Abstract
Background
Estimating energy requirements forms an integral part of developing diet and activity interventions. Current estimates often rely on a product of physical activity level (PAL) and a resting metabolic rate (RMR) prediction. PAL estimates, however, typically depend on subjective self-reported activity or a clinician’s best guess. Energy-requirement models that do not depend on an input of PAL may provide an attractive alternative.
Methods
Total daily energy expenditure (TEE) measured by doubly labeled water (DLW) and a metabolic chamber from 119 subjects obtained from a database of pre-intervention measurements measured at Pennington Biomedical Research Center were used to develop a metabolic ward and free-living models that predict energy requirements. Graded models, including different combinations of input variables consisting of age, height, weight, waist circumference, body composition, and the resting metabolic rate were developed. The newly developed models were validated and compared to three independent databases.
Results
Sixty-four different linear and nonlinear regression models were developed. The adjusted R2 for models predicting free-living energy requirements ranged from 0.65 with covariates of age, height, and weight to 0.74 in models that included body composition and RMR. Independent validation R2 between actual and predicted TEE varied greatly across studies and between genders with higher coefficients of determination, lower bias, slopes closer to 1, and intercepts closer to zero, associated with inclusion of body composition and RMR covariates. The models were programmed into a user-friendly web-based app available at: http://www.pbrc.edu/research-and-faculty/calculators/energy-requirements/ (Video Demo for Reviewers at: https://www.youtube.com/watch?v=5UKjJeQdODQ)
Conclusions
Energy-requirement equations that do not require knowledge of activity levels and include all available input variables can provide more accurate baseline estimates. The models are clinically accessible through the web-based application.
Introduction
Developing target energy deficits for diet or exercise interventions [1] or to determine food requirements for the military logistics [2] requires accurate knowledge of baseline energy requirements. The doubly labeled water (DLW) method [3] is the gold standard for estimating energy requirements in weight-stable populations, but is expensive and places a clinical burden on participants. As a result, DLW is rarely applied in large-scale studies or programs. In these cases, mathematical models [4, 5] provide an affordable and scalable alternative.
The most frequently applied mathematical approach first calculates the resting metabolic rate (RMR) from well-known validated regression models that only require knowledge of participant age, height, gender, and weight [6, 7]. The predicted RMR is then multiplied by the physical activity level (PAL) to obtain the estimated energy requirement.
Measured PAL, which is the ratio between measured total daily energy expenditure (TEE) and measured RMR is highly variable ranging from 1.1 to 2.5 [8]. Estimating an individual’s PAL either relies on average population values or additional knowledge about the individual’s habitual activity. In the latter case, PAL is frequently determined from participant questionnaires that categorize individuals into activity ranges, such as sedentary, moderately active, and very active [9]. The activity ranges are then assigned a PAL that reflects the classified activity range. For example, PAL = 1.4 for sedentary, PAL = 1.6 for moderately active, and PAL = 2.0 for very active [9]. Another approach for setting PAL is by using output from wearable technology to classify participants into activity ranges and then assigning PAL to each activity category [10].
In addition to the error that may be involved in gauging individual PAL, model-predicted RMR also has built-in error [6, 7, 11]. The product of PAL and RMR consequentially yields multiplicative error which is highly undesirable. In order to address this problem, several investigators have supported models that do not require an estimate of PAL [12, 13] and instead directly estimate energy requirements from inputs, such as weight, height, gender, and age. However, while at a basic level, an investigator/clinician may only have access to age, height, and weight variables, whereas some clinical interventions simultaneously measure additional known predictors of TEE, such as waist circumference, body composition, and/or RMRs. Unfortunately, models that include a comprehensive variety of such additional measurements do not exist.
Here, we fill this gap by developing a class of energy-requirement prediction equations that include combinations of potential measured explanatory variables. The new models do not depend on individual PAL and were developed from data collected at a single research center over multiple years using rigorous and uniform protocols. The models were programmed into a user-friendly web-based platform available at: http://www.pbrc.edu/research-and-faculty/calculators/energy-requirements/ (Video Demo for Reviewers at https://www.youtube.com/watch?v=5UKjJeQdODQ) to facilitate easy access and widespread use.
Methods
In an effort to maximize potential utility, we developed a class of prediction equations using combinations of predictors selected to represent variables that many investigators or clinicians will have or could have been available to them. For example, an investigator may have measured waist circumference but not body composition. Alternatively, an investigator may have measured the RMR but not physical activity.
To comprehensively meet different scenarios, energy-requirement predictions were developed for eight different combinations of explanatory variables. These combinations were
(Model A) Age, height, and weight
(Model B) Variables from Model A and waist circumference
(Model C) Variables from Model A and fat mass (FM) and fat-free mass (FFM)
(Model D) Variables from Model B and FM and FFM
(Model E) Variables from Model A and the RMR
(Model F) Variables from Model B and RMR
(Model G) Variables from Model C and RMR
(Model H) Variables from Model D and RMR
Body composition and energy budgets are different between males and females [14, 15]. As a result, we developed gender-specific models as advocated by others [14, 15].
Subjects
Pennington Biomedical Research Center data
Participant’s data for this paper were taken from the Pennington Center Longitudinal Study (PCLS), which is an ongoing investigation of the associations between obesity and lifestyle behaviors and how they relate to the development of chronic diseases, such as cardiovascular disease and type 2 diabetes mellitus. The PCLS sample is comprised of de-identified data obtained from research participants who enrolled in nutrition, weight loss, and other physiologic, interventional, or observational clinical trials conducted at Pennington Biomedical Research Center since 1992. Only data that pertain to a pre-intervention period (i.e., prior to an intervention) or a cross-sectional study are included in the PCLS database that was analyzed for this paper. Participants reported no change in weight and were screened for illnesses that may induce weight change. The current cohort was derived from a data query that pulled DLW data in adults (>18 years) and the corresponding data for body composition (DXA) and the RMR (Deltatrac II metabolic cart) if it occurred within 30 days of the DLW measurement. Demographic information, including age, height, and gender was also retained. All PCLS procedures and the data analysis plan for this study were approved by the Pennington Biomedical Research Center Institutional Review Board.
Statistical methods
Data assembly
The PCLS consisting of seven different files containing different input variables was supplied by the Pennington Biomedical Research Center compiled database, which generally differed with respect to the subjects. These files were logged separately within PCLS because they contained different measurements, such as body composition or the RMR; however, subjects that had both would appear on separate sheets. Some subjects overlapped in several sets; however, each individual subject was identified by a unique ID number. This did not mean that the subjects participated in different studies, but rather they overlapped because multiple measurements were performed. Depending on time of measurement, subject body composition was measured with the 4500 DXA or the Luna iDXA. All FM and FFM were converted into iDXA measurements using regression formulas developed internally at the Pennington Biomedical Research Center. After this conversion, a program was written in the statistical software package, R (R Core Team, 2013) to merge the worksheets into one file. Two independent coauthors (AP and DT) verified that all data were retained in the merged file. In the final database (N = 119) used for model development, average male BMI was 27.70 ± 3.11 kg/m2 and the average BMI for females was 26.86 ± 4.79 kg/m2. Average male age was 58.55 ± 24.43 and average female age was 53.96 ± 24.79. All PCLS procedures and the data analysis plan for this study were approved by the Pennington Biomedical Research Center Institutional Review Board.
Model development
Regression models were developed using the linear regression package in the statistical software package R (R Core Team, 2013). Gender-specific regression models with explanatory variables described in models A–H were developed. Model development was repeated in each category including linear, squared, and interaction terms. Determining whether nonlinear terms up to powers of two contribute to quality over linear models was evaluated using the Akaike information criteria (AIC). Model quality statistics of R2, adjusted R2, and root mean square error (RMSE) were calculated for each model.
Comparison to the existing models
We compared the developed models with three existing models that predict TEE on independent data that was not used to derive the model. The first comparison was with the model published by Vinken et al. [13]. The independent variables of the Vinken model were age, height, weight, and gender that comprised our Model A. The second comparison was with the model proposed by Cunningham [16], which was derived through a review of the literature. Independent variables of the Cunningham model were FM and FFM. Because we incorporated additional explanatory variables in models that included FM and FFM, a direct comparison was not possible; however, validations on datasets that had body composition were possible. We additionally compared Model A to energy requirements predicted by the product of a PAL of 1.6 and the Mifflin St. Jeor RMR formula [7].
Independent validation data
The models were evaluated on independent data that included DLW-measured TEE and combinations of measured covariates in Models A–H. A Bland–Altman analysis of measured versus predicted TEE was performed in Microsoft Excel (Seattle, WA, 2011). The R2 value, bias, and linear trend in the error were separately calculated for males and females.
Code availability
The model code is provided in Supplementary Materials Computer Code.
Institute of Medicine database
The Institute of Medicine DLW database [17] (N = 334 (males), N = 432 (females), BMI = 25.8 ± 5.5 kg/m2) was also used to evaluate the models. The database contained basic demographic data, body weights, and RMR which constitute input variables in Models A, E, Vinken, and 1.6 × RMR. We compared Models A, E, Vinken, and the traditional product of 1.6 (PAL) and RMR, where RMR was estimated using the Mifflin St. Jeor model [7] against measured TEE using a Bland–Altman analysis performed in Microsoft Excel (Seattle, WA, 2011).
Mayo Clinic dataset
We applied baseline data from 20 participants from a study conducted at the Mayo Clinic [18], evaluating the effects of non-exercise adaptive thermogenesis on overfeeding. The original study participants (N = 21) were approximately half-lean and half of them were individuals with obesity (BMI = 28.5 ± 6.2 kg/m2). All study protocols were approved by the Mayo Clinic Institutional Review Board, and written informed consent was obtained from each participant prior to data collection. The database contained DXA-measured body composition, and demographic/anthropometric information. Models A, C, Vinken, Cunningham, and the product of 1.6 and RMR estimated by the Mifflin St. Jeor equations were tested using the Mayo Clinic data through a Bland–Altman analysis in Microsoft Excel (Seattle, WA, 2011).
The South Carolina Energy Balance Study dataset
The Energy Balance Study was a multiyear observational study of energy balance, whose methodology has been described in detail previously [19]. Briefly, the participants were healthy young adults, aged ≥21 and ≤35 years, and with a body mass index (BMI) ≥ 20 and ≤35 kg/m2. Individuals were ineligible for the study for reasons that might influence body weight status (chronic health conditions, use of medications to lose weight, initiation, or cessation of smoking in the previous 6 months, a history of depression/anxiety, those taking selective serotonin inhibitors for any reason, and pregnancy in the previous 12 months, among other exclusion criteria). All study protocols were approved by the University of South Carolina Institutional Review Board, and written informed consent was obtained from each participant prior to data collection.
The study retained DLW-measured TEE, DXA measured by FM and FFM, RMR by indirect calorimetry, waist circumference, and all other required demographic/anthropometric variables required for model simulation. The free-living models (A–H), the Vinken model, the Cunningham model, and the product of 1.6 and Mifflin St. Jeor estimated RMR were evaluated using a Bland–Altman analysis performed in Microsoft Excel (Seattle, WA, 2011).
Results
Subjects
Table 1 contains a summary of subject age (years), BMI (kg/m2), and TEE (kcal/day) by gender for each study used in model development and validation. The measurements available for each study also appear in Table 1.
Table 1.
Subject characteristics with available measurements
| Study | N | Age (years) | BMI (kg/m2) | TEE (kcal/day) | Available measurementsa |
|---|---|---|---|---|---|
| PBRC model development | Males | Males | Males | Male | A, H, W, and WC |
| 56 | 59 ± 24.44 | 27.70 ± 3.11 | 2964.61 ± 796.20 | FFM and FM | |
| Females | Females | Females | Females | RMR | |
| 69 | 54 ± 24.79 | 26.86 ± 4.79 | 2174.49 ± 442.87 | ||
| Institute of Medicine model validation | Males | Males | Males | Males | A, H, W, and RMR |
| 334 | 50.45 ± 19.75 | 26.08 ± 5.14 | 2672.20 ± 676.29 | ||
| Females | Females | Females | Females | ||
| 432 | 47.95 ± 20.10 | 25.60 ± 5.70 | 2305.43 ± 500.53 | ||
| Mayo Clinic model validation | Males | Males | Males | Males | A, H, W, and FM |
| 11 | 34.90 ± 8.10 | 27.99 ± 5.91 | 2951.52 ± 599.39 | FFM | |
| Females | Females | Females | Females | ||
| 12 | 40.75 ± 6.73 | 28.95 ± 6.60 | 2432.00 ± 292.30 | ||
| Energy Balance model validation | Males | Males | Males | Males | A, H, W, and WC |
| 102 | 27.55 ± 3.93 | 25.91 ± 3.66 | 3092.76 ± 451.90 | FM and FFM | |
| Females | Females | Females | Females | RMR | |
| 90 | 28.22 ± 3.62 | 25.65 ± 4.52 | 2318.52 ± 336.75 |
A = age (years), W = weight (kg), H = height (cm), WC = waist circumference (cm), FM = fat mass (kg), FFM = fat-free mass (kg), RMR = resting metabolic rate (kcal/day)
Models
A total of 64 models were developed. Evaluation of the statistics of R2, adjusted R2 and multiple R2, and testing of models with terms selected using AIC revealed that nonlinear terms did not contribute enough to the overall predictions to warrant inclusion of further analysis. Therefore, only the linear models were retained for independent validation.
Table 2 contains the total number of subjects used to derive each model, the derived model, adjusted R2, and RMSE of the remaining 32 models. In most cases, the adjusted R2 improved and the RMSE decreased as the number of available model variables increased. With explanatory variables of age, height, weight, and waist circumference, they could only explain 66% of the variance of TEE in males and 68% of the variance in females. Inclusion of FFM and FM improved the adjusted R2 to 0.72 in males and 0.71 in females. Notably, adjusted R2 was higher (over 0.71) when either RMR or body composition covariates were included.
Table 2.
Developed models that predict energy requirements from different combinations of input variables
| Gender | N | Modela | Adj R2 | RMSE |
|---|---|---|---|---|
| Males | ||||
| 53 | 3916.32 − 19.21A + 27.18W − 12.29H | 0.65 | 453.80 | |
| 52 | 5672.23 − 16.998A + 37.842W − 20.28H − 14.096WC | 0.66 | 446.15 | |
| 51 | 5791.79 − 16.318A + 22.60W − 31.90H + 6.14FM + 14.57FFM | 0.66 | 437.10 | |
| 50 | 6630.84 − 15.48A + 31.56W − 34.24H − 8.53WC + 2.18FM + 11.66FFM | 0.66 | 434.52 | |
| 49 | 2764.38 − 11.53A + 6.78W − 16.73H + 1.99RMR | 0.73 | 401.83 | |
| 48 | 4009.45 − 10.19A + 14.98W − 22.11H − 9.87WC + 1.93RMR | 0.73 | 397.52 | |
| 47 | 3497.2283 − 11.3305A + 10.2868W − 23.0481H − 4.1253FM + 2.9667FFM + 1.8602RMR | 0.72 | 399.73 | |
| 46 | 4375.74 − 10.47A + 20.30W − 25.42H − 9.02WC − 9.04FM − 0.53FFM + 1.86RMR | 0.72 | 396.53 | |
| Females | ||||
| 66 | 563.78 − 8.79A + 14.31W + 6.58H | 0.68 | 244.58 | |
| 65 | 663.56 − 8.24A + 15.83W + 6.22H − 2.07WC | 0.67 | 244.29 | |
| 61 | 1293.24 − 6.73A − 18.10W − 2.89H + 48.26FM + 27.03FFM | 0.72 | 227.39 | |
| 62 | 1200.34 − 7.21A − 21.21W − 2.74H + 2.22WC + 50.45FM + 28.10FFM | 0.71 | 227.10 | |
| 63 | 179.17 − 5.99A + 6.14W + 4.80H + 0.85RMR | 0.73 | 223.43 | |
| 62 | 364.16 − 5.04A + 8.76W + 4.07H − 3.65WC + 0.86RMR | 0.73 | 222.53 | |
| 61 | 715.86 − 5.18A − 17.47W − 0.63H + 38.15FM + 19.56FM + 0.65RMR | 0.74 | 215.54 | |
| 60 | 726.18 − 5.11A − 17.05W − 0.64H − 0.29WC + 37.83FM + 19.39FFM + 0.65RMR | 0.74 | 215.54 | |
A = age (years),W = weight (kg), H = height (cm), WC = waist circumference (cm), FM = fat mass (kg), FFM = fat-free mass (kg), RMR = resting metabolic rate (kcal/day)
Model validation
Tables 3 and 4 include the equation of the regressed line between actual and predicted bias, which is the mean difference between actual and predicted TEE, and the 95% confidence interval of the bias by each validation database. The quality of validation varied greatly by the study when the validation was being performed on and by gender. For example, the coefficient of determination in actual versus predicted for Model A in males was 0.53 when tested on the IOM study data, 0.67 for the Mayo Clinic study, and 0.19 for the Energy Balance study. For females, the coefficient of determination in actual versus predicted was 0.37 for the IOM study, 0.91 for the Mayo Clinic study, and 0.40 for Energy Balance.
Table 3.
Independent validation results: males
| Dataset | Model | Actual vs. predicted | R 2 | Bias (kcal/day) actual–predicted | 95% CI |
|---|---|---|---|---|---|
|
| |||||
| Institute of Medicine (N = 334) | |||||
| A | 0.64x + 1087.6 | 0.53 | −15.00 | [−951.19,920.61] | |
| E | 0.75x + 986.5 | 0.55 | −251.11 | [−1216.96,714.75] | |
| 1.6 × RMR | 0.40x + 1490.9 | 0.52 | 297.81 | [−647.61,1243.24] | |
| Vinken | 0.56x + 1337.6 | 0.55 | −33.62 | [−927.41,860.16] | |
| Mayo Clinic (N = 10) | |||||
| A | 0.74x + 1277.0 | 0.67 | −509.44 | [−1185.88,166.00] | |
| C | 0.68x + 1219.3 | 0.68 | −265.80 | [−927.07,395.48] | |
| 1.6 × RMR | 0.44x + 1598.3 | 0.63 | 40.83 | [−723.94,805.61] | |
| Vinken | 0.53x + 1829.1 | 0.62 | −455.61 | [−1190.14,278.91] | |
| Cunningham | 0.49x + 1256.1 | 0.68 | 239.18 | [−474.96,953.32] | |
| Energy Balance (N = 102) | |||||
| A | 0.31x +2467.2 | 0.19 | −417.89 | [−1118.74,282.96] | |
| B | 0.41x + 1464.1 | 0.40 | −492.54 | [−1186.85,201.78] | |
| C | 0.51x + 1726.2 | 0.36 | −269.20 | [−921.41,383.01] | |
| D | 0.59x + 790.7 | 0.49 | −352.69 | [−1013.64,308.26] | |
| E | 0.48x + 1255.5 | 0.47 | −384.87 | [−1065.38,295.65] | |
| F | 0.64x + 1502.8 | 0.42 | −436.68 | [−1103.09,229.72] | |
| G | 0.35x + 1534.8 | 0.41 | 410.33 | [−183.16,1003.82] | |
| H | 0.66x + 1422.3 | 0.44 | −420.90 | [−1074.50,232.70] | |
| 1.6 × RMR | 0.35x + 1534.8 | 0.34 | 127.25 | [−467.85,722.34] | |
| Vinken | 0.32x + 2447.2 | 0.30 | −414.16 | [−1028.56,200.23] | |
| Cunningham | 0.59x + 790.69 | 0.49 | 342.70 | [−182.69,868.09] | |
Table 4.
Independent validation results: females
| Dataset | Model | Actual vs. predicted | R 2 | Bias (kcal/day) actual–predicted | 95% CI |
|---|---|---|---|---|---|
| Institute of Medicine (N = 432) | A | 0.47 × +1116.2 | 0.37 | 103.21 | [−582.38,788.80] |
| E | 0.507 × +1106.6 | 0.39 | 40.06 | [−631.43,227.08] | |
| 1.6 × RMR | 0.51 × +926.7 | 0.36 | 205.79 | [−492.61,365.09] | |
| Vinken | 0.69 × +860.23 | 0.38 | −148.01 | [−859.38,278.42] | |
| Mayo Clinic (N = 12) | A | 1.0 × −135.56 | 0.91 | 16.26 | [−176.04,208.57] |
| C | 0.79 × +409.3 | 0.89 | 104.55 | [−97.89,307.00] | |
| 1.6 × RMR | 1.189 × −546.4 | 0.91 | 105.33 | [−131.49,342.16] | |
| Vinken | 1.40 × −632.2 | 0.90 | −342.45 | [−698.90,14.00] | |
| Cunningham | 1.09 × −340.9 | 0.89 | 131.90 | [−91.86,355.66] | |
| Energy balance (N = 102) | A | 0.31x + 2467.2 | 0.40 | −83.01 | [−594.78,428.69] |
| B | 0.41x + 1464.1 | 0.40 | −85.17 | [−595.02,424.69] | |
| C | 0.56x + 1028.5 | 0.55 | −18.69 | [−463.84,426.46] | |
| D | 0.54x + 1083.9 | 0.57 | −7.78 | [−441.20,425.63] | |
| E | 0.48x + 1255.5 | 0.47 | − 58.49 | [−539.08,422.09] | |
| F | 0.49x + 1243.5 | 0.48 | −62.38 | [−537.86,413.10] | |
| G | 0.55x + 1062.2 | 0.58 | −13.61 | [−444.09,416.86] | |
| H | 0.55x + 1063.0 | 0.58 | −14.70 | [−445.14,415.75] | |
| 1.6 × RMR | 0.48x + 1173 | 0.41 | 154.50 | [−324.92,633.93] | |
| Vinken | 0.52x + 1617.6 | 0.39 | −508.69 | [−1043.04,25.66] | |
| Cunningham | 0.59x + 790.69 | 0.49 | 28.31 | [−485.86,542.48] |
Only the Energy Balance study included all measurements to test Models A–H. Similar to the model development results, there were improvements with the addition of body composition and/or RMR, however, these improvements were not uniform. That is, simply including each additional covariate did not improve the coefficient of determination between observed TEE and predicted TEE. Additionally, existing models in some cases performed better than some of our developed models, and in some cases they did not. This difference can be observed even on the same dataset and across genders. For example, in males for the Energy Balance study, the Cunningham model and Model D had the highest R2s, while for females, Model D and Model H had the highest R2 values. In the majority of validations, the bias was negative, indicating that the predicted energy requirements are on average overestimating the actual energy requirements. In addition, all models tend to overestimate high TEE and underestimate low TEE (Figures 1 and 2 in the supplementary materials).
Discussion
Here, we derived and independently validated a class of models that predict energy requirements and do not require an input of PAL. Independent variables include different combinations of measurements a clinical intervention may have access to, such as age, height, gender, weight, waist circumference, RMR, and body composition.
To date, this type of model development has been limited due to few databases that include DLW-measured TEE with a simultaneous variety of other clinical measurements. Past models have either depended on smaller-sized datasets and fewer explanatory variables that were accessible to individual investigators [13] or pooled datasets that varied in protocol, standards, and subject samples [17]. In contrast, our models were developed using carefully controlled data collected over multiple years at the Pennington Biomedical Research Center and tested on independent datasets that contained some or all of the explanatory variables used to develop the models.
Variability in predicting energy requirements
Our results are consistent with others that found that at least 65% of the variation in TEE can be explained through predictive equations [13] with this number improving after inclusion of FFM [16]. Because our study had access to several large DLW datasets which included different combinations of independent variables, we were also able to test the predictions of our models and existing models on independent datasets that had not been used to develop the models. High variability was observed when conducting the independent validations. There are several reasons that explain this variation. First, independent validation results in lower R2 values than those attained during model development. This is because linear regression analysis minimizes the residuals in the development dataset by definition, and thus a small increase in the unexplained variation about the model will appear in a cross-validation dataset. Second, other studies were generated in different laboratories and during different time periods. For example, the IOM database was generated in multiple laboratories during the years when laboratories were first applying the DLW method. It is possible that protocols in the other studies differed from those normalized at the Pennington Biomedical Research Center and that this may have resulted in a larger analytical variation [20]. Additionally, as seen in Table 1, some subject samples differed in age and BMI than the dataset used to develop the models. Notably, this variation in validation was also apparent in existing models, such as the Vinken and Cunningham models. Finally, the validation results include upper bounds imposed by measurement error in body composition and TEE. Even with the most rigorous protocols, DXA-measured FM and FFM has about 4% error [21] and DLW-measured TEE has an analytical coefficient of variation of 5% [22].
Challenges in using a universal model to accurately predict TEE
Our findings involving the newly developed and existing models point out challenges in using a universal model to predict TEE. While the database used for model development was geographically restricted to the state of Louisiana, and while the age and BMI of participants widely ranged, we are still limited by the depth and breadth of the subject sample. Moreover, existing models also varied in their ability to predict consistently across datasets. These inconsistent validations across datasets prohibit the use of one model to predict energy requirements across populations. Two approaches could be used to improve consistency. A cluster analysis in a pooled large DLW database could be used to identify key differences between populations. Future model development could target these different resulting clusters to develop population-specific models [23]. A second approach is the one used by Sabounchi et al. [24] to model the RMR. The authors reviewed the literature, performed a meta-analysis, and developed population-specific models based on the aggregate findings. Until such data-driven personalized models are developed, clinicians should be cognizant of the variability in models and triangulate all activity information that is available; this includes the participant self-report and data obtained from activity monitors if available.
Estimation using activity monitors
With the advent of activity monitors directly available on smartphones, it may be tempting to rely on energy requirements from direct output of activity monitors or to use activity monitor output to estimate PAL. While individual studies sometimes report good agreement in comparison to DLW-measured energy expenditure [25], these studies are often conducted in small samples of healthy or lean subjects. These findings are not replicated in systematic reviews [26–28], which reveal that while movement type is well predicted, energy expenditure is poorly predicted and highly variable. Additionally, to our knowledge, today, there does not exist a validated model that transforms accelerometer output directly to PAL. These gaps could potentially be filled by similar approaches that we suggested for characterizing DLW data. Yet, still the variability from model predictions and the variability in accelerometer predictions suggest that at this date, all information should be used to triangulate how clinicians should estimate energy requirements. One avenue for future work is to automate such an aggregation using classifier models [29].
Model limitations
There are several functional properties of the models that were revealed from the analysis presented here. For example, the intercepts of the validation analysis are not close to zero. Second, the validations had poorer performance at higher and lower body weights. These suggest a nonlinear formulation of the model that was not considered using polynomials as we did here. In fact, there is evidence that TEE obeys a power law rule [30], however, the power law models only ~30% of the variance explained in TEE.
There are also likely additional variables that contribute to TEE that either cannot be easily measured or that we simply do not understand well enough to include defined variables as model terms. In fact, the validation lines of regression have intercepts that are not close to zero and this suggests either omission of important variables or a model form that is not linear or polynomial as we have suggested here. Despite these reservations, an initial estimate of energy requirements remains integral to all weight change interventions, and the best possible prediction based on available measurements should be employed.
Conclusion
Energy-requirement equations that do not require knowledge of activity levels and include all available input variables are useful for providing baseline estimates. The developed PAL-free energy-requirement models are clinically accessible through the web-based application.
Supplementary Material
Footnotes
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
Electronic supplementary material The online version of this article (https://doi.org/10.1038/s41366-018-0168-0) contains supplementary material, which is available to authorized users.
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