Harris-Benedict Equation and Resting Energy Expenditure Estimates in Critically Ill Ventilator Patients

This observational transversal study conducted at the adult ICU of the University Hospital of Ribeirão Preto Medical School, University of São Paulo, from February 2011 to June 2012 and from April 2013 to November 2013. All the patients and/or relatives agreed to participate in the study and signed a written informed consent, approved by the research ethics committee (process number 8227/2011).

The sample comprised 205 patients (115 men, 56.1%; 90 women, 43.9%) admitted to the ICU, receiving mechanical ventilation, with a fraction of inspired oxygen less than 0.6 within the first 48 hours of admission. Patients with air leak, aerial fistula, very high positive end-expiratory pressure, or brain death and patients who did not provide the signed informed consent were excluded.

The patients underwent indirect calorimetry on a portable calorimeter DELTATRAC II Metabolic Monitor (Datex-Ohmeda) for 30 minutes in stable condition in a calm environment, with no manipulation of the upper airways or of the ventilator settings for at least 30 minutes. Gas exchange measurements should be enough to ensure correct interpretation of the results obtained, avoiding periods of unstable conditions, such as alterations of settings on the mechanical ventilator and tracheal aspiration.⁹  In this context, we considered that the steady state is often defined as 5 consecutive minutes during which oxygen consumption and carbon dioxide production vary by ±10% as validated previously.¹⁷  The protocol was initiated after the DELTATRAC II equipment had warmed up for 30 minutes. The gas and pressure had been calibrated according to the manufacturer’s instructions. All the patients were undergoing mechanical ventilation via multiprocessed ventilators (Savina or Evita XL, Drägermedical).

During the first 48 hours of admission to the ICU, REE was calculated with the HB equation; 3 different sources of body weight were employed: body weight determined by bed scale, ideal body weight, and predicted body weight.

The versions of the HB equation for men and women are as follows, with W equal to weight in kilograms, H the height in centimeters, and A the age in years: 66.47 + (13.75 × W) + (5 × H) − (6.75 × A) for men and 665.1 + (9.563 × W) + (1.85 × H) − (4.676 × A) for women. The ideal body weight was calculated from the height in meters: 22.5 × H²  for men and 21.5 × H²  for women. Predicted body weight was calculated from the height in centimeters: 50 + 0.91 (H − 152.4) for men and 45.5 + 0.91 (H − 152.4) for women.

After these data were obtained, the sample was divided according to the following criteria: age, sex, and BMI. In all the groups, the values achieved by using the HB equation (REE_HB1, REE_HB2, and REE_HB3) were compared with values for REE_IC. Stratification by age afforded 3 groups: 18 to 30 years, 31 to 60 years, and more than 60 years old. For BMI, 5 groups were formed on the basis of the World Health Organization’s BMI table: less than 18.5, 18.5 to 24.9, 25.0 to 29.9, 30.0 to 39.9, and 40 or greater.

The study population was also divided into 3 subgroups, according to REE_IC: less than 1200 kcal/d, 1200–1800 kcal/d, and greater than 1800 kcal/d. The REE_IC obtained for these subgroups was compared with REE_HB1, REE_HB2, and REE_HB3. Because the group REE_HB1 was the only group that provided slightly better agreement with REE_IC, it was subdivided to investigate whether this trend would remain in the subgroups.

Data distribution was evaluated by D’Agostino Pearson, Kolmogorov-Smirnov, and Shapiro-Wilk normality tests. Considering that the distribution of all variables was nonparametric, the Wilcoxon test was used at a significance level lower than .05 (P < .05). Data for all the variables are presented as the median (minimum-maximum).

After this analysis, the data were compared by the Bland-Altman method,^18,19  which allowed us to describe the agreement between 2 quantitative measurements obtained by different methods. The Bland-Altman method is used to analyze the difference between 2 paired measurements with respect to the mean of 2 measurements. For better agreement, it is recommended that 95% of the data be included in ±1.96 SD of the mean of the difference and that the bias be close to zero. Analyses of limits of agreement were conducted for each predictive equation, stratified for sex, age, and BMI, to identify the different levels of agreement between these individual groups.

All the analyses were conducted with the aid of MedCalc Statistical Software Version 12.2.

The sample comprised 205 critically ill patients (115 men and 90 women) undergoing mechanical ventilation, with a median age of 57 (18–89) years, median weight of 71 (29–131) kg, and median height of 165 (145–188) cm. The median score on the Acute Physiology and Chronic Health Evaluation II²⁰  was 24 (4–47), and the median death risk was 53% (4%–98%). Diagnoses of sepsis (n = 90, 43.9%) and pneumonia (n = 55, 26.8%) predominated in this population (Table 1). Of the 205 evaluated patients, 120 (58.5%) were discharged from the ICU and 85 (41.5%) died.

Considering all the variables (sex, age, and BMI), comparison between REE_IC and REE_HB by the nonparametric Wilcoxon test did not reveal any differences between REE_IC and REE_HB1. The exception was the group of patients aged between 18 and 30 years—in this group, the difference between REE_IC and REE_HB1 was significant (P = .02). All the groups showed a significant difference (P < .05) between REE_IC and REE_HB2 and REE_HB3, except for the group of patients aged between 18 and 30 years (P = .24 for REE_HB2; P = .24 for REE_HB3) and the group of patients with a BMI between 18.5 and 24.9 (P = .90 for REE_HB2; P = .86 for REE_HB3).

Subdivision of the population into 3 groups on the basis of REE_IC (REE_IC < 1200 kcal/d, REE_IC between 1200 and 1800 kcal/d, and REE_IC >1800 kcal/d) showed that, compared with indirect calorimetry, the HB equation overestimated REE for most of the patients in the group with an REEIC less than 1200 kcal/d (n = 51, 96%). In the group with an REEIC greater than 1800 kcal/d (n = 32, 82%), the HB equation underestimated REE for most patients. Finally, in the group with an REEIC between 1200 and 1800 kcal/d, overestimation and underestimation also occurred, but the difference between REE_IC and REE_HB was no greater than 10%, the lowest among the 3 REE_IC groups. Figures 1 and 2 illustrate the aforementioned subgroups.

The median REE_IC was 1430 (540–2420) kcal/d, whereas the median REE_HB1, REE_HB2, and REE_HB3 were 1463 (873–2486) kcal/d, 1325 (911–1877) kcal/d, and 1313 (869–1917) kcal/d, respectively.

The differences between the median REE_IC and the median REE_HB1, REE_HB2, and REE_HB3 were −33 (2.3%), 105 (7.34%), and 117 (8.18%) kcal/d, respectively. If the median REE_IC (reference standard) is considered as 100%, the median REE_HB2 and REE_HB3 were approximately 92% of the median REE_IC.

According to the Bland-Altman analysis, REE_HB2 and REE_HB3 did not agree well with REE_IC; the limits of agreement varied between +796.1 kcal/d and −559.6 kcal/d for REE_HB2 and between +809.2 kcal/d and −564.7 kcal/d for REE_HB3 (Figure 3). Considering the studied population (n = 205), REE_IC and REE_HB1 agreed the best: the bias was −18.8 kcal/d, which was the value closest to 0. Nevertheless, REE_HB1 was still overestimated by +555.3 kcal/d and underestimated by −593.0 kcal/d.

Comparison of the results for the subgroups stratified according to sex, age, and BMI demonstrated that, in the case of stratification by sex, REE_IC and REE_HB1 agreed better.

Stratification of the study population into 3 subgroups according to age—between 18 and 30 years (12.68%), between 31 and 60 years (45.37%), and more than 60 years (41.95%)— showed that agreement between REE_IC and REE_HB1 was better for patients aged between 31 and 60 years, with bias of 8.5 kcal/d. With respect to the limits of agreement, patients aged between 18 and 30 years presented positive values of +403.3, +559.9, and +582.2 kcal/d, and negative values of −691.2, −736.8, and −751.7 kcal/d for comparison of REE_IC with REE_HB1, REE_HB2, and REE_HB3, respectively. Patients aged between 31 and 60 years displayed positive limits of agreement of 608.2, 839.8, and 849.2 kcal/d, and negative limits of agreement of 591.2, 515.5, and 521.1 kcal/d for comparison of REE_IC with REE_HB1, REE_HB2, and REE_HB3, respectively. Patients more than 60 years old had positive limits of agreement of 529.8, 783.5, and 796.9 kcal/d and negative limits of agreement of 550.9, 516.9, and 519.7 kcal/d for comparison of REE_IC with REE_HB1, REE_HB2, and REE_HB3, respectively.

The population was distributed into 5 subgroups with respect to BMI: 5.4% (n = 11) with BMI less than 18.5, 42.0% (n = 86) with a BMI of 18.5 to 24.9, 28.3% (n = 58) with a BMI of 25.0 to 29.9, 21.5% (n = 44) with a BMI of 30 to 39.9, and 2.9% (n = 6) with a BMI of 40 or greater. REE_IC and REE_HB agreed better in the subgroup with a BMI of 18.5 to 24.9 (eutrophic), with bias of −3.9 kcal/d for REE_HB2, −4.7 kcal/d for REE_HB1, and −4.9 kcal/d for REE_HB3). For the eutrophic patients, the positive limits of agreement were 561.8, 573.7, and 579.7 kcal/d and the negative limits of agreement were 570.9, 581.6, and 589.1 kcal/d for comparison of REE_IC with REE_HB1, REE_HB2, and REE_HB3, respectively. With regard to BMI, analysis of all the limits of agreement for the studied population evidenced overestimation of values within the range of +287.2 to +1138.8 kcal/d, and underestimation within the range of −75.7 to −909.5 kcal/d (Tables 2 and 3).

A review of the literature clearly shows that most studies adopt indirect calorimetry, and not predictive equations, as the most accurate method for measuring REE.^21–24  Many researchers have stated that the difficulty in measuring REE accurately often culminates in inadequate nutritional intervention; that is, the daily calorie requirement is either underestimated or overestimated.^24,25  Provision of insufficient energy to critically ill patients can result in loss of muscle mass and significant elimination of nitrogen in the urine, which rapidly deteriorates the patient’s health and nutritional status. On the other hand, the excessive provision can result in other situations, such as hypercapnia and infectious complications.

In 2013, McClave et al²⁶  published a review in which they compared REE_IC with REE calculated via predictive equations. Those authors verified that the equations were not very accurate, especially with respect to the variable BMI, and that the corresponding results were inadequate to calculate nutritional support in critically ill patients. In the present work, comparison between REE_IC and REE_HB calculated on the basis of different sources of body weight also revealed underestimated and overestimated REE in all the evaluated groups for the variables sex, age, and BMI.

Frankenfield et al²⁷  conducted a validation study to compare REE_IC with REE calculated by using predictive equations. That study involved 202 critically ill patients undergoing mechanical ventilation who had received a diagnosis of traumatic injury, had undergone surgery, or were clinical patients. The patients were subdivided into groups according to age (< 60 years and ≥ 60 years) and BMI (< 30 and ≥ 30). The authors evaluated 17 equations. The HB equation furnished accuracy of 34% for all the groups; the accuracy was 46% when the authors used the correction factor HB × 1.25. The Penn State equation afforded the best accuracy: 67% in all the groups and 77% in the elderly with BMI less than 30.

Compared with any other equation, the HB equation has been the most frequent object of validation studies. Since the original work of Harris and Benedict, approximately 138 formulas have been published by 40 different authors, all based on different sources of body weight.^11–14,28 

Although the HB equation is accurate for predicting the energy requirements within a healthy population, it is not as reliable for critically ill patients.^{14,25,29–32}  In fact, REE_IC and REE_HB did not agree well in the population investigated herein. Application of the Wilcoxon test to compare REE_IC with REE_HB1 did not reveal any significant differences for most of the population; however, it is worth noting that this test compares median values, which might constitute a limitation when one compares the extremes of a group. This limitation became evident when we divided the population into 3 groups according to REE_IC: the extreme REE_IC values disagreed with REE_HB1 the most, with underestimated REE in the group with an REE_IC less than 1200 kcal/d and overestimated REE in the group with REE_IC greater than 1800 kcal/d. The difference persisted in the intermediate REE_IC group (between 1200 and 1800 kcal/d), but it was smaller than in the other 2 groups.

In an effort to explain this discrepancy, another relevant aspect to consider is the fact that the HB equation does not take clinical variables that could also interfere in metabolism into account; for example, fever and use of vasoactive drugs or sedation, which could increase or decrease REE, respectively. Additionally, acute diseases, which were the main issue in our population, are known to elevate REE. Together, these aspects could explain why the HB equation does not reflect REE reliably.

Researchers in countless studies agree that indirect calorimetry is the reference standard method for measuring REE in critically ill patients. Nevertheless, most ICUs do not have this equipment, which is expensive and requires skilled staff for its operation. Certainly the cost to the patient when the actual caloric needs are not precisely calculated is high, translating into damage such as decreased immunity and its consequences, such as the occurrence of infectious diseases, worsening the prognosis and prolonging the hospital stay, also increasing the costs to the health system. Unfortunately, no cost-effectiveness studies have been done to compare indirect calorimetry with other methods, and such studies are essential to get an idea of the budget impact for patients, their families, and the hospital of using indirect calorimetry versus other methods to calculate energy demand in critically ill patients. Fortunately, technological advances have enabled the development of more compact and less costly calorimeters coupled to mechanical ventilators, which facilitates their routine use. This convenience may aid widespread use of this method among health professionals, especially those who work in ICUs.

The present study demonstrated the poor accuracy of the HB equation for calculating REE in our sample. Agreement between REE_IC and REE_HB1 evidenced a bias of −18.8 kcal/d between the methods, with underestimation or overestimation in all the cases, as verified by Bland-Altman analysis. Even the subgroup with better statistical agreement did not furnish a clinically acceptable level of agreement. Therefore, the HB equation cannot substitute for indirect calorimetry for estimating REE in critically ill patients even if one uses the body weight measured with a bed scale.

This study had some limitations. To begin with, REE_IC and REE_HB measurement took place within the first 48 hours of patient’s admission to the ICU. Although energy metabolism undergoes dynamic changes in critically ill patients, this study did not assess such alterations. Second, evaluation of the factors that could affect REE_IC measurement, such as type of diet and administration route, did not occur on an individual basis, because the routine practice in the ICU involved prescription of a diet that ensured an adequate amount of calories to the patient. Besides, energy provision may not have interfered in our assessment because this was a paired study that compared 2 different methods for the same patient. Finally, the ventilation mode was not recorded at the time of assessment, because this parameter does not affect indirect calorimetry variables in critically ill patients.³³ 

In conclusion, our findings corroborated published evidence that indirect calorimetry is better than other methods for measuring REE in critically ill patients undergoing mechanical ventilation. Using indirect calorimetry ensures that critically ill patients receive more accurate nutritional support. Moreover, the attempt to use different sources of body weight failed to improve the accuracy of the HB equation for predicting REE in critically ill patients.

Regarding REE measurement in critically ill patients undergoing mechanical ventilation, our results showed that the Harris-Benedict equation is not reliable as a substitute for indirect calorimetry, regardless of the source of body weight.