## Statistical Background and Definitions (2019)

**Definitions: **

Basal metabolic rate (BMR) and basal energy expenditure (BEE) are the same and **resting metabolic rate (RMR)** and resting energy expenditure (REE) are the same. However, there is a small difference between basal and resting. The terms BMR and BEE are interchangeable, and the terms **RMR **and REE are interchangeable, but the terms basal and resting are not. BMR is the metabolic rate of the body at absolute rest defined as fasted overnight and awake but measured within 30 minutes of awakening in the morning without movement prior to measurement. **RMR** is the metabolic rate of the body at relative rest defined as fasted for at least 4 hours and awake, preferably but not necessarily in the morning and without the requirement for no movement in the hours prior to measurement. A rest recovery period is required immediately before the test. A measurement of **RMR **allows for dressing and traveling to the test site whereas a BMR measurement usually involves an overnight stay at the test site. BMR is slightly lower than **RMR**. In critically ill patients, the fasting requirement is waived because feedings are usually continuous rather than intermittent.

Total metabolic rate (TMR), also called **total energy expenditure (TEE)** is the sum total of all energy expended by the body in 24 hours (basal metabolic rate, thermic effect of feeding and movement/activity).

**Statistical Background **

Bias and accuracy are qualitative terms whose definitions can vary slightly depending on their application. Most applications of these concepts relate to epidemiology or to the comparison of measurement techniques against a gold standard. The application in the current review is to compare a mathematical calculation (not a measurement) to a measurement considered to be a gold standard. As such, we need to define bias and accuracy as used in the current review.

Bias will be defined as a significant tendency for the predicted value to underestimate or overestimate the measured value. An unbiased predictive equation is one in which the differences between the estimated and measured value does not trend in either direction. The **preferred** statistical definition of bias is either a 95% confidence interval of the difference between the two values to exclude zero, or the mean difference between the two values to be significantly different from zero. A **less preferred** statistical definition is a simple statistically significant difference between the mean predicted value and the mean measured value. When this is the only bias indicator available in the source papers, the prediction method will be labeled as **probably **biased.

Accuracy will be defined as the percentage of predicted values falling within ±10% of the measured value. Although this may be the most clinically relevant measure of validity, it is limited by the fact that the threshold for declaring a prediction method valid is up to the individual user of the information. Another small limitation is that the selection of a 10% threshold is somewhat arbitrary. However, given that day-to-day biological and instrument variation in measurements of RMR can be 3-5%, a 10% threshold for accuracy of a predictive equation seems reasonable, and in fact this threshold has been used at least since the 1920’s in this type of validation work.

Of special note, Bland Altman statistics have become among the most common validity tests in this field of work and therefore should be explained. A Bland Altman plot compares the **difference **between two quantities (on the y-axis) against the **mean** of the two quantities on the x-axis. The reason for comparing to the mean of the two quantities rather than the one quantity considered the gold standard is that sometimes the gold standard is in error and the alternate quantity is true (this seems highly unlikely in the scenario of the current work in which the alternate quantity is a calculation and not a measurement). Three pieces of information can be produced from a Bland Altman plot:

- Mean difference between the two quantities, which can be tested for being significantly different from zero and if so, be labeled fixed bias (underestimation or over estimation). Not all authors report the mean difference and even fewer test the difference inferentially.
- Correlation of the difference between the two quantities against the mean of the two quantities. If there is a linear relationship present, proportional bias is said to exist. Again, not all authors report if this correlation exists, but it is sometimes visually obvious in a Bland Altman plot.
- Calculation of the value 1.96 standard deviations above the mean difference and 1.96 standard deviations below the mean difference. This is an indicator of the degree of variation around the means of the two quantities and is labeled Limit of Agreement (LOA). The LOA should capture 95% of all the differences observed between the two quantities being compared, and the lower the LOA the better. A limitation of the LOA is that an inferential test statistic does not exist to determine if the LOA is within an acceptable range. This is completely a judgement on the part of the reader. The standard applied for this project for an acceptable LOA is 25% of mean RMR. This range is based on two studies of predictive equations in healthy people.

**References**

Ludbrook J. Comparing methods of measurement. Clin Exp Pharm Physiol 1997; 24: 193-203.

Walther BA, Moore JL. The concepts of bias, precision, and accuracy, and their use in testing the performance of species richness estimators, with a literature review of estimator performance. *Ecography.* 2005; 28: 815-829.

Boothby WM, Sandiford I. Summary of the basal metabolism data on 8,614 subjects with especial reference to the normal standards for the estimation of the basal metabolic rate. *J Biol Chem *1922; 54: 783-803.

Krouwer JS. Why Bland Altman plots should use X, not (Y+X)/2 when X is a reference method.* Stat Med. *2008; 27: 778-780.

Weijs PJM. 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.

Frankenfield DC. Bias and accuracy of resting metabolic rate equations in non-obese and obese adults. *Clin Nutr. *2013; 32: 976-982.