± 1.88	1.71 (1.30 to 2.13)	< 0.001	0.750	0.574*/0.330	2.28/2.35	0.42 (0.15 to 0.60)
Li et al. (2019)23 Higher BMI	4.30 ± 1.74	1.95 (1.53 to 2.36)	< 0.001	0.850	0.563*/0.317	2.30/2.49	0.37 (0.08 to 0.57)
Equations using the above parameters plus hip or waist circumference
Larsson et al. (2006)24	4.04 ± 2.47	2.26 (1.77 to 2.75)	< 0.001	0.840	0.475*/0.225	2.45/2.87	0.35 (0.07 to 0.54)
Equations used to estimate LST
Change in LST from DXA: 6.26 ± 2.79 kg
Equations only using weight, age, sex, or BMI
Lee et al. (2017)28	5.08 ± 2.28	1.18 (0.75 to 1.60)	< 0.001	0.490	0.569*/0.324	2.30/2.11	0.51 (0.33 to 0.63)
Yu et al. (2013)31	3.42 ± 1.67	2.84 (2.42 to 3.26)	< 0.001	1.200	0.532*/0.283	2.37/3.18	0.27 (–0.04 to 0.50)
Kulkarni et al. (2013)30	5.77 ± 2.40	0.48 (0.05 to 0.92)	0.029	0.200	0.569*/0.324	2.30/1.86	0.55 (0.44 to 0.65)
Equations using the above parameters plus hip or waist circumference
Lee et al. (2017)28	4.98 ± 2.58	1.32 (0.85 to 1.80)	< 0.001	0.500	0.522*/0.272	2.38/2.35	0.47 (0.29 to 0.60)
Salamat et al. (2015)25†	3.83 ± 1.48	2.46 (1.98 to 2.94)	< 0.001	1.100	0.556*/0.309	2.26/2.62	0.34 (0.00 to 0.57)

*P<0.05 for the correlation coefficients; ^†For this equation (n=88).

FFM, fat-free mass; LST, lean soft tissue; DXA, dual-energy X-ray absorptiometry; CI, confidence interval; r, Pearson correlation coefficient; r², coefficient of determination; SEE, standard error estimate; MAE, mean absolute error; ICC, intraclass correlation coefficient; BMI, body mass index.

Figure 1.

Individual differences between dual-energy X-ray absorptiometry (DXA) and the various predictive equations for estimating fat-free mass (FFM) and lean soft tissue (LST) are reported. For each equation, the number and percentage of participants exhibiting discrepancies of ±1 kg (highlighted in green), ±2 kg (orange), ±3 kg (red), and ±5 kg (gray) from the DXA measurements are presented. The equations are ordered from the least accurate to the most accurate, based on the number of participants showing a difference of less than or equal to 1 kg. BMI, body mass index.

An analysis of equations designed to estimate LST revealed that only the equation developed by Salamat et al.²⁵ exhibited no significant differences from the DXA estimations (mean difference of 0.03 kg, P=0.971, MAE=5.11, and ICC=0.81). The Pearson correlation coefficients were nearly perfect, ranging from 0.88 to 0.95. All equations showed good agreement with the DXA values, with ICCs ranging from 0.81 to 0.92. When the LST measurements obtained via DXA were compared at the individual level with values predicted by the existing equations, all predictive models exhibited limited accuracy (Fig. 1). Among them, the equation proposed by Lee et al.²⁸ demonstrated the best performance, with 15% of participants showing a discrepancy of less than 1 kg relative to the DXA measurement, 44% exhibiting a discrepancy within ±3 kg, and 68% showing a discrepancy within ±5 kg.

The analysis of the equations’ accuracy in estimating pre- to postsurgery changes in FFM and LST (Table 4) revealed that all models significantly underestimated FFM. The discrepancies between the DXA-derived values and those estimated by the equations ranged from 1.71 kg with the Li et al.²³ equation to 3.00 kg with the Janmahasatian et al.²⁹ equation. The corresponding effect sizes for those differences were all classified as large. The Pearson correlation coefficients were generally moderate to large, ranging from 0.475 to 0.574. The six equations tested demonstrated poor agreement with DXA, with ICC values below 0.50. Comparable patterns were observed for the equations estimating LST, with all models yielding significant underestimations of the actual values. These ranged from 0.48 kg with the Kulkarni et al.³⁰ equation to 2.84 kg with the Yu et al.³¹ equation. The effect sizes varied from small for the Kulkarni et al.³⁰ model to large for the Yu et al.³¹ model. The Pearson correlation coefficients for LST estimates ranged from 0.52 to 0.57, and the ICCs were all below 0.56.

Fig. 2 presents a comparison of the changes from pre-surgery to 1 month post-surgery for FFM and LST, showing the values from DXA and each equation for each participant. The equations are presented in descending order, beginning with the worst-performing equation (lowest number of participants with less than a 1 kg difference between the DXA change and equation estimation change) and concluding with the best performing equation (highest number of participants with less than a 1 kg difference between the DXA change and equation estimation change).

Figure 2.

Individual differences between changes in dual-energy X-ray absorptiometry (DXA) values from pre- to post-surgery and changes in the different equations from pre- to post-surgery. The number and percentage of participants who showed a ±1 kg difference (green font), ±2 kg difference (orange font), and ±3 kg difference (red font) between DXA and each equation are presented. FFM, fat-free mass; LST, lean soft tissue; BMI, body mass index.

For FFM, the Li et al.²³ equation demonstrated the best performance (25% of participants exhibited a discrepancy of less than 1 kg between the DXA-FFM change values and equation estimation change values, with 70% showing less than a 3 kg difference). The Li et al.²³ equation for higher BMIs was the second best performing equation, with 22% of participants showing less than a 1 kg difference between the DXA and equation estimations and 66% showing less than a 3 kg difference.

For LST, the Kulkarni et al.³⁰ equation showed the best performance (40% of participants presented less than a 1 kg difference between the DXA LST and equation estimation change values, with 76% showing less than a 3 kg difference). The Lee et al.²⁸ equation was the second best performing equation, with 29% of participants showing less than a 1 kg difference between the DXA values and equation estimations.

DISCUSSION

In this study, we aimed to assess the accuracy of existing equations that estimate FFM and LST from variables that are easily obtained in clinical practice, using DXA as the reference method, in patients with type II obesity or higher. Before BS, when all participants exhibited high BMIs, the Li et al.²³ equation for higher BMIs showed a high degree of accuracy in predicting FFM. Conversely, the Salamat et al.²⁵ equation was the most accurate predictor of LST at the group level. However, both equations performed poorly in follow-up assessments. Specifically, they underestimated changes in body composition, with mean errors of 1.95 kg for FFM and 2.46 kg for LST, respectively. Furthermore, when the efficacy of the methods was evaluated at the individual level, a low percentage of participants showed a difference of less than 1 kg between the DXA results and the equation estimations. This suggests that alternative methods should be explored for assessing these body components in BS patients.

The fact that the Li et al.²³ equation for higher BMI was the best equation at the group level was not surprising because it was the only one developed in a sample of participants with a BMI between 25 and 40 kg/m². Although the original authors used a Lunar densitometer (GE HealthCare), whereas we used Hologic densitometers, the mean difference between their equation and our DXA measurements was 0.01 kg, which would suggest that the equation is highly consistent across different DXA systems and might be robust enough to provide accurate estimates of FFM in populations with elevated BMI. This minimal discrepancy could support the potential applicability of the Li et al.²³ equation for higher BMIs in clinical and research settings. Nevertheless, in our assessment of this equation’s ability to track longitudinal changes, it underestimated FFM loss by an average of 1.95 kg. Consequently, for a participant who lost 6.25 kg as measured by DXA, the equation estimated a loss of only 4.30 kg. It was surprising to find that the equation developed by the same authors²³ for participants with a BMI of 18.5 to 25 kg/m² showed a slightly improved performance, with a difference from the DXA value of only 1.71 kg. This could be explained by the fact that the equation developed in the normal BMI range might have benefited from a more homogeneous sample with less variability in body composition, thereby improving its precision in estimating changes over time. Additionally, the model's assumptions or predictors might align more closely with the patterns of FFM loss observed after BS, regardless of the initial BMI category.

Although the aforementioned equations seem accurate at the group level, we caution clinicians and researchers who wish to assess FFM or LST changes at the individual level because we found that the Li et al.²³ equation enabled estimates within ±1 kg of the DXA measurement for only 15% of participants, and the Li et al.²³ equation for higher BMI did so for only 11%. Expanding the threshold to ±5 kg improved concordance to 76% and 75%, respectively. These results suggest that the currently available predictive equations are not accurate enough to assess FFM at the individual level.

Similar results were found when evaluating pre- to post-surgery changes at the individual level. Although the mean difference between the DXA values and equations was statistically significant, it seemed to be low (1.71 and 1.95 kg in the Li et al.²³ and Li et al.²³ for higher BMI, respectively). Nevertheless, when comparing methods at the individual level only 25% (Li et al.²³ equation) and 22% (Li et al.²³ for higher BMIs equation) of participants were classified within the ±1 kg group. When the threshold for agreement was expanded to ±3 kg, the proportion of participants with concordant values increased to 70% and 66%, respectively. We did not include ±5 kg limits of agreement in the graphs depicting individual changes in FFM or LST because the magnitude of change was relatively small (e.g., mean change in FFM 6.25 kg). In this context, a 3 kg discrepancy represents a nearly 50% difference, which is substantial. In contrast, during the initial assessment (e.g., FFM 59.01 kg), a 5 kg difference generally corresponded to less than a 10% discrepancy. Therefore, applying wider limits of agreement would have been less meaningful for evaluating changes over time.

When focusing on LST at the group level, the Salamat et al.²⁵ equation demonstrated satisfactory performance, exhibiting a nonsignificant mean difference of 0.03 kg between methods. Nonetheless, an evaluation of the Salamat equation’s capacity to adequately perform a follow-up examination revealed a substantial discrepancy of 2.46 kg, compared with DXA. The Kulkarni et al.³⁰ equation emerged as the most precise equation for follow-up assessment at the group level, exhibiting a mean difference of 0.48 kg. Consequently, if an average mean loss of 6.25 kg is measured through DXA, the Kulkarni et al.³⁰ equation would predict a loss of 5.77 kg at the group level. Taking into account that only age, height, and weight are needed to estimate LST through this equation, it appears to be a strong option for estimating LST at a clinical level due to its simplicity, low cost, and ease of application. Nevertheless, when we examined the results at the individual level, both the Salamat et al.²⁵ and the Kulkarni et al.³⁰ equations performed poorly, classifying only 15% and 7% of participants, respectively, within the ±1 kg group. The equation developed by Lee et al.²⁸ demonstrated the most favorable outcomes at the individual level. Nevertheless, its performance was still suboptimal, with only 15% of participants exhibiting a discrepancy of less than 1 kg from the DXA measurements, 44% demonstrating a discrepancy of less than 3 kg, and 68% showing a discrepancy of less than 5 kg. Therefore, the current equations for estimating LST are not accurate at the individual level in patients with type II or higher obesity, and they should not be used to prescribe individualized treatments.

In the context of evaluating the precision of individual changes after surgery, the Kulkarni et al.³⁰ equation demonstrated satisfactory performance: 40% of the participants had an LST difference of less than 1 kg between methods, 60% had a difference of less than 2 kg, and 76% had an LST difference of less than 3 kg between methods.

The findings of this study indicate that although predictive equations such as those proposed by Li et al.²³ for higher BMIs and Salamat et al.²⁵ demonstrate strong performance at the group level, their accuracy can largely be attributed to the compensatory effects of underestimation and overestimation of FFM or LST in individual cases. Consequently, the group mean obtained from these equations is comparable to the values obtained from DXA. However, substantial variability was observed among individual participants, suggesting that these methods might not be equally reliable for all cases. A review of the data revealed that 67% of estimations performed with the Li et al.²³ for higher BMI equation showed a difference of more than 3 kg between methods, and 75% of estimations from the Salamat et al.²⁵ equation showed a difference of more than 3 kg. Consequently, using these equations to estimate FFM or LST for drug prescriptions is not recommended because their inaccuracies at the individual level could lead to inappropriate dosing decisions in clinical settings. Given the substantial variability observed in FFM and LST estimations, relying on existing equations for pharmacological applications could result in suboptimal drug efficacy or unintended adverse effects. Instead, more precise measurement techniques such as DXA should be considered when determining body composition for pharmacological purposes.

The selection of appropriate tools for the assessment of body composition is of critical importance for future clinicians and researchers.¹⁷ An alternative method for assessing FFM or LST is the use of bioelectrical impedance analysis (BIA). The use of this methodology in individuals with obesity remains a subject of controversy,³² especially during rapid weight loss periods, when alterations in hydration status are usually noticed. Consequently, these methods should not be considered suitable replacements due to their susceptibility to measurement error. Although some systematic reviews have suggested that multifrequency BIA can provide acceptable estimates, those conclusions are generally derived from group-level analyses, with many studies failing to report individuallevel accuracy.³³ In this line of research, a study that used BIA to evaluate a wide cohort of patients with mild to severe obesity suggested that new equations adapted for patients with obesity should be developed.³⁴

This study has several strengths, including a large and homogeneous sample of patients with type II obesity or higher and the use of DXA as the reference method for body composition assessment. However, it is important to acknowledge certain limitations, including the use of two distinct DXA models (Hologic Horizon and Hologic Discovery) that were not cross-validated. Nevertheless, those models have demonstrated excellent agreement in previous studies assessing bone mineral density, thereby supporting the comparability of measurements between devices.³⁵ A further limitation of this study is the absence of standardized protocols across centers for measuring waist and hip circumferences.

This study has determined that the most suitable equation for estimating FFM in individuals with type II obesity or higher is the Li et al.²³ equation for higher BMI. However, in the event of an intervention targeting weight loss with the intention of subsequent follow-up, we advocate the use of the Li et al.²³ equation, which demonstrated an initial mean discrepancy of 0.5 kg in comparison to DXA. However, the individual accuracy of this equation was demonstrated in only 25% of participants. Furthermore, when performing a follow-up assessment, both of the Li et al.²³ equations showed a mean difference of more than 1.5 kg and performed poorly at the individual level. When the objective is to assess LST, we recommend that the Salamat et al.²⁵ equation be used. However, if the objective is to evaluate alterations induced by body weight loss, it might instead be advisable to use the Kulkarni et al.³⁰ equation, which demonstrated the best performance in tracking acute changes in LST. Although all of the equations tested here could be suitable for group-level estimations, their application at the individual level is not recommended for cross-sectional assessment or monitoring changes over time because a substantial proportion of our participants exhibited large discrepancies between the predictive equations and reference DXA measurements.

Further research is needed to develop predictive models with enhanced precision and reliability for individuals with class II obesity or greater, thereby improving their utility in clinical practice and follow-up assessments. Recent advances highlight promising directions, including the use of computed tomography-derived assessments of visceral and subcutaneous fat distribution, which could offer more accurate reference standards for model development and be more closely associated with cardiometabolic diseases than general measures of total fat.³⁶ Machine learning-based approaches have also been used to capture complex, non-linear relationships between anthropometric variables and body composition outcomes, offering predictive accuracy superior to that of traditional regression models.³⁷ Moreover, the development of predictive equations tailored to BS patients is an important research direction because these individuals experience unique alterations in body composition and metabolism following substantial weight loss. Future models must undergo rigorous internal and external validation to ensure their reproducibility, and an emphasis on interpretability and clinical feasibility will be essential to facilitate integration into both obesity care and long-term patient monitoring.

In conclusion, this study demonstrates that, although certain anthropometric equations can approximate DXA-derived FFM and LST in people with class II obesity or greater at the group level, their accuracy is highly variable at the individual level. Consequently, relying on existing equations for personalized clinical decisionmaking is not recommended. Our findings underscore the need for new predictive models that account for the unique body composition dynamics found in severe obesity, particularly in the context of BS. The development of more robust and individualized tools could enhance preoperative assessment, postoperative monitoring, and long-term metabolic outcomes in this population.

SUPPLEMENTARY MATERIALS

Supplementary materials can be found online at https://doi.org/10.7570/jomes25065.