Accuracy of Calculated Metabolic Rate in Athletes: Best and Worst Equations are +3% to -17% Off Measured RMR | Plus: Spreadsheet to Calculate Your RMR With Each Equation

Wouldn't it be cool if you could simply plug your computer into a USB-slot at the back of your head to read out your energy status...? Ah, no, it wouldn't! It's already scary enough how much Fitbit, Garmin, and co know about us.

This is by no means the only problem with metabolic research, these days, but it's one that's really getting on my (and probably also your) nerves. It's all about the sick and obese. It is thus no wonder that you will easily find papers that assess how the Nelson, Mifflin, Harris-Benedict and other equations that are commonly used are off wrt the real energy requirements of the average obese type II diabetic. What you'll be hard-pressed to find, though, is data on their accuracy in athletes.

I have addressed this issue before, but with the publication of a recent paper in the Journal of Strength and Conditioning Research there's now more data available than from all the previous studies I've seen.
The purpose of the study was to determine the accuracy of five different resting metabolic rate (RMR) prediction equations in male and female athletes.

• Nelson Equation (cf. Nelson 1991) -- RMR (kcal/day) = 25.80 x Fat-Free mass(kg) + 4.04 x Fat mass(kg)
• Mifflin-St. Jeor Equation (cf. Bullough 1995) -- RMR (kcal/day) = 9.99 x weight(kg) + 6.25 x height(cm) - 4.92 x age + 166 x Sex (males, 1; females, 0) -161 
• Harris-Benedict Equation (cf. Brožek 1963) -- revised equation for men RMR (kcal/day) = 66.47+ 13.75 x Weight(kg) + 5 x Height(cm) – 6.76 x Age(yrs.); for women RMR (kcal/day) = 655.1 + 9.56 x Weight(kg) + 1.85 x Height(cm) – 4.68 x Age(yrs.)
• De Lorenzo Equation (cf. Carpenter 1995) -- RMR (kcal/day) = -857 + 9 x Weight(kg) + 11.7 x Height(cm) 
• Cunningham Equation (cf. Cunningham 1980) -- RMR (kcal/day) = 500 + 22 x Fat-Free mass(kg)

Twenty-two female (19.7± 1.4 yrs.; 166.2 ± 5.5 cm; 63.5 ± 7.3 kg; 49.2 ± 4.3 kg of Fat-Free Mass; 23.4 ± 4.4 BF%) and twenty-eight male (20.2 ± 1.6 yrs.; 181.9 ± 6.1 cm; 94.5 ± 16.2 kg; 79.1 ± 7.2 kg of FFM; 15.1 ± 8.5% BF) athletes were recruited to participate in one day of metabolic testing.

"Assessments comprised RMR measurements via indirect calorimetry and body composition analyses via air displacement plethysmography. One-way repeated measures analysis of variance with follow up paired t-tests were selected to determine differences between indirect calorimetry and five RMR prediction equations. Linear regression analysis was used to assess the accuracy of each RMR prediction method. An alpha level of p < 0.05 was used to determine statistical significance" (Jagim 2017). 

What Andrew R. Jagim and colleagues found is in contrast to what studies in the non-athletic population show (Woolf 2015; Namazi 2016; Willis 2016), which tend to show both, over- and underestimations, depending on the equation that was used.

Figure 1: Measured (bottom) and calculated RMR in men (orange) and women (blue) - the percentages next to the bars are the relative differences between the respective calculation and the actual measurement (Jagim 2017).

In the study at hand, however, "[a]ll of the prediction equations significantly underestimated RMR". Moreover, the scientists found that...

Click image to open spreadsheet to calculate your RMR; obviously, you will have to change the data at the top

• the Cunningham equation had the smallest mean difference (-165 kcals); 
• in males, the Harris-Benedict equation was found to be the best prediction formula with the lowest root mean square prediction error (RMSPE) value of 284 kcals;
• in females, the Cunningham equation was found to be the best prediction equation with the lowest RMSE value of 110 kcals. 

In view of the fact that all of these equations "consistently [...] underestimate[d] RMR in male" athletes and tends to do the same in female athletes, you should exercise caution when you're using them on yourself or clients...

Figure 2: The relationships between constant error (actual – predicted RMR) and average RMR ((measured + predicted)/2) for males (A) (n = 28) and females (B) (n = 21) in the current sample of athletes. The solid line represents mean of constant error. Dashed lines represent ± 1.96 SD of constant error. RMR = resting metabolic rate. *P < 0.05 (Jagim 2017).

...get suspicious if they don't gain in a planned caloric surplus, it could be the way you calculated the energy needs that is messing with the results. And keep in mind: Figure 2 tells you that individuality is still key - eventually, food logging and extrapolating from that will thus always be the most reliable way to estimate the actual energy requirements of an individual.
References:

• Brožek, Josef, et al. "Densitometric analysis of body composition: revision of some quantitative assumptions." Annals of the New York Academy of Sciences 110.1 (1963): 113-140.
• Buchholz, Andrea C., Mahroukh Rafii, and Paul B. Pencharz. "Is resting metabolic rate different between men and women?." British Journal of Nutrition 86.6 (2001): 641-646.
• Bullough, Richard C., et al. "Interaction of acute changes in exercise energy expenditure and energy intake on resting metabolic rate." The American journal of clinical nutrition 61.3 (1995): 473-481.
• Cunningham, John J. "A reanalysis of the factors influencing basal metabolic rate in normal adults." The American journal of clinical nutrition 33.11 (1980): 2372-2374.
• Jagim, Andrew R., et al. "The accuracy of resting metabolic rate prediction equations in athletes." The Journal of Strength & Conditioning Research (2017).
• Namazi, Nazli, et al. "Accuracy of the common predictive equations for estimating resting energy expenditure among normal and overweight girl university students." Journal of the American College of Nutrition 35.2 (2016): 136-142.
• Nelson, Karl M., et al. "Prediction of resting energy expenditure from fat-free mass and fat mass." The American journal of clinical nutrition 56.5 (1992): 848-856.
• Willis, Erik A., et al. "Predicting resting energy expenditure in young adults." Obesity research & clinical practice 10.3 (2016): 304-314.