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Low accuracy of predictive equations for resting metabolic rate in overweight women after weight loss

Open AccessPublished:March 29, 2021DOI:https://doi.org/10.1016/j.nutos.2021.03.006

      Summary

      Background & Aims

      The better equation to predict resting metabolic rate (pRMR) to use for overweight individuals mainly after weight loss is unclear. This study aimed to identify the best equation to pRMR in overweight adult women before and after a nutritional intervention aiming to lose weight.

      Methods

      Thirty overweight adult women were enrolled in this study. Subjects underwent 6-month energy-restricted diet intervention. Anthropometrics and body composition measures were evaluated. Nine equations that are widely used to pRMR were performed based on anthropometric and body composition parameters. Measured RMR (mRMR) was obtained by indirect calorimetry. A new equation to predict resting metabolic rate (npRMR) was also developed by multiple regression analysis based on anthropometric and body composition variables. The validity of the equations was investigated through comparisons, accuracy, and agreement tests.

      Results

      Before the nutrition intervention, only the Mifflin equation was similar to mRMR, with a mean difference of 12kcal and 83% of accuracy. The mean weight loss was 4.2% after 6 months. Following weight loss, only the Owen equation was similar to mRMR, with a mean difference of −33 kcal. However, this equation showed low accuracy (63%). All the others equations showed reduction of accuracy, increase of bias and overestimation of RMR. A npRMR was calculated, and this showed a lower mean difference to mRMR with 70% of accuracy.

      Conclusions

      Out of the nine resting metabolic rate equations evaluated only the Mifflin equation was similar to mRMR before intervention. Interestingly, after weight loss none of the assessed equations were reliable to pRMR. Based on that we propose a new equation that showed greater accuracy and lower mean difference when compared with mRMR.

      Key words

      1. Introduction

      Overweight and obesity are global health public problems defined as abnormal or excessive fat accumulation, being important risk factors for chronic diseases [
      • van Reedt Dortland A.K.
      • Giltay E.J.
      • van Veen T.
      • Zitman F.G.
      • Penninx B.W.
      Longitudinal relationship of depressive and anxiety symptoms with dyslipidemia and abdominal obesity.
      ]. Indeed, excessive body fat represents a major threat to the health of people due to the associated increase in the incidence of medical co-morbidities, such as diabetes, cardiovascular diseases and cancer [
      • van Reedt Dortland A.K.
      • Giltay E.J.
      • van Veen T.
      • Zitman F.G.
      • Penninx B.W.
      Longitudinal relationship of depressive and anxiety symptoms with dyslipidemia and abdominal obesity.
      ,
      World Health Organization
      W: Global Health Observatory (GHO) data: overweight and obesity.
      ].The world prevalence of adult women obesity has increased over the last decades, rising from 22.7% in the 1970's to 39.0% in 2016 [
      World Health Organization
      W: Global Health Observatory (GHO) data: overweight and obesity.
      ]. Conversely, intervention programs for weight loss reach on average 20% of success rate, defined as the loss of 5 to 10% of the initial weight, for at least one year [
      • Wing R.R.
      • Phelan S.
      Long-term weight loss maintenance.
      ,
      • St-Onge M.
      • Rabasa-Lhoret R.
      • Strychar I.
      • Faraj M.
      • Doucet E.
      • Lavoie J.M.
      Impact of energy restriction with or without resistance training on energy metabolism in overweight and obese postmenopausal women: a montreal Ottawa new emerging team group study.
      ,
      • Krentz A.J.
      • Fujioka K.
      • Hompesch M.
      Evolution of pharmacological obesity treatments: focus on adverse side-effect profiles.
      ].
      Any nutritional intervention program based on a dietary planning requires the knowledge of individual energy requirements, which depends on accurate methods for the calculation of total energy expenditure (TEE) [
      • Flack K.D.
      • Siders W.A.
      • Johnson L.
      • Roemmich J.N.
      Cross-validation of resting metabolic rate prediction equations.
      ]. In this regard, to know precisely the resting metabolic rate (RMR) is fundamental since it is the major component of TEE [
      • Donahoo W.T.
      • Levine J.A.
      • Melanson E.L.
      Variability in energy expenditure and its components.
      ]. However, indirect calorimetry (IC), the gold standard technique that more accurate evaluates the RMR, is an expensive method requiring a complex protocol and trained staff to handle it, hampering its wide use in the clinical practice [
      • Frankenfield D.C.
      Bias and accuracy of resting metabolic rate equations in non-obese and obese adults.
      ,
      • Jesus P.
      • Achamrah N.
      • Grigioni S.
      • Charles J.
      • Rimbert A.
      • Folope V.
      • et al.
      Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit.
      ].
      In this context, many equations were developed to predict RMR (pRMR) in distinct populations with different sex, nutritional status, presence of medical conditions, age or body composition [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ]. While the limitations of predictive equations are clear, their use is still common in clinical practice. Indeed, in 2019, a Scientific Symposium was organized by the European Society for Clinical Nutrition and Metabolism (ESPEN) to commemorate the centenary of the publication of Harris and Benedict's equations for estimating energy expenditure, highlighting the progress of energy expenditure assessment measures and what is currently known about these [
      • Bendavid I.
      • Lobo D.N.
      • Barazzoni R.
      • Cederholm T.
      • Coeffier M.
      • de van der Schueren M.
      • et al.
      The centenary of the Harris-Benedict equations: How to assess energy requirements best? Recommendations from the ESPEN expert group.
      ].
      Therefore, to select a single formula of pRMR that can be widely used is a challenge. Furthermore, the estimate of TEE based on anyone of these formulas may not be accurately, which consequently will influence the weight loss treatment and the achievement of the expected goals [
      • Siervo M.
      • Boschi V.
      • Falconi C.
      Which REE prediction equation should we use in normal-weight, overweight and obese women?.
      ,
      • Muller M.J.
      • Enderle J.
      • Bosy-Westphal A.
      Changes in energy expenditure with weight gain and weight loss in humans.
      ]. Previous studies evaluating equations to estimate RMR after weight loss in overweight individuals [
      • Siervo M.
      • Boschi V.
      • Falconi C.
      Which REE prediction equation should we use in normal-weight, overweight and obese women?.
      ,
      • Ruiz J.R.
      • Ortega F.B.
      • Rodriguez G.
      • Alkorta P.
      • Labayen I.
      Validity of resting energy expenditure predictive equations before and after an energy-restricted diet intervention in obese women.
      ] showed low accuracy values and absence of a precise formula to assess RMR after weight loss.
      The objective of the current study was twofold: (i) to analyze the validity of predictive formulas to estimate the resting metabolic rate in overweight women before and after weight loss; (ii) to develop a predictive equation to estimate RMR in overweight adult women after weight loss.

      2. Materials and methods

      This cross-sectional study conducted in Hospital das Clínicas at the Universidade Federal de Minas Gerais (UFMG) from January 2016 to March 2018. This research was approved by the Ethics Committee at the UFMG (CAAE: 30409114.8.0000.5149). All volunteers signed the informed consent prior the beginning of the research.

      2.1 Subjects

      Overweight and obese women (body mass index − BMI ≥ 25 kg/m2 and < 35 kg/m2) aged between 18 to 59 years old were recruited via online advertisements. Exclusion criteria were: (i) any chronic health conditions (e.g. diabetes, hypertension, chronic renal failure, heart and liver diseases, endocrine diseases); (ii) previous surgery for weight loss; (iii) medications known to affect TEE (total energy expenditure); (iv) pregnancy and breastfeeding; (v) smoking and (vi) alcohol abuse (>2 doses/day).
      The sample size was estimated in 27 participants to detect a difference in resting metabolic rate of 221 kcal after 5% of weight loss, with standard deviation of the change of 169 kcal [
      • Siervo M.
      • Boschi V.
      • Falconi C.
      Which REE prediction equation should we use in normal-weight, overweight and obese women?.
      ], considering the confidence level of 95.0% and statistical power of the 90.0% test [
      • Hulley S.B.
      • Cummings S.R.
      • Grady D.
      • Newman T.
      Designing clinical research.
      ].

      2.2 Study procedures

      After 12 h of fasting, volunteers were assessed in the outpatient clinic where body composition and anthropometric parameters were assessed. The analyses included body weight, height and waist circumference (WC), bioelectrical impedance and indirect calorimetry (IC).
      Weight and height were obtained by a mechanical balance (Filizola®), with a stadiometer coupled. Participants used light clothes without shoes. This measure was used to calculate BMI (weight/height2). WC was measured in the smallest abdominal circumference [
      WHO
      WHO: waist circumference and waist–hip ratio: report of a WHO expert consultation.
      ].
      Body composition was measured by bioelectrical impedance, using the device Quantum X® (RJL Systems), after 12 hours of fasting. Resistance and reactance measurements were used to determine fat-free mass (FFM) and fat mass (FM) in kilogram and percentage, with the device formula. The test was performed in a comfortable and calm room. The patients were instructed to: (i) do not exercise at least 8 hours previously; (ii) do not drink alcohol in the previous 12 hours and (iii) remain lie quietly during the entire test.
      RMR was defined by indirect calorimetry using the QUARK-RMR® device (COSMED, Rome, Italy) as validated by previous studies [
      • Ashcraft C.M.
      • Frankenfield D.C.
      Validity test of a new open-circuit indirect calorimeter.
      ,
      • Blond E.
      • Maitrepierre C.
      • Normand S.
      • Sothier M.
      • Roth H.
      • Goudable J.
      • et al.
      A new indirect calorimeter is accurate and reliable for measuring basal energy expenditure, thermic effect of food and substrate oxidation in obese and healthy subjects.
      ]. The volunteers were instructed to fast for 12 hours and to refrain from drinking coffee or black tea and exercising 24h before assessment. The VO2 and VCO2 were measured during 15 minutes with the participants lying down and awaken, after a 30-minute resting period in the supine position. RMR was calculated by the Weir's equation: [(3.941xVO2) + (1.106xVCO2) x 1440] [
      • Weir J.B.
      New methods for calculating metabolic rate with special reference to protein metabolism.
      ].
      Measured RMR (mRMR) was compared to predicted RMR (pRMR) considering equations shown in Table 1. These equations were selected by screening previous publications based on their frequency of use and clinical relevance [
      • Frankenfield D.C.
      Bias and accuracy of resting metabolic rate equations in non-obese and obese adults.
      ,
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ,
      • Aliasgharzadeh S.
      • Mahdavi R.
      • Asghari Jafarabadi M.
      • Namazi N.
      Comparison of indirect calorimetry and predictive equations in estimating resting metabolic rate in underweight females.
      ,
      • Liu H.Y.
      • Lu Y.F.
      • Chen W.J.
      Predictive equations for basal metabolic rate in Chinese adults: a cross-validation study.
      ,
      • Mifflin M.D.
      • St Jeor S.T.
      • Hill L.A.
      • Scott B.J.
      • Daugherty S.A.
      • Koh Y.O.
      A new predictive equation for resting energy expenditure in healthy individuals.
      ,
      • Owen O.E.
      • Kavle E.
      • Owen R.S.
      • Polansky M.
      • Caprio S.
      • Mozzoli M.A.
      • et al.
      A reappraisal of caloric requirements in healthy women.
      ,
      • Fullmer S.
      • Benson-Davies S.
      • Earthman C.P.
      • Frankenfield D.C.
      • Gradwell E.
      • Lee P.S.
      • et al.
      Evidence analysis library review of best practices for performing indirect calorimetry in healthy and non-critically ill individuals.
      ,
      • Muller M.J.
      • Bosy-Westphal A.
      • Klaus S.
      • Kreymann G.
      • Luhrmann P.M.
      • Neuhauser-Berthold M.
      • et al.
      World Health Organization equations have shortcomings for predicting resting energy expenditure in persons from a modern, affluent population: generation of a new reference standard from a retrospective analysis of a German database of resting energy expenditure.
      ,
      • Schofield W.N.
      Predicting basal metabolic rate, new standards and review of previous work.
      ,
      World Health Organization
      ]. These equations rely on weight, height and age parameters, and one of them also includes body composition data [
      • Muller M.J.
      • Enderle J.
      • Bosy-Westphal A.
      Changes in energy expenditure with weight gain and weight loss in humans.
      ]. The actual body weight was used in the calculations of all the equations.
      Table 1Equations used to predict resting metabolic rate in overweight adult women.
      Mifflin (1990)9.99 × weight + 6.25 × height − 4.92 × age − 161
      Harris-Benedict (1918)665 + 9.56 × weight + 1.84 × height − 4.67 × age
      Owen (1986)795 + 7.18 × weight
      WHO/FAO/UNU (1985)8.7 × weight + 829
      WHO/FAO/UNU (wt+ht) (1985)8.7 × weight + (25 × height2) + 865
      Liu (1985)(13.88 × weight) + (4.16× height) − (3.43 × age) – 112,4 + 54.34
      Müller (2004)(0.08961 × FFM + 0.05662 × FM + 0.667) × 238.84
      Schofield (1985)14.8 × weight + 487
      Schofield (wt + ht) (1985)13.6 × weight + 283 × height2 + 98
      wt + ht = weight + height; FFM = fat free mass; FM = fat mass.

      2.3 Nutritional intervention

      Overweight volunteers were followed up during six months. Nutritional intervention included energy-restricted diet and evaluation of anthropometric and body composition measures. The diet plan was based on the total energy expenditure obtained by the formula: mRMR (obtained by indirect calorimetry) x MET Compendium + 10% of Thermal Effect of Food [
      • St-Onge M.
      • Rabasa-Lhoret R.
      • Strychar I.
      • Faraj M.
      • Doucet E.
      • Lavoie J.M.
      Impact of energy restriction with or without resistance training on energy metabolism in overweight and obese postmenopausal women: a montreal Ottawa new emerging team group study.
      ]. Restriction of 513 to 770 kcal was proposed to favor a loss of 2 to 4 kg per month [
      • St-Onge M.
      • Rabasa-Lhoret R.
      • Strychar I.
      • Faraj M.
      • Doucet E.
      • Lavoie J.M.
      Impact of energy restriction with or without resistance training on energy metabolism in overweight and obese postmenopausal women: a montreal Ottawa new emerging team group study.
      ]. Macronutrient intake ranges were 55–65% carbohydrate, 20–25% protein and 25–30% lipid as recommended by the Dietary Reference Intake [
      IOM
      IoM: dietary reference intakes for energy, carbohydrate, fiber, fat, fatty acids, cholesterol, protein, and amino acids.
      ].

      2.4 Statistical analyses

      Data were organized in the Microsoft Office Excel version 2007 and analyzed using the software Statistical Package for the Social Sciences® (SPSS) version 19.0 and Stata® version 11.2. After consistency analysis, normality of the quantitative variables was tested by the Kolmogorov-Smirnov test. Estimates of frequency (absolute and relative), central tendency (means and medians) and dispersion (standard deviation, minimum and maximum values) were performed. In addition, Pearson or Spearman correlations and Wilcoxon test or paired samples t-test were applied.
      Wilcoxon test or paired samples t-test were used to assess differences between the mRMR and pRMR by equations for non-parametric and parametric variables, respectively. The 95% confidence interval (95% CI) of the difference between pRMR and mRMR was calculated. Predictions between 90% and 110% of mRMR were considered accurate measurements at the individual level. Predictive values less than 90% or more than 110% of mRMR were classified as underestimates and overestimates, respectively [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ,
      • Weijs P.J.
      Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults aged 18-65 y.
      ,
      • Weijs P.J.
      • Vansant G.A.
      Validity of predictive equations for resting energy expenditure in Belgian normal weight to morbid obese women.
      ,
      • Hasson R.E.
      • Howe C.A.
      • Jones B.L.
      • Freedson P.S.
      Accuracy of four resting metabolic rate prediction equations: effects of sex, body mass index, age, and race/ethnicity.
      ]. The mean percentage difference between pRMR and mRMR (bias) was the measurement of accuracy at the group level [
      • Jesus P.
      • Achamrah N.
      • Grigioni S.
      • Charles J.
      • Rimbert A.
      • Folope V.
      • et al.
      Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit.
      ,
      • Hasson R.E.
      • Howe C.A.
      • Jones B.L.
      • Freedson P.S.
      Accuracy of four resting metabolic rate prediction equations: effects of sex, body mass index, age, and race/ethnicity.
      ]. Bland Altman analysis for all the equations vs indirect calorimetry were used before and after weight loss.
      The new equation to predict RMR (npRMR) was developed by multiple linear regression, with the mRMR obtained by indirect calorimetry as reference. The variables with value of p ≤ 0.20, obtained in the bivariate analysis, were tested in the model. The backward method was used. The significance of the final model was evaluated by the F test of the analysis of variance and the quality of the fit by the coefficient of determination (R2). The residues were evaluated according to the assumptions of normality, homoscedasticity, linearity and independence. In addition, the verification of multicollinearity between the variables included in the model was performed.

      3. Results

      Anthropometric measures before and after the intervention of 30 overweight women are shown in Table 2. The mean age was 43±1.7 years old. The percentage of overweight was 33,3% and 66,7% of obesity. All anthropometric variables reduced after six months of dietary treatment including reduction of 4.2 ± 1.1% in body weight, 3.6 ± 2.9% reduction in waist circumference and 1.3 ± 1.2% reduction in free fat mass. After the intervention, the measured RMR also decreased 8.6%, totaling an average reduction of 122.9 ± 29.1kcal.
      Table 2Characteristics of a cohort of 30 Brazilian overweight women before and after the weight loss intervention program.
      VariableBefore interventionAfter interventionP-value
      Mean ± SDMean ± SD
      Weight (kg)79.9 ± 8.076.1 ± 7.2<0.001
      Paired Sample T-test.
      BMI (kg/m2)31.1 ± 2.729.5 ± 2.5<0.001
      Paired Sample T-test.
      WC (cm)89.5 ± 5.786.2 ± 5.4<0.001
      Wilcoxon test.
      FFM (kg)46.1 ± 5.144.7 ± 4.2<0.001
      Wilcoxon test.
      FFM (%)57.7 ± 3.158.9 ± 2.90.012
      Paired Sample T-test.
      FM (Kg)33.8 ± 4.331.3 ± 4.1<0.001
      Paired Sample T-test.
      FM (%)42.3 ± 3.141.0 ± 2.90.012
      Paired Sample T-test.
      mRMR (kcal)1,422.9 ± 163.31,300.0 ± 135.0<0.001
      Wilcoxon test.
      BMI = Body Mass Index; WC = Waist Circumference; mRMR = measured Resting Metabolic Rate; FFM = Fat Free Mass; FM = Fat Mass.
      a Paired Sample T-test.
      b Wilcoxon test.
      Table 3, Table 4 shows the measured resting metabolic rate (mRMR) and the results of the nine equations to predict metabolic rate (pRMR) in overweight women before and after the nutritional intervention. Before the intervention, the Mifflin was the only equation that had similarity with the measured RMR (Table 3). All the other equations did not have a good accuracy and, apart from the Owen equation, overestimated the measured RMR in a range from 47% to 97%.
      Table 3Comparison between the predicted and measured resting metabolic rate for a cohort of 30 Brazilian overweight women before intervention.
      Overweight women before interventionKcal/dayP
      Wilcoxon test.
      DifferencePrediction
      Kcal/d95% CIBias
      The mean percentage difference between pRMR and mRMR (group level).
      (%)
      Accuracy
      Predictions between 90% and 110% of mRMR (individual level).
      % (n)
      Underestimation % (n)Overestimation % (n)
      Measured RMR1,422.9 ± 163.3------
      Mifflin1,429.4 ± 100.70.262−6.5 ± 131.4−55.5; 42.6−183 (25)7 (2)10 (3)
      Harris-Benedict1,524.2 ± 83.8<0.001−101.2 ± 133.9−151.2; −51.2−850 (15)3 (1)47 (14)
      Owen1,369.3 ± 57.80.04153.7 ± 130.25.0; 102.3380 (24)17 (5)3 (1)
      WHO/FAO/UNU1,529.1 ± 72.1<0.001−106.2 ± 127.6−153.9; −58.5−847 (14)6 (2)47 (14)
      WHO/FAO/UNU (wt+ht)1,524.1 ± 70.4<0.001−101.2 ± 127.2−148.7; −53.7−847 (14)6 (2)47 (14)
      Liu1,684.6 ± 120.7<0.001−261.6 ± 123.2−307.7; −215.6−1913 (4)87 (26)
      Muller1,603.4 ± 146.2<0.001−180.4 ± 117.2−224.1; −136.6−1337 (11)63 (19)
      Schofield1,670.8 ± 119.1<0.001−247.8 ± 118.3−291.9; −203.7−1820 (6)80 (24)
      Schofield (wt+ht)1,915.2 ± 136.8<0.001−492.2 ± 120.2−537.1; −447.3−353 (1)97 (29)
      WT: weight; HT: height; CI: confidence interval; WHO/FAO/UNU: World Health Organization/Food and Agriculture Organization of The United Nations/United Nations University.
      a Wilcoxon test.
      b The mean percentage difference between pRMR and mRMR (group level).
      c Predictions between 90% and 110% of mRMR (individual level).
      Table 4Comparison between the predicted and measured resting metabolic rate for a cohort of 30 Brazilian overweight women after intervention.
      Overweight women after interventionkcal/dayP
      Paired Sample T-test.
      DifferencePrediction
      Kcal/d95% CIBias
      The mean percentage difference between pRMR and mRMR (group level).
      (%)
      Accuracy
      Predictions between 90% and 110% of mRMR (individual level).
      % (n)
      Underestimation % (n)Overestimation % (n)
      Measured RMR1,300.0 ± 135.0
      Mifflin1,390.7 ± 92.90.001−90.7 ± 130.9−139.6; −41.7−857 (17)43 (13)
      Harris-Benedict1,487.1 ± 76.5<0.001−187.1 ± 123.1−233.0; −141.1−1537 (11)63 (19)
      Owen1,341.5 ± 52.20.084−41.4 ± 126.6−88.7; 5.8−467 (20)3 (1)30 (9)
      WHO/FAO/UNU1,491.2 ± 63.3<0.001−191.1 ± 127.6−238.7; −143.4−1640 (12)60 (18)
      WHO/FAO/UNU (wt + ht)1,487.0 ± 62.7<0.001−187.0 ± 127.4−234.6; −139.5−1543 (13)57 (17)
      Liu1,630.7 ± 109.2<0.001−330.7 ± 136.9−381.8; −279.6−2610 (3)90 (27)
      Muller1,538.2 ± 129.7<0.001−238.2 ± 150.1−294.3; −182.1−1930 (9)-70 (21)
      Schofield1,613.4 ± 107.6<0.001−313.4 ± 140.3−365.8; −261.0−257 (2)93 (28)
      Schofield (wt + ht)1,862.3 ± 125.8<0.001−562.3 ± 155.7−620.4; −504.1−44100 (30)
      npRMR1,300.0 ± 80.11,000−0.0004 ± 108.6−40.6; 40.60.6870 (21)13 (4)17 (5)
      WT: weight; HT: height; CI: confidence interval; npRMR: new equation to predict RMR; WHO/FAO/UNU: World Health Organization/Food and Agriculture Organization of The United Nations/United Nations University.
      a Paired Sample T-test.
      b The mean percentage difference between pRMR and mRMR (group level).
      c Predictions between 90% and 110% of mRMR (individual level).
      After weight loss associated with dietary intervention, only the Owen equation was good to estimate RMR (Table 4). Even the Mifflin equation, that had a good accuracy to predict RMR before intervention, did not have a good accuracy when the women lost weight, with the accuracy dropping from 83% to 57%. Although the Owen equation was similar to mRMR after the intervention, its individual accuracy was less than 70%. All the other equations presented with even lower values of accuracy, also overestimating the RMR in a range from 43 to 100%.
      Fig. 1 shows the Bland Alman analyses between predictive equations and indirect calorimetry before and after weight loss. It is clear that the measures do not agree, showing statistically significant bias in all analyzes, except for Mifflin equation before weight loss (p = 0.234) and Owen after weight loss (p = 0.312).
      Fig. 1
      Fig. 1Bland Altman analysis for all the predictive equations evaluated vs indirect calorimetry, before and after weight loss. a. Mifflin's equation vs indirect calorimetry before (left) and after weight loss (right). b. Harris Benedict's equation vs indirect calorimetry before (left) and after weight loss (right). c. Owen's equation vs indirect calorimetry before (left) and after weight loss (right). d. WHO/FAO/UNU's equation vs indirect calorimetry before (left) and after weight loss (right). e. WHO/FAO/UNU's equation (weight + height) vs indirect calorimetry before (left) and after weight loss (right). f. Liu's equation vs indirect calorimetry before (left) and after weight loss (right). g. Muller's equation vs indirect calorimetry before (left) and after weight loss (right). h. Schofield's equation vs indirect calorimetry before (left) and after weight loss (right). i. Schofield's equation (weight + height) vs indirect calorimetry before (left) and after weight loss (right).
      Fig. 1
      Fig. 1Bland Altman analysis for all the predictive equations evaluated vs indirect calorimetry, before and after weight loss. a. Mifflin's equation vs indirect calorimetry before (left) and after weight loss (right). b. Harris Benedict's equation vs indirect calorimetry before (left) and after weight loss (right). c. Owen's equation vs indirect calorimetry before (left) and after weight loss (right). d. WHO/FAO/UNU's equation vs indirect calorimetry before (left) and after weight loss (right). e. WHO/FAO/UNU's equation (weight + height) vs indirect calorimetry before (left) and after weight loss (right). f. Liu's equation vs indirect calorimetry before (left) and after weight loss (right). g. Muller's equation vs indirect calorimetry before (left) and after weight loss (right). h. Schofield's equation vs indirect calorimetry before (left) and after weight loss (right). i. Schofield's equation (weight + height) vs indirect calorimetry before (left) and after weight loss (right).
      In this context, it is important to propose new equations to estimate RMR after weight loss. Accordingly, we suggest a new predicting equation to be used after weight loss. For this purpose, we considered variables that were positively correlated with mRMR: baseline weight (p = 0.024), final weight (p = 0.059), BMI (p = 0.049), WC (p = 0.004) and FFMkg (p = 0.015). In the final model, the variables BMI, WC and FFMkg remained, explaining 35,2% of the RMR value variability (Fig. 1). This new equation (Table 5) showed higher accuracy (70%), and also a smaller difference to the mRMR (−0.0004 kcal, ±108.6 kcal) in comparison with the other equations after weight loss (Table 4).
      Table 5Proposed equation for calculating RMR of overweight women after weight loss.
      npRMR (kcal) = 1,064.69 + (24.18 × BMI) − (12.81 × WC) + (13.96 × FFMkg)
      BMI: Body Mass Index (kg/m2); WC: Waist circumference (cm); FFMkg: Fat Free Mass, kilogram.
      Backward method: β0:1,064.69; R2: 0.3524; p=0.001.

      4. Discussion

      Obesity is a pandemic health problem. One of the biggest challenges during obesity treatment is the maintenance of weight loss. Besides that, with weight loss, the estimation of energy requirement changes, and it has been complex to accurately establish this value. Actually, predictive equations of RMR are reliable in obese individuals, but it is debatable the best predictive equation for RMR estimation after weight loss [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ,
      • Bendavid I.
      • Lobo D.N.
      • Barazzoni R.
      • Cederholm T.
      • Coeffier M.
      • de van der Schueren M.
      • et al.
      The centenary of the Harris-Benedict equations: How to assess energy requirements best? Recommendations from the ESPEN expert group.
      ].
      Among the nine equations evaluated in this study, only the Mifflin equation was similar to mRMR in overweight women at baseline, i.e. before intervention. After weight lost, not even the Mifflin equation remained comparable to mRMR, presenting a considerable reduction of accuracy. These findings are clinically relevant, and indicate that the validity of the RMR predictive equations vary according to changes in the body weight and body composition. In addition, these data suggest the need to identify better estimates and/or equations to predict RMR in women undergoing an energy-restricted diet intervention in order to maintain weight loss or promote weight stabilization over time.
      Before intervention, two equations presented individual accuracy greater than 70% (‘ideal’ value) [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ] and after weight loss none of the equations presented individual accuracy above this value. In line with these observations, Weijs et al. (2010) and Krüger et al. (2015) found a reduction in the accuracy of the equations as the BMI reduces, while Siervo et al. (2003) pointed out that weight loss is responsible to increase the overestimation of the predictive resting metabolic rate equations [
      • Siervo M.
      • Boschi V.
      • Falconi C.
      Which REE prediction equation should we use in normal-weight, overweight and obese women?.
      ,
      • Weijs P.J.
      • Vansant G.A.
      Validity of predictive equations for resting energy expenditure in Belgian normal weight to morbid obese women.
      ,
      • Krüger R.L.
      • Lopes A.L.
      • Gross J.S.
      • Macedo R.C.O.
      • Teixeira B.C.
      • Álvaro R.O.
      Validation of predictive equations for basal metabolic rate in nonobese and obese subjects.
      ].
      Previous studies showed that the Mifflin equation was accurate in obese subjects before weight loss, although it did not reach predictions of 80% in most of them [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ,
      • Weijs P.J.
      Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults aged 18-65 y.
      ,
      • Madden A.M.
      • Mulrooney H.M.
      • Shah S.
      Estimation of energy expenditure using prediction equations in overweight and obese adults: a systematic review.
      ]. The Mifflin equation was adequate in overweight and obese Belgian women, but was less precise for Dutch obese subjects [
      • Weijs P.J.
      Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults aged 18-65 y.
      ,
      • Weijs P.J.
      • Vansant G.A.
      Validity of predictive equations for resting energy expenditure in Belgian normal weight to morbid obese women.
      ]. A systematic review by Frankenfield et al. (2005) reported that the Mifflin equation provides the best prediction of RMR for obese individuals compared to other equations [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ]. More recently, Krüger et al. (2015) showed that RMR predictive equations overestimated RMR in overweight women, except the Mifflin equation, when compared with mRMR [
      • Krüger R.L.
      • Lopes A.L.
      • Gross J.S.
      • Macedo R.C.O.
      • Teixeira B.C.
      • Álvaro R.O.
      Validation of predictive equations for basal metabolic rate in nonobese and obese subjects.
      ]. Despite the above mentioned evidence, there is no consensus regarding the use of a preferential RMR equation for obese individuals, and the conclusion may change according to BMI subgroups and analysis methods [
      • Weijs P.J.
      Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults aged 18-65 y.
      ,
      • Madden A.M.
      • Mulrooney H.M.
      • Shah S.
      Estimation of energy expenditure using prediction equations in overweight and obese adults: a systematic review.
      ]. Therefore, caution must be taken when applying predictive equations for RMR in overweight and obese individuals.
      After the intervention, there was a decrease in mRMR, similar as seen in the literature [
      • Ruiz J.R.
      • Ortega F.B.
      • Rodriguez G.
      • Alkorta P.
      • Labayen I.
      Validity of resting energy expenditure predictive equations before and after an energy-restricted diet intervention in obese women.
      ,
      • Poli V.F.
      • Sanches R.B.
      • Moraes A.D.
      • Fidalgo J.P.
      • Nascimento M.A.
      • Andrade-Silva S.G.
      • et al.
      Resting energy expenditure in obese women: comparison between measured and estimated values.
      ]. Concomitant with the mRMR reduction, the pRMR obtained by the Mifflin equation was no longer similar to the mRMR. The equation that showed similar results with the mRMR was the Owen equation, but with low accuracy. Actually, there was a reduction of accuracy, an increase of bias and overestimation of the RMR with all the equations after weight loss. Ruiz et al. (2011) investigated the validity of RMR predictive equations in obese Caucasian pre-menopausal women before and after interventions for weight loss. Similar to our results, the equation of Mifflin had the highest accuracy at baseline, but, this level of accuracy was lost after a 12-week energy-restricted diet. In addition, the lowest bias and larger accuracy was found with the Owen equation after the intervention [
      • Ruiz J.R.
      • Ortega F.B.
      • Rodriguez G.
      • Alkorta P.
      • Labayen I.
      Validity of resting energy expenditure predictive equations before and after an energy-restricted diet intervention in obese women.
      ].
      The reduction in the accuracy of equations after weight loss in overweight subjects was also verified for Siervo et al. (2003) in young Caucasian women [
      • Siervo M.
      • Boschi V.
      • Falconi C.
      Which REE prediction equation should we use in normal-weight, overweight and obese women?.
      ]. Poli et al. (2016), studying Brazilian obese women engaged in an interdisciplinary approach to promote an active lifestyle, healthy nutritional habits and weight loss [
      • Poli V.F.
      • Sanches R.B.
      • Moraes A.D.
      • Fidalgo J.P.
      • Nascimento M.A.
      • Andrade-Silva S.G.
      • et al.
      Resting energy expenditure in obese women: comparison between measured and estimated values.
      ]. The authors showed a wide variation in the accuracy of the pRMR before and after weight loss. Conversely, no significant differences between mRMR e pRMR were reported by Harris–Benedict and FAO/WHO/United Nations University (UNU) with a bias <5% before and after the therapy [
      • Harris J.A.
      • FG B.
      A biometric study of human basal metabolism.
      ,

      FAO/WHO/UNU: Energy and protein requirements. . (WHO Wtrs ed. Geneva.

      ]. The accuracy of these equations increased after weight loss, however with accuracy < 50% [
      • Poli V.F.
      • Sanches R.B.
      • Moraes A.D.
      • Fidalgo J.P.
      • Nascimento M.A.
      • Andrade-Silva S.G.
      • et al.
      Resting energy expenditure in obese women: comparison between measured and estimated values.
      ].
      The new equation developed in this study had the highest accuracy (70%) among all predictive equations evaluated after weight loss. It also had the lowest value of overestimation (17%) comparing with the other equations. The overestimation of RMR may affect weight loss and contribute to withdraw of nutritional interventional [
      • Frankenfield D.
      • Roth-Yousey L.
      • Compher C.
      Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
      ,
      • Wilms B.
      • Schmid S.M.
      • Ernst B.
      • Thurnheer M.
      • Mueller M.J.
      • Schultes B.
      Poor prediction of resting energy expenditure in obese women by established equations.
      ,
      • Schusdziarra V.
      • Wolfschlager K.
      • Hausmann M.
      • Wagenpfeil S.
      • Erdmann J.
      Accuracy of resting energy expenditure calculations in unselected overweight and obese patients.
      ].
      Oliveira et al. (2018) also proposed a new equation to predict RMR for women with class III obesity and found that weight, height, age, abdominal circumference, FFM and FM were positively correlated with RMR, but did not evaluate the similarity after weight loss [
      • de Oliveira B.A.P.
      • Nicoletti C.F.
      • de Oliveira C.C.
      • Pinhel M.A.S.
      • Quinhoneiro D.C.G.
      • Noronha N.Y.
      • et al.
      A new resting metabolic rate equation for women with class III obesity.
      ]. The new equation proposed in our study included only 3 variables: BMI, WC and FFM (kg), being more useful in clinical practice.
      Our study has some limitations. We studied only women, however we chose it avoid the sex effect on RMR. We used bioelectrical impedance instead of dual energy X-ray absorptiometry to define body composition. Bioelectrical impedance allows reliable results and is more useful in clinical practice. On the other hand, the strength of the study includes duration of follow-up, over than other previously researches.

      5. Conclusion

      In conclusion, our data indicate low accuracy of RMR prediction equations after overweight women lose weight. Herein we highlight the real necessity to develop new formulas to accurately predict the RMR during weight loss treatment. In this sense, we propose an alternative predictive equation for overweight and obese class I women that are losing weight. Our research group is developing other study to validate the new equation proposed.

      Funding/Acknowledgements

      This study was partly funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES); Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); and Pró-Reitoria de Pesquisa da UFMG.

      Author contributions

      A.V.M.F. designed the research; N.M.M., A.M.S.R., G.B.P.F and B.L.M conducted research; N.M.M, M.I.T.D.C, L.C.S. and A.V.M.F analyzed data; N.M.M., A.M.S.R., L.C.S., A.L.T. and A.V.M.F wrote the paper; A.L.T. and M.I.T.D.C provided essential materials; A.V.M.F. had primary responsibility for the final content. All authors read and approved the final manuscript.

      Declaration of competing interest

      No conflict to report.

      References

        • van Reedt Dortland A.K.
        • Giltay E.J.
        • van Veen T.
        • Zitman F.G.
        • Penninx B.W.
        Longitudinal relationship of depressive and anxiety symptoms with dyslipidemia and abdominal obesity.
        Psychosom Med. 2013; 75: 83-89
        • World Health Organization
        W: Global Health Observatory (GHO) data: overweight and obesity.
        World Health Organization, Geneva2017
        • Wing R.R.
        • Phelan S.
        Long-term weight loss maintenance.
        Am J Clin Nutr. 2005; 82: 222S-225S
        • St-Onge M.
        • Rabasa-Lhoret R.
        • Strychar I.
        • Faraj M.
        • Doucet E.
        • Lavoie J.M.
        Impact of energy restriction with or without resistance training on energy metabolism in overweight and obese postmenopausal women: a montreal Ottawa new emerging team group study.
        Menopause. 2013; 20: 194-201
        • Krentz A.J.
        • Fujioka K.
        • Hompesch M.
        Evolution of pharmacological obesity treatments: focus on adverse side-effect profiles.
        Diabetes Obes Metab. 2016; 18: 558-570
        • Flack K.D.
        • Siders W.A.
        • Johnson L.
        • Roemmich J.N.
        Cross-validation of resting metabolic rate prediction equations.
        J Acad Nutr Diet. 2016; 116: 1413-1422
        • Donahoo W.T.
        • Levine J.A.
        • Melanson E.L.
        Variability in energy expenditure and its components.
        Curr Opin Clin Nutr Metab Care. 2004; 7: 599-605
        • Frankenfield D.C.
        Bias and accuracy of resting metabolic rate equations in non-obese and obese adults.
        Clin Nutr. 2013; 32: 976-982
        • Jesus P.
        • Achamrah N.
        • Grigioni S.
        • Charles J.
        • Rimbert A.
        • Folope V.
        • et al.
        Validity of predictive equations for resting energy expenditure according to the body mass index in a population of 1726 patients followed in a Nutrition Unit.
        Clin Nutr. 2015; 34: 529-535
        • Frankenfield D.
        • Roth-Yousey L.
        • Compher C.
        Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.
        J Am Diet Assoc. 2005; 105: 775-789
        • Bendavid I.
        • Lobo D.N.
        • Barazzoni R.
        • Cederholm T.
        • Coeffier M.
        • de van der Schueren M.
        • et al.
        The centenary of the Harris-Benedict equations: How to assess energy requirements best? Recommendations from the ESPEN expert group.
        Clin Nutr. 2020; 40: 690-701
        • Siervo M.
        • Boschi V.
        • Falconi C.
        Which REE prediction equation should we use in normal-weight, overweight and obese women?.
        Clin Nutr. 2003; 22: 193-204
        • Muller M.J.
        • Enderle J.
        • Bosy-Westphal A.
        Changes in energy expenditure with weight gain and weight loss in humans.
        Curr Obes Rep. 2016; 5: 413-423
        • Ruiz J.R.
        • Ortega F.B.
        • Rodriguez G.
        • Alkorta P.
        • Labayen I.
        Validity of resting energy expenditure predictive equations before and after an energy-restricted diet intervention in obese women.
        PLoS One. 2011; 6e23759
        • Hulley S.B.
        • Cummings S.R.
        • Grady D.
        • Newman T.
        Designing clinical research.
        Fourth ed. 2013
        • WHO
        WHO: waist circumference and waist–hip ratio: report of a WHO expert consultation.
        World Health Organization, Geneva2011
        • Ashcraft C.M.
        • Frankenfield D.C.
        Validity test of a new open-circuit indirect calorimeter.
        JPEN J Parenter Enteral Nutr. 2015; 39: 738-742
        • Blond E.
        • Maitrepierre C.
        • Normand S.
        • Sothier M.
        • Roth H.
        • Goudable J.
        • et al.
        A new indirect calorimeter is accurate and reliable for measuring basal energy expenditure, thermic effect of food and substrate oxidation in obese and healthy subjects.
        E-SPEN, the European E-Journal of Clinical Nutrition and Metabolism. 2011; 6: e7-e15
        • Weir J.B.
        New methods for calculating metabolic rate with special reference to protein metabolism.
        J Physiol. 1949; 109: 1-9
        • Aliasgharzadeh S.
        • Mahdavi R.
        • Asghari Jafarabadi M.
        • Namazi N.
        Comparison of indirect calorimetry and predictive equations in estimating resting metabolic rate in underweight females.
        Iran J Public Health. 2015; 44: 822-829
        • Liu H.Y.
        • Lu Y.F.
        • Chen W.J.
        Predictive equations for basal metabolic rate in Chinese adults: a cross-validation study.
        J Am Diet Assoc. 1995; 95: 1403-1408
        • Mifflin M.D.
        • St Jeor S.T.
        • Hill L.A.
        • Scott B.J.
        • Daugherty S.A.
        • Koh Y.O.
        A new predictive equation for resting energy expenditure in healthy individuals.
        Am J Clin Nutr. 1990; 51: 241-247
        • Owen O.E.
        • Kavle E.
        • Owen R.S.
        • Polansky M.
        • Caprio S.
        • Mozzoli M.A.
        • et al.
        A reappraisal of caloric requirements in healthy women.
        Am J Clin Nutr. 1986; 44: 1-19
        • Fullmer S.
        • Benson-Davies S.
        • Earthman C.P.
        • Frankenfield D.C.
        • Gradwell E.
        • Lee P.S.
        • et al.
        Evidence analysis library review of best practices for performing indirect calorimetry in healthy and non-critically ill individuals.
        J Acad Nutr Diet. 2015; 115 (1417-1446 e1412)
        • Muller M.J.
        • Bosy-Westphal A.
        • Klaus S.
        • Kreymann G.
        • Luhrmann P.M.
        • Neuhauser-Berthold M.
        • et al.
        World Health Organization equations have shortcomings for predicting resting energy expenditure in persons from a modern, affluent population: generation of a new reference standard from a retrospective analysis of a German database of resting energy expenditure.
        Am J Clin Nutr. 2004; 80: 1379-1390
        • Schofield W.N.
        Predicting basal metabolic rate, new standards and review of previous work.
        Hum Nutr Clin Nutr. 1985; 39: 5-41
        • World Health Organization
        Roa W.E. W: physical status: the use and interpretation of anthropometry. 1996 (Genova)
        • IOM
        IoM: dietary reference intakes for energy, carbohydrate, fiber, fat, fatty acids, cholesterol, protein, and amino acids.
        The National Academies Press, Washington, DC2005
        • Weijs P.J.
        Validity of predictive equations for resting energy expenditure in US and Dutch overweight and obese class I and II adults aged 18-65 y.
        Am J Clin Nutr. 2008; 88: 959-970
        • Weijs P.J.
        • Vansant G.A.
        Validity of predictive equations for resting energy expenditure in Belgian normal weight to morbid obese women.
        Clin Nutr. 2010; 29: 347-351
        • Hasson R.E.
        • Howe C.A.
        • Jones B.L.
        • Freedson P.S.
        Accuracy of four resting metabolic rate prediction equations: effects of sex, body mass index, age, and race/ethnicity.
        J Sci Med Sport. 2011; 14: 344-351
        • Krüger R.L.
        • Lopes A.L.
        • Gross J.S.
        • Macedo R.C.O.
        • Teixeira B.C.
        • Álvaro R.O.
        Validation of predictive equations for basal metabolic rate in nonobese and obese subjects.
        Rev Bras Cineantropom Desempenho Hum. 2015; 17: 73-81
        • Madden A.M.
        • Mulrooney H.M.
        • Shah S.
        Estimation of energy expenditure using prediction equations in overweight and obese adults: a systematic review.
        J Hum Nutr Diet. 2016; 29: 458-476
        • Poli V.F.
        • Sanches R.B.
        • Moraes A.D.
        • Fidalgo J.P.
        • Nascimento M.A.
        • Andrade-Silva S.G.
        • et al.
        Resting energy expenditure in obese women: comparison between measured and estimated values.
        Br J Nutr. 2016; 116: 1306-1313
        • Harris J.A.
        • FG B.
        A biometric study of human basal metabolism.
        Proc Natl Acad Sci U S A. 1918; 4
      1. FAO/WHO/UNU: Energy and protein requirements. . (WHO Wtrs ed. Geneva.

        • Wilms B.
        • Schmid S.M.
        • Ernst B.
        • Thurnheer M.
        • Mueller M.J.
        • Schultes B.
        Poor prediction of resting energy expenditure in obese women by established equations.
        Metabolism. 2010; 59: 1181-1189
        • Schusdziarra V.
        • Wolfschlager K.
        • Hausmann M.
        • Wagenpfeil S.
        • Erdmann J.
        Accuracy of resting energy expenditure calculations in unselected overweight and obese patients.
        Ann Nutr Metab. 2014; 65: 299-309
        • de Oliveira B.A.P.
        • Nicoletti C.F.
        • de Oliveira C.C.
        • Pinhel M.A.S.
        • Quinhoneiro D.C.G.
        • Noronha N.Y.
        • et al.
        A new resting metabolic rate equation for women with class III obesity.
        Nutrition. 2018; 49: 1-6