Background: There are several predictive equations for estimating resting metabolic rate (RMR) in healthy humans. Concordance of these equations against measured RMR is variable, and often dependent on the extent of RMR. Part of the discrepancy may be due to an insufficient accuracy of metabolic carts, but this accuracy can be improved via a correction procedure. Objective: To determine the validity of predictive RMR equations by comparing them against measured and corrected (i.e. the reference) RMR. Methods: RMR was measured, in 69 healthy volunteers (29 males/40 females; 32±8 years old; BMI 25.5±3.8 kg/m2) and then corrected by simulating gas exchange through pure gases and high-precision mass-flow regulators. RMR was predicted using 13 published equations. Bland–Altman analyses compared predicted vs. reference RMRs. Results: All equations correlated well with the reference RMR (r>0.67; P<0.0001), but on average, over-predicted the reference RMR (89–312 kcal/d; P<0.05). Based on Bland–Altman analyses, 12 equations showed a constant bias across RMR, but the bias was not different from zero for nine of them. Three equations stood out because the absolute difference between predicted and reference RMR was equal or lower than 200 kcal/d for >60% of individuals (the Mifflin, Oxford and Müller equations). From them, only the Oxford equations performed better in both males and females separately. Conclusion: The Oxford equations are a valid alternative to predict RMR in healthy adult humans. Gas-exchange correction appears to be a good practice for the reliable assessment of RMR.

Introduction

Determination of resting metabolic rate (RMR) is essential for establishing the energy requirements of vital body functions and is essentially measured by determination of oxygen consumption (VO2) and carbon dioxide production (CO2) by using indirect calorimetry [1]. However, indirect calorimetry is expensive, time-consuming and not always feasible, which has encouraged the development of predictive equations based on body mass/composition, sex and age [2]. Among them, the Schofield equations were conventionally accepted in 1985 by the World Health Organization (WHO) and then ratified as valid in the Joint of the Food and Agricultural Organization of the United Nations, WHO, and United Nations University Expert Consultation held in 2001 [3]. Even so, alternative equations are commonly applied and often preferred by researchers and clinicians, despite the fact that in most cases, only subtle advantages are noted [3–5].

Recently, Flack et al. [5] compared several RMR predictive equations against measured values in 30 healthy adult humans. That study found that the pioneering Harris–Benedict and Schofield equations were more accurate compared with later predictive equations. However, all equations underestimated RMR in individuals with high RMR, an observation also noted in other studies [6,7]. The lack of accuracy of these equations may be explained by the fact that body mass, sex and age only predict 50–70% of the whole variance in RMR [8]. Furthermore, the fat-free mass-to-fat mass ratio often decreases as body mass increases, which may also contribute to the inaccuracy, especially in individuals with high RMR [9]. Body composition-based equations have consequently been generated [10,11], despite the inherent analytical and feasibility difficulties for body-composition assessment. Although this approach appears more accurate, RMR-dependent bias still remains [12].

Additional factors may therefore influence the validity of RMR predictive equations, including the accuracy of the reference method (i.e. indirect calorimetry) to determine and then compare RMR. Indeed, some metabolic carts have insufficient accuracy when tested through ethanol burning [13] or infusion of pure gases [14]. Moreover, moderate to poor concordance has been reported among metabolic carts with limits of agreement between calorimeters of ±300 kcal/d or higher [15]. These constraints led Schadewaldt et al. [14] to design a method to enhance the accuracy and comparability of gas exchange assessment. The method is based on the simulation of a given VO2 and VCO2 by infusing N2 (to dilute air O2 concentration) and CO2 through high-precision mass-flow regulators into the metabolic cart. By comparing measured (from the metabolic cart) and expected (from high-precision mass-flow regulators) readouts, gas-exchange accuracy after each assessment is determined, and then VO2 and VCO2 can be corrected.

We recently applied this procedure to correct gas exchange (RMR and respiratory quotient) under fasting and feeding conditions [16]. We found that the average uncorrected RMR was 7% (∼130 kcal/d) higher than the corrected RMR. Moreover, at high RMR, the difference between uncorrected and corrected values is larger. We also noted that the predictive power of body mass, sex and age was 12% higher when corrected vs. uncorrected RMR was considered. Therefore, this correction protocol appeared to provide information of improved quality, so it can be considered a reference method to assess the validity of RMR predictive equations.

RMR predictive equations are largely used to define energy supply under a variety of conditions (e.g. pregnancy, lactation, weight recovery). In addition, these equations are used to assess the validity of dietary records collected at the individual and population level [17]. Here we assessed the validity of 13 published RMR predictive equations vs. RMR determined with an indirect calorimetry system of improved reliability (i.e. reference RMR). We also compared RMR predictive equations vs. uncorrected RMR.

Methods

Subjects

Sixty-nine participants living in Santiago, Chile were recruited by advertising (Table 1). They were all healthy, as determined by physical examination, past and current medical history, and routine blood tests including biochemical profiles, lipid profiles, thyroid-stimulating hormone, free thyroxine, electrolytes, creatinine, and hemogram. They had stable body weights (change <2 kg over the past 3 months) and none performed regular physical activity (<60 min/week) or took medication except oral contraceptives in some females (12 out of 40). The protocol was approved by the Ethical Board at Pontificia Universidad Católica de Chile, and participants provided written informed consent.

Table 1
Characteristics of the participants
 Mean±SD Range 
Male/female (n, [%]) 29/40 [42/58] 
Lean/overweight/obese (n, [%]) 34/25/10 [49/36/15] 
Age (years) 32.7±8.2 21.0–54.0 
Body mass (kg) 71.5±13.6 50.3–114.9 
Height (m) 1.67±0.08 1.54–1.85 
Body mass index (kg/m225.5±3.8 19.2–34.7 
 Mean±SD Range 
Male/female (n, [%]) 29/40 [42/58] 
Lean/overweight/obese (n, [%]) 34/25/10 [49/36/15] 
Age (years) 32.7±8.2 21.0–54.0 
Body mass (kg) 71.5±13.6 50.3–114.9 
Height (m) 1.67±0.08 1.54–1.85 
Body mass index (kg/m225.5±3.8 19.2–34.7 

Experimental design

Participants were instructed to avoid vigorous physical activity for the day preceding metabolic testing, and to maintain their customary dietary pattern. In addition, alcohol, tobacco and caffeine-containing drinks were not allowed for the 12 h before testing. On the testing day, overnight fasted participants arrived at the facility by public transportation. Upon arrival (∼8.00 a.m.), participants emptied their bladders and body weight was then determined, followed by insertion of a catheter into an antecubital peripheral vein, which was kept patent by a saline infusion (∼5 ml/h). Afterwards, they rested for 30 min in the supine position under thermoneutral (using a blanket as requested) and quiet conditions prior to RMR determination. VO2 and VCO2 were determined at 30-s intervals for 20 min, and only values from the last 10 min were considered for analysis. During RMR assessment (conducted between 8.45 and 9.30 a.m.), blood samples were drawn through the catheter at minutes 5 and 15 of initiated RMR determination. All measurements were conducted in Santiago, which is located at 570 meters above sea level.

Metabolic cart system

Gas exchange was determined using the same instrument during the entire study (VMax Encore 29n with canopy system; SensorMedics Co., Yorba Linda, CA). This instrument has an infrared CO2 analyzer (accuracy: ±0.02%; resolution: 0.01%) and electrochemical (galvanic fuel cell) sensor for O2 detection (accuracy: ±0.02%; resolution: 0.01%). Flow rate (measured by a mass flow sensor) was adjusted to maintain the fraction of expired CO2 between 0.5 and 1.0%; such a level is typically achieved with a flow rate of 25 to 35 l/min. The precision of the instrument calculated from experiments simulating VO2 and VCO2 through a N2/CO2 mixture infusion is 1.1% for VO2 and 1.2% for VCO2.

Gas-exchange analysis and correction procedure

On each testing day, the flow sensor was calibrated with a 3-L syringe, while gas analyzers were calibrated with standardized gases (16% O2/4% CO2 and 26% O2). After gas-exchange assessment, indirect calorimetry correction was performed using high-precision mass-flow regulators (series 358; 0–2 l/min; Analyt-MTC [Müllheim, Germany]), pure N2 (>99.999%) and pure CO2 (>99.9999%) as previously described [14]. Sufficient N2 and CO2 fluxes were infused into the hose until they matched the participant’s VO2 and VCO2. Then, corrected VO2 and VCO2 corresponded to values displayed for N2 flow (×0.2646) [18] and CO2 flow in the respective mass-flow regulators. Weir’s equation was used to determine the RMR from gas exchange which was expressed under conditions of standard temperature, pressure and humidity [19]:

 
formula

where RMR is measured in kcal/d, VO2 and VCO2 are measured in litres/day and Nu corresponds to urinary nitrogen excretion equivalent to 12 g/d. Within-subject variability (i.e. coefficient of variation) in RMR calculated from 20 determinations taken over the 10-min period was 7%. Room temperature was maintained at 23±1°C, and humidity ranged between 30% and 40%. The measured and corrected RMR was considered as the reference RMR.

Gas exchange simulation

On five separate days, gas exchange was simulated by infusing known fluxes of pure N2 (>99.999%) and pure CO2 (>99.9999%) through the high-precision mass-flow regulators. Pure N2 and CO2 were infused for 15 min at different flow rates to simulate respective VO2 and VCO2 values of 90 and 99 ml/min, 135 and 140 ml/min, 189 and 191 ml/min, 225 and 224 ml/min, 270 and 291 ml/min and 314 and 317 ml/min (at standard temperature, pressure and humidity). These flow rates simulated metabolic rates of 672, 993, 1328, 1636, 1995 and 2288 kcal/d respectively. Expected values were compared with observed metabolic rate values.

RMR predictive equations

Thirteen published predictive equations were arbitrarily selected for analysis. These equations are: WHO [3] as the conventionally accepted ones resulting from Schofield’s work; Oxford [2], which also considered Schofield’s dataset, but excluded Italian subjects while including individuals from the tropics; Harris–Benedict [20], a pioneering equation proposed in 1919; Mifflin [21], which was generated in North America as an alternative to Harris–Benedict equations; Livingston [22], which was intended to perform better by using proper scaling of body mass to predict RMR in North-American people; Frankenfield [23], also designed from North American people; ten Haaf [24], intended to predict RMR in healthy recreational athletes from North Europe; Weijs [6], intended to predict RMR in US and Dutch adults; Korth [25], generated from North European individuals; Müller [26] designed as an alternative to the WHO equations in modern, affluent German society; Lazzer [27] intended to predict RMR in severely obese Italian women; De Lorenzo [28], also for Italian individuals of different weight status; and de la Cruz [4], intended to predict RMR in the Spanish population. All these equations predict RMR from body weight, age and sex (the Lazzer equation considers only females). Height is also included in the equations proposed by Harris–Benedict, Mifflin, ten Haaf, Korth, Weijs and Lazzer. Table 2 shows sex distribution, body size, and age of the individuals included to generate each equation.

Table 2
Characteristics of the individuals included in each study for generating resting metabolic rate predictive equations
 n Males/females (%) Body mass (kg) Body mass index (kg/m2Age (years) 
 Mean±SD Range Mean±SD Range Mean±SD Range 
WHO 4726 75/25 Not reported Not reported Not reported 18–60 
Harris–Benedict 239 57/43 Not reported 25–124 Not reported Not reported 21–70 
Mifflin 498 51/49 79±17 46–143 27±5 17–42 46±14 19–78 
ten Haaf 90 59/41 70±10 53–100 22±2 18–27 23±5 18–35 
Korth 104 48/52 79±15 49–135 26±4 18–41 37±15 21–68 
Livingston 655 46/54 Not reported 33–278 Not reported Not reported 18–95 
Weijs 136 30/70 Not reported Not reported 25–40 Not reported 
Frankenfield 337 28/72 93* Not reported 33* Not reported 42* 18–85 
Lorenzo 320 40/60 77* 44–123 28* 19–40 36* 18–59 
Lazzer 182 0/100 114* Not reported 45* Not reported 44* 19–60 
Oxford 6528 59/41 59* Not reported 22* Not reported 29* Not reported 
Müller 1046 37/63 78.0±23.0 Not reported 27.1±7.7 Not reported 44.2±17.3 Not reported 
de la Cruz 95 47/53 64* Not reported 22* Not reported 42* 23–63 
 n Males/females (%) Body mass (kg) Body mass index (kg/m2Age (years) 
 Mean±SD Range Mean±SD Range Mean±SD Range 
WHO 4726 75/25 Not reported Not reported Not reported 18–60 
Harris–Benedict 239 57/43 Not reported 25–124 Not reported Not reported 21–70 
Mifflin 498 51/49 79±17 46–143 27±5 17–42 46±14 19–78 
ten Haaf 90 59/41 70±10 53–100 22±2 18–27 23±5 18–35 
Korth 104 48/52 79±15 49–135 26±4 18–41 37±15 21–68 
Livingston 655 46/54 Not reported 33–278 Not reported Not reported 18–95 
Weijs 136 30/70 Not reported Not reported 25–40 Not reported 
Frankenfield 337 28/72 93* Not reported 33* Not reported 42* 18–85 
Lorenzo 320 40/60 77* 44–123 28* 19–40 36* 18–59 
Lazzer 182 0/100 114* Not reported 45* Not reported 44* 19–60 
Oxford 6528 59/41 59* Not reported 22* Not reported 29* Not reported 
Müller 1046 37/63 78.0±23.0 Not reported 27.1±7.7 Not reported 44.2±17.3 Not reported 
de la Cruz 95 47/53 64* Not reported 22* Not reported 42* 23–63 

*Average calculated from data in the original article (it takes into account differences in sample size among groups).

Statistical analysis

Results are presented as means±SD. Bias (predicted−measured) in RMR was analyzed by Student’s t-test. Limits of agreement were calculated as

 
formula

Concordance between predicted and measured values was assessed by the Pearson correlation coefficient and Bland–Altman analyses. Slopes and intercepts of bias as a function of RMR were calculated by regression analysis, compared using covariance analysis, and tested for homoscedasticity. Repeated measures one-way ANOVA with Bonferroni post-hoc was used to analyze gas exchange simulation experiments. Analyses were performed using SAS version 9.2 (SAS Institute, Cary, NC, USA) or Prism 7.0c (GraphPad Software, La Jolla, CA, USA). The significance level was set at 5%.

Results

Bias in predicted vs. reference RMR

Considering predictive equations of RMR in males and females, average predicted RMR ranged between 1507 (Mifflin) and 1730 kcal/d (de la Cruz), while reference RMR was 1418±241 kcal/d. The average bias (predicted−reference RMR) for each equation displayed positive values, which fluctuated between 89 kcal/d (Mifflin) and 312 kcal/d (de la Cruz) (Table 3).

Table 3
Analysis of predicted vs. reference resting metabolic rate.
 Predicted RMR (kcal/d) Comparison vs. reference (measured and corrected) resting metabolic rate 
 Average bias (kcal/d)† Low absolute bias (% of subjects) Under-predicted (% of subjects) Over-predicted (% of subjects) Slope (kcal/d per 100 kcal/d) Intercept (kcal/d) 
WHO 1588±250 170±135* 56.5 1.4 42.0 4±7 109±106 
 (−101–441)      
Harris–Benedict 1590±233 172±126* 58.0 0.0 42.0 -3±7 221±102* 
 (−81–425)      
Mifflin 1507±226 89±131* 78.3 2.9 18.8 -7±7 186±105 
 (−174–352)      
ten Haaf 1680±254 262±138* 34.8 0.0 65.2 6±7 169±111 
 (−15–539)      
Korth 1656±283 238±162* 44.9 1.4 53.6 18±8* -38±119 
 (−87–563)      
Livingston 1526±218 108±130* 71.0 2.9 26.1 -11±7 263±106* 
 (−153–369)      
Weijs 1560±261 142±138* 59.4 1.4 39.1 8±7 26±110 
 (−135–419)      
Frankenfield 1526±226 108±129* 73.9 1.4 24.6 -7±7 208±104* 
 (−151–367)      
Lorenzo 1586±236 168±127* 55.1 1.4 43.5 -2±7 198±103 
 (−87–423)      
Lazzer 1407±126 117±115* 70.0 2.5 27.5 -20±14 393±195 
 (−114–348)      
Oxford 1538±244 120±128* 68.1 2.9 29.0 2±7 96±100 
 (−137–377)      
Muller 1552±231 134±129* 65.2 1.4 33.3 -4±7 197±104 
 (−125–393)      
de la Cruz 1730±254 312±143* 21.7 0.0 78.3 6±7 222±117 
 (25–599)      
 Predicted RMR (kcal/d) Comparison vs. reference (measured and corrected) resting metabolic rate 
 Average bias (kcal/d)† Low absolute bias (% of subjects) Under-predicted (% of subjects) Over-predicted (% of subjects) Slope (kcal/d per 100 kcal/d) Intercept (kcal/d) 
WHO 1588±250 170±135* 56.5 1.4 42.0 4±7 109±106 
 (−101–441)      
Harris–Benedict 1590±233 172±126* 58.0 0.0 42.0 -3±7 221±102* 
 (−81–425)      
Mifflin 1507±226 89±131* 78.3 2.9 18.8 -7±7 186±105 
 (−174–352)      
ten Haaf 1680±254 262±138* 34.8 0.0 65.2 6±7 169±111 
 (−15–539)      
Korth 1656±283 238±162* 44.9 1.4 53.6 18±8* -38±119 
 (−87–563)      
Livingston 1526±218 108±130* 71.0 2.9 26.1 -11±7 263±106* 
 (−153–369)      
Weijs 1560±261 142±138* 59.4 1.4 39.1 8±7 26±110 
 (−135–419)      
Frankenfield 1526±226 108±129* 73.9 1.4 24.6 -7±7 208±104* 
 (−151–367)      
Lorenzo 1586±236 168±127* 55.1 1.4 43.5 -2±7 198±103 
 (−87–423)      
Lazzer 1407±126 117±115* 70.0 2.5 27.5 -20±14 393±195 
 (−114–348)      
Oxford 1538±244 120±128* 68.1 2.9 29.0 2±7 96±100 
 (−137–377)      
Muller 1552±231 134±129* 65.2 1.4 33.3 -4±7 197±104 
 (−125–393)      
de la Cruz 1730±254 312±143* 21.7 0.0 78.3 6±7 222±117 
 (25–599)      

†Results are presented as means±SD (limits of agreement).

Average bias was calculated as predicted−measured RMR (kcal/d). Low absolute bias is an absolute difference between predicted − measured RMR equal or lower than 200 kcal/d. Under- and over-predicted correspond to percentage of individuals (out of 69 or 40 [Lazzer] individuals) having a bias <−200 or >200 kcal/d, respectively. Slopes and intercepts calculated from the regression between average RMR (between predicted and measured RMR in x axis) and the bias (predicted−reference RMR in y axis). A positive slope means that the higher the average RMR, the higher the bias.

*P<0.05 different from zero.

Proportion of individuals with under- and over-predicted RMR

Between 22% (de la Cruz) and 78% (Mifflin) of the individuals had an absolute bias (i.e. absolute difference in predicted−reference RMR) equal or lower than 200 kcal/d, an arbitrary cutoff. In most or all remaining individuals, equations over-predicted RMR (Table 3).

Correlation analysis of predicted vs. reference RMR

Associations between predicted and reference RMR were consistent across equations including males and females, with Pearson r-values between 0.82 and 0.86 (P<0.0001). The Lazzer equation (only for females) showed a weaker association (r=0.67; P<0.0001).

Concordance analysis of predicted vs. reference RMR

For each Bland–Altman plot (Figure 1), we calculated the slopes and intercepts of the regressions (Table 3). Slopes ranged between −20 (Lazzer) and 18 (Korth) kcal/d per each 100 kcal/d. Only Korth´s equation displayed a slope significantly different from zero when predicted vs. reference RMR were compared. Besides, intercept values higher than zero were observed for the Harris–Benedict, Livingston, and Frankenfield equations. Of note, data homoscedasticity was met for all equations.

Bland–Altman plots for comparison of predicted and reference resting metabolic rate

Figure 1
Bland–Altman plots for comparison of predicted and reference resting metabolic rate

Reference (measured and corrected) resting metabolic rate was compared to the resting metabolic rate estimated with the equations from (A) WHO, (B) Harris–Benedict, (C) Mifflin, (D) ten Haaf, (E) Korth, (F) Livingston, (G) Weijs, (H) Frankenfield, (I) Lorenzo, (J) Lazzer, (K) Oxford, (L) Müller, and (M) de la Cruz. Mean resting metabolic rate represents the average of predicted and reference resting metabolic rate (kcal/d).

Figure 1
Bland–Altman plots for comparison of predicted and reference resting metabolic rate

Reference (measured and corrected) resting metabolic rate was compared to the resting metabolic rate estimated with the equations from (A) WHO, (B) Harris–Benedict, (C) Mifflin, (D) ten Haaf, (E) Korth, (F) Livingston, (G) Weijs, (H) Frankenfield, (I) Lorenzo, (J) Lazzer, (K) Oxford, (L) Müller, and (M) de la Cruz. Mean resting metabolic rate represents the average of predicted and reference resting metabolic rate (kcal/d).

Comparative analysis of the validity of predictive equations

Three criteria were considered to identify equations with high validity (i.e. high concordance with reference RMR): (i) slope and (ii) intercept not different from zero in the regression from the Bland–Altman analysis, and (iii) at least 75% of individuals with an absolute bias equal or lower than 200 kcal/d. Only the Mifflin equation met all three criteria, while the WHO, Oxford, de la Cruz, ten Haaf, Weijs, Müller, Lorenzo and Lazzer equations met the first two criteria (Table 4).

Table 4
Criteria to establish validity of predictive equations based on the reference resting metabolic rate
 Slope equal to zero Intercept equal to zero ≥75% 
WHO Yes Yes No 
Harris–Benedict Yes No No 
Mifflin Yes Yes Yes 
ten Haaf Yes Yes No 
Korth No Yes No 
Livingston Yes No No 
Weijs Yes Yes No 
Frankenfield Yes No No 
Lorenzo Yes Yes No 
Lazzer Yes Yes No 
Oxford Yes Yes No 
Muller Yes Yes No 
de la Cruz Yes Yes No 
 Slope equal to zero Intercept equal to zero ≥75% 
WHO Yes Yes No 
Harris–Benedict Yes No No 
Mifflin Yes Yes Yes 
ten Haaf Yes Yes No 
Korth No Yes No 
Livingston Yes No No 
Weijs Yes Yes No 
Frankenfield Yes No No 
Lorenzo Yes Yes No 
Lazzer Yes Yes No 
Oxford Yes Yes No 
Muller Yes Yes No 
de la Cruz Yes Yes No 

Slopes and intercepts calculated from the regression between average RMR (between predicted and reference RMR in x axis) and the bias (predicted−reference RMR [kcal/d] in the y axis). *At least 75% of individuals with an absolute difference between predicted−reference RMR equal or lower than 200 kcal/d.

Further analyses compared the concordance of four selected equations vs. the reference RMR by grouping individuals by sex and weight status. Selected equations were the Mifflin, Oxford and Müller ones, as these have with the highest validity (based on the percentage of subjects with low absolute bias [>60%], and the analysis of slopes/intercepts). It is worth mentioning that Lazzer´s equation was not included despite having high concordance with the reference RMR, because this equation only considered severely obese females. In turn, we included the WHO equation because it is the one conventionally accepted as valid. Supplementary Table 1 summarizes the results. Regarding sex, in males, only the Oxford equation showed a slope not different from zero, whereas a positive intercept was observed across the four equations. In females, the WHO and Oxford equations displayed slopes and intercepts not different from zero. Regarding weight status, individuals were separated in lean (BMI<25 kg/m2) and overweight/obese (BMI>25 kg/m2), and all equations showed slopes and intercepts not different from zero.

Concordance analysis of predicted vs. measured but uncorrected RMR

The same analyses comparing predicted vs. reference RMR were repeated comparing predicted vs. measured but uncorrected RMR (Supplementary Table 2). Briefly, when Bland–Altman plots were considered (not shown), eight out of 13 equations had a negative slope, while 11 out of 13 displayed an intercept different from zero. Homoscedasticity was met for all equations.

Comparison of simulated vs. measured metabolic rate

In simulation experiments, the average metabolic rate measured was higher than expected (197±32 kcal/d, P<0.0001). The extent of overestimation increased linearly up to a simulation of 1636 kcal/d, and then leveled off (Figure 2A). Expressed as a percentage, the average metabolic rate measured was 13.8±1.8% higher than expected (P<0.0001). This percentage of overestimation was constant along the range of simulated metabolic rates (Figure 2B).

Bias at different simulated metabolic rates

Figure 2
Bias at different simulated metabolic rates

Results are presented as (A) absolute values in kcal/d, and as (B) relative values as percentage. *P<0.05, **P<0.01 vs. the immediately lower simulated metabolic rate (Bonferroni post-hoc test). RM, repeated measures.

Figure 2
Bias at different simulated metabolic rates

Results are presented as (A) absolute values in kcal/d, and as (B) relative values as percentage. *P<0.05, **P<0.01 vs. the immediately lower simulated metabolic rate (Bonferroni post-hoc test). RM, repeated measures.

Discussion

We applied an indirect calorimetry procedure of enhanced accuracy to search for RMR predictive equations of high validity for healthy adult humans. On average, all tested equations showed RMR values higher than the reference RMR. This pattern is in contrast with an earlier report [5] that found similar or lower predicted vs. (uncorrected) measured RMR. Such a discrepancy may be attributed to the fact that gas-exchange correction determined a decrease in RMR relative to uncorrected measured RMR. Indeed, several equations predicted RMR at a similar extent (on average) when compared with uncorrected RMR.

In addition to using the average RMR to assess concordance of predictive equations with the reference RMR, here we used a stronger approach, i.e. regression analysis of Bland–Altman plots. It is of note that bias (i.e. predicted−reference RMR in kcal/d) was constant across the whole the span of RMR in all equations, except Korth’s. Such constant bias (i.e. slope not different from zero) is not commonly observed when gas-exchange correction is not conducted [5–7], and coincidently, was not observed with our uncorrected RMR data. Thus, it has been often reported that measured (uncorrected) RMR becomes higher than its prediction as RMR increases [5,7]. Such loss of predictive power in individuals with high RMR has been attributed to inter-individual differences in organ size as fat-free mass increases [5]. However, we claim that such error may be analytical. In our simulation experiments, we noted that by augmenting simulated metabolic rates, the bias (i.e. measured−simulated RMR in kcal/d) constantly increased up to a certain limit. Therefore, one can anticipate that prediction equations will underestimate measured RMR to a greater extent in individuals with high RMR. Importantly, when gas-exchange correction was conducted, this effect was removed (slopes not different from zero). Thus, regression analyses of Bland–Altman plots showed that 12 equations had a constant bias across RMR, but the bias was not different from zero for nine of them. The Mifflin, Oxford and Müller equations showed the highest proportion of individuals from both gender and broad weight status with a small absolute difference (≤200 kcal/d) between predicted and reference RMR.

It is interesting to identify which factors determine the validity of those equations. Notably, those equations were derived from RMR measured using metabolic carts that were not subjected to correction protocols. Perhaps those metabolic carts did not require correction because their accuracy was high enough. Alternatively, those metabolic carts did require gas-exchange correction, and the high concordance we observed between reference and predicted RMR was merely coincidental. Large sample sizes should minimize any influence of insufficient accuracy in RMR determination. That factor could thus enhance the validity of the Mifflin, Oxford and Müller equations, which included at least 500 individuals for their generation. Still, the WHO and Livingston equations also included large sample sizes though their validity was not high enough. Other factors such as the subject’s characteristics (e.g. weight status, sex and age) may therefore play a role. However, differences in average and range values, or sex distribution, between our participants and those of each study do not seem to discriminate equations with low or high validity.

RMR equations have shown differential predictive power according to ethnicity. In general, these studies concluded that predictive equations overestimate measured (uncorrected) RMR [11,29–31]. In our study, despite the selected equations being mostly developed in the Caucasian population, many of them performed fairly well in our admixed Chilean population when the reference RMR was considered. The design of the Oxford equations included individuals from Central America, who may be closer to Chilean genetic structure [32]. Whether this situation explains why we observed the highest validity for the Oxford equations is uncertain. The Mifflin and Müller equations, which did not include Hispanic/Latin American individuals, also reached high validity. Thus, to what extent phenotypic/genotypic similarities and differences between our participants and original populations account for validity of each equation is speculative.

Separate analyses of validity according to sex and weight status were conducted for the Mifflin, Oxford, Müller, and WHO equations. In males, none of these equations showed high concordance against the reference RMR. Only the Oxford equations displayed non-significant bias as a function of RMR, whereas a positive intercept was noted. In females, the predicted RMR was well approached by the Oxford and WHO equations. All these equations showed high concordance in lean and overweight/obese individuals. Weight status and/or body composition would therefore not account for the different validity observed by sex. In fact, the Lazzer equation, which was developed in severely obese females, showed similar statistical concordance with the reference RMR as other equations coming from normal-weight women.

Our findings suggest that the conventionally accepted equation (i.e. WHO) has superiority relative to several equations; however, it performs worse than the Mifflin, Oxford or Müller equations. From these three equations, Mifflin had a better validity when the whole group was considered. However, the Oxford equations appear to be a better option considering its concordance for sex, particularly in males. The Oxford equations were generated from re-analysis of the original work of Schofield. This re-analysis excluded Italian individuals as they showed high RMR probably due to different lifestyle and body composition. Additionally, individuals from tropics (whom tend to have lower RMR) were included in the re-analysis. Taken together, Oxford equations yield RMR values comparatively lower than WHO equation in adult individuals [2]. Such findings confirmed that predicting RMR with WHO equations overestimates measured RMR across different populations [2,26]. It is worth emphasizing that our selection of the Mifflin, Oxford or Müller equations as those of highest validity is based on the comparison with the reference RMR, i.e. measured and corrected. In contrast, none of those equations would have been selected based on analysis of measured and uncorrected RMR. Indeed, Weijs, Korth and ten Haaf equations showed highest concordance when compared against measured and uncorrected RMR.

Additional factors related to the determination of RMR by indirect calorimetry may also contribute to the lack of validity of certain equations. Firstly, the equation used to express metabolic rate in kcal/d from gas exchange. The Weir equation is the most often used while the Brouwer and Consolazio equations are less commonly utilized [19]. It is not common practice to report which equation was used. At similar gas exchange and urinary nitrogen content, these equations can yield differences up to 60 kcal/d. Secondly, the magnitude of protein oxidation (i.e. urinary nitrogen excretion) considered for calculating 24-h RMR. Because RMR is measured for less than 30 min, taking or not into account protein oxidation will have a negligible influence on RMR over that period (≤1 kcal/h). However, given that RMR is often expressed for 24 hours, assuming zero protein oxidation (certainly wrong) will overestimate RMR by ∼30 kcal/d. Again, it is not routinely reported whether urinary nitrogen excretion was considered for calculating RMR. We here used the Weir equation and considered a fixed protein oxidation of 75 g/d (equivalent to 12 g of urinary nitrogen), a value rather acceptable for individuals included in our study. Finally, in our study we cannot neglect the potential influence of blood sampling during gas exchange analysis on RMR, which can alter respiratory pattern, and increase arousal of participants. In any case, such influence seems minor considering that observed within-subject variability in RMR over the 10-min period was 7%, a value considered to be acceptable [33].

In conclusion, predicting RMR is widely used at an individual and global level. For instance, governmental and non-governmental organizations responsible for providing food at the population level must estimate energy requirements from RMR. The high prevalence of obesity across lifespan, which appears to keep increasing, prompts the appropriate determination of energy requirements as a first step to prevent exacerbated energy balance. Our findings suggest that when compared with the reference RMR (measured and corrected), three equations have superior validity, i.e. Mifflin, Oxford and Müller. From those equations, only Oxford showed superiority to predict RMR in males. Therefore, we support Oxford equations as a valid alternative to predict RMR in healthy adults. We also encourage the analysis of gas exchange accuracy for reliable assessment of RMR.

Author Contribution

J.E.G. designed the research and supervised human experiments. J.E.G., M.A.C., C.P.L. and R.F.V. analyzed the data. J.E.G. wrote the paper and has primary responsibility for final content. All authors read, edited and approved the final manuscript.

Competing Interests

The authors declare that there are no competing interests associated with this manuscript.

Funding

This work was funded by FONDECYT-Chile [grants 1130217 and 1170117]. M.A.C. is supported by a PhD fellowship from Pontificia Universidad Católica de Chile.

Abbreviations

     
  • BMI

    body mass index

  •  
  • RMR

    resting metabolic rate

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Supplementary data