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Effect of BMI on Prediction of Accelerometry-Based Energy Expenditure in Youth


Medicine & Science in Sports & Exercise: December 2012 - Volume 44 - Issue 12 - p 2428–2435
doi: 10.1249/MSS.0b013e318267b8f1
Applied Sciences

Purpose The objective of this study is to determine the effect of body mass index (BMI) on level of agreement between six previously established prediction equations for three commonly used accelerometers to predict summary measures of energy expenditure (EE) in youth.

Methods One hundred and thirty-one youth between the ages of 10–17 yr and BMI from 15 to 44 kg·m−2 were outfitted with hip-worn ActiGraph GT1M (Pensacola, FL), Actical (MiniMiter/Respironics, Bend, OR), and RT3 (StayHealthy, Monrovia, CA) accelerometers and spent approximately 24 h in a whole-room indirect calorimeter while performing structured and self-selected activities. Five commonly used regression and one propriety equations for each device were used to predict the minute-to-minute EE (normalized to METs), daily physical activity level (PAL), and time spent in sedentary, light, moderate, and vigorous physical activity intensity categories. The calculated values were compared with criterion measurements obtained from the room calorimeter.

Results All predictive equations, except RT3, significantly over- or underpredicted daily PAL (P < 0.001), with large discrepancies observed in the estimate of sedentary and light activity. Discrepancies between actual and estimated PAL ranged from 0.05 to 0.68. In addition, BMI represented a modifier for two ActiGraph predictive equations (AG1 and AG2), affecting the accuracy of physical activity–related EE predictions.

Conclusion ActiGraph (AG3) and the RT3 closely predicted overall PAL (within 4.2% and 6.8%, respectively) as a group. When adjusting for age, sex, and ethnicity, Actical (AC1 and AC2) and ActiGraph (AG3) were not influenced by BMI. However, a gap between some hip-worn accelerometer predictive and regression equations was demonstrated compared with both criterion measurement and each other, which poses a potential difficulty for interstudy (e.g., different accelerometers) and intrastudy (e.g., BMI and adiposity) comparisons.

Supplemental digital content is available in the text.

1Division of Gastroenterology, Department of Pediatrics, Vanderbilt University Medical Center, Nashville, TN; 2Vanderbilt Institute for Energy and Environment, Climate Change Research Network, Vanderbilt University, Nashville, TN; 3Division of Gastroenterology, Department of Medicine, Vanderbilt University Medical Center, Nashville, TN; 4Department of Biostatistics, Vanderbilt University Medical Center, Nashville, TN; and 5National Institute of Diabetes and Digestive and Kidney Disease/Diabetes, Endocrinology, and Obesity Branch, National Institutes of Health, Bethesda, MD

Address for correspondence: Maciej S. Buchowski, Ph.D., Division of Gastroenterology, Hepatology and Nutrition, Department of Medicine, Vanderbilt University Medical Center, 1161 21st Avenue South, MedicalCenter North, Room A4103, Nashville, TN 37232-2260; E-mail:

Submitted for publication March 2012.

Accepted for publication June 2012.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (

An estimated 17% of children and adolescents in the United States are currently obese (7), and a sedentary lifestyle with diminished physical activity (PA) is considered one of the major contributors to this epidemic (22). Several health organizations and government agencies currently recommend 60 min of moderate-to-vigorous exercise daily for children and adolescents, but even by self-reports, the majority of youth do not achieve these criteria (5,11). Thus, accurate measurement of PA and PA-related energy expenditure (PAEE) is imperative to assess the association of PA and health in both clinical and epidemiological studies.

In recent years, accelerometers have emerged as the monitors of choice for measuring free-living PAEE because of their objectivity, reliability, minimal participant burden, versatility, and relative cost efficiency (20,29,41). Accelerometry is particularly appealing to measure PA in youth because of the inherent limitations of collecting self-report data within this population (2,13). However, the accurate characterization of the relation between accelerometer data output and energy expenditure (EE) has been challenging (9,23). Predictive equations for youth have been developed for specific accelerometer devices on the basis of a variety of activities at different levels of intensity (e.g., ambulatory activities and some forms of exercise) in relatively homogenous populations (34). However, results from studies with adults suggest varying accuracy of predictive equations in overweight and obese subjects (16). Validating the accuracy of these equations across a wide body mass index (BMI) range in predicting PAEE during both normal daily activities and structured bouts of PA is integral to determining their use as a measurement tool (3).

Accelerometers can be used to measure the rate and intensity of body movements in up to three planes (12). Collected data, in the form of counts per period termed epoch (set by the investigator), are the most commonly used method to represent dynamic PA levels. The data can also be incorporated into predictive equations to estimate gross EE or METs during studies performed in both standardized laboratory-based and free-living conditions. Recent studies in adults and children have found that some equations systematically under- or overpredicted EE at different levels of PA intensity (9,26,31). These errors are hypothesized to be a result of the different EE conditions under which the particular predictive equations were developed and validated (26), including variability in the actual activities monitored. This point was further highlighted in a recent study be Trost et al. (39), in which intensity-related accelerometer cut points were assessed in children. They demonstrated a wide range of classification accuracy of the five independently developed cut points evaluated.

The objective of this study was to build upon these previous studies by examining the validity of PAEE estimates for a set of commercially available accelerometers (ActiGraph, Actical, and RT3) in a large heterogeneous health youth study population with the gold standard reference of a whole-room indirect calorimeter. We compared the validity of commonly used monitor-specific equations in predicting PAEE and PA intensity distribution across a wide BMI range on the basis of both structured bouts of PA and self-selected activities. In addition, we examined the effect of BMI, sex, and ethnicity on these predictions.

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One hundred and thirty-one youths, between the ages of 10 and 17 yr (62 male and 69 female), participated in the study, with about half of each group self-describing themselves as African-American. All volunteers were healthy as determined by a physical examination by a board-certified pediatrician, did not take any medications known to alter EE, did not have any limitations or difficulties performing exercise, and were nonsmokers. Participants were recruited using flyers, email distribution lists, and personal contacts. All participants and their parent or legal guardian signed an informed consent document (participants under the age of 13 yr signed an informed assent document) approved by the university-affiliated institutional review board. The characteristics of these participants are shown in Table 1.



During a screening visit conducted by research personnel, details of the study were discussed and all questions answered. Participants were asked to maintain normal daily routines but avoid any unusual PA and stress (such as strenuous exercise) on the day before the study was conducted at the Vanderbilt Clinical Research Center. No dietary restrictions were stipulated before the study visit.

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Anthropometric Measures

Body mass was measured by the research staff to the nearest 0.1 kg with a digital scale (Detecto-Medic; Detecto Scales, Inc, Northbrook, IL) with the participants wearing light clothing and no shoes. Stature was measured using a wall-mounted stadiometer (Perspective Enterprises, Portage, MI) and body composition using dual-energy x-ray absorptiometry (software enCORE 2007, version 11.40.004; GE Lunar Prodigy, Madison, WI). BMI was calculated as a ratio of weight (kg) to the square of the stature (meters squared). For the purpose of statistical analysis, participants were also categorized to a normal (BMI <85th percentile for sex and age), overweight (BMI ≥85th percentile to <95th percentile for sex and age), or obese (BMI ≥95th percentile for sex and age) BMI category (6).

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Study Design and Protocol

All participants completed one overnight stay (approximately 24 h) in a whole-room indirect calorimeter. The room calorimeter is an airtight room with windows and an airtight pass and is equipped with a toilet, sink, desk, chair, telephone, multimedia, and exercise equipment. A computerized system with a touch monitor and an audible signal prompts participants to start and finish each standardized PA. An intercom system allows research staff to communicate with the person inside the room. The room ensures high-precision measurements in a controlled environment and seminaturalistic conditions (i.e., not wearing a breathing mask) and allows for adjusting the intensity of any PA task to the individual’s capability. Technical details of the indirect calorimeter measurement approach have been reported elsewhere (36). During the stay, participants followed a protocol that included two structured activity sessions, which occurred at set times during the study period (nonrandomized). The duration and intensity of activity sessions were predetermined to simulate an average, free-living PA profile. The morning session included self-paced ambulatory activities such as walking or jogging. The afternoon session involved sedentary activities such as desk work. Each structured activity was performed for 10 min and was followed by a 10-min rest to allow the EE measurement to reach proximal steady state before the next activity. Previous accelerometer validation studies have similarly used structured activity periods lasting less than 10 min, on the basis of the short but sustained PA episodes that characterize the free-living patterns of children (27,32). Meals were scheduled at specific times (breakfast, lunch, supper, afternoon snack, and evening snack), with participants able to choose from two meal plans (each structured to provide similar caloric, macronutrient, and micronutrient content). Participants were asked to go to bed no later than 10:00 p.m. During times when no specific activity was scheduled (5 h), participants were encouraged to engage in their normal daily PA patterns. During the nonsleeping time, each participant wore the three accelerometer devices mounted on their hip (anterior torso) on the dominant side. The waking period was defined as time from entering the room until going to bed in the evening and confirmed by the room calorimeter.

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Energy Expenditure Measures

Measurements of EE during rest and performing PA tasks (PAEE) were calculated from measured rates of oxygen (O2) consumption and carbon dioxide (CO2) production using Weir’s equation (44). The accuracy and precision of our metabolic chamber for measuring EE as determined by routine alcohol combustion tests were 99.2% ± 0.5% (mean ± SD) over 24 h and 98.6% ± 2.1% over 30 min.

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Sleeping EE (kcal·min−1)

Sleeping EE (SEE) was calculated as the average EE during sleep between 1:00 a.m. and 4:00 a.m. Any periods with significant movement recorded by the room calorimeter were removed from the SEE calculations.

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PA-related EE (PAEE)

PAEE during performance of each PA task was calculated as a ratio of EE to SEE (kcal·min−1) and expressed as METs (30).

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PA level categories

For standardized interpretation, cutoff points according to MET values have been established to distinguish between levels of intensity that correspond with levels of activity used in making public health predictions. These categories (termed physical activity levels (PAL)) include sedentary (1–1.5 METs), light (1.5–3 MET), moderate (3–6 METs), and intense/vigorous (>6 METs) (8).

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Commercially available accelerometers, frequently used in studies with adults and youth, including the ActiGraph GT1M (Pensacola, FL), the Actical (MiniMiter/Respironics, Bend, OR), and the RT3 (StayHealthy, Monrovia, CA) were used. Both the ActiGraph and Actical are primarily sensitive to motion in one plane (vertical). The RT3 is a triaxial accelerometer, which reports activity in three orthogonal directions and the vector magnitude of the three measurements. Technical specifications for each type of monitor have been previously reported (1,14,32,42). The ActiGraph GT1M, which was used without a signal filter, is no longer commercially available; however, it remains used in research and has been demonstrated to have similar vertical axis output in comparison with its successors, the ActiGraph GT3X and GT3X+ (33). The monitors report activity counts, a device-specific output that represents the average intensity of acceleration events occurring over a user-defined measurement epoch. For this study, all monitors were attached to a belt secured at the waist with monitors positioned on the hip (dominant side), and data from each monitor were acquired in 1-min epochs to facilitate 24-h data recording. After data were downloaded, each data set was time synchronized with the minute-to-minute data from the room calorimeter.

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Prediction equations

Activity count data for each monitor were collected using 1-min epochs and converted to measures of PA intensity (EE, PAEE, or METs) using both published (ActiGraph and Actical) and proprietary (RT3) equations (14,28,29,34,40). All models were then treated equally to result in individually normalized PAEE in METs on a minute-by-minute basis. Three regression equations were tested for the ActiGraph, two equations for the Actical in youth, and one equation for the RT3 (Table 2). The regression equation for the RT3 monitor is proprietary, and consequently, the exact structure is not reported. Acquired data were analyzed using both MET-based categorical predictions and daily PAL, which was computed as the average of the minute-by-minute MET predictions during the study interval.



PAL represents the ratio of mean EE and SEE and is an important outcome measure because it reflects the cumulative duration and intensity of PA episodes in each day (19). In the present study, the average PAL during waking was by design similar to averages found in previous population studies (21,25) to mimic a free-living PA pattern, in which 90% of the day is engaged in “sedentary” and “light” activity (40% and 50%, respectively), 8% in “moderate” activity, and only 2% in “vigorous” activity. Given the objective of categorizing daily PAL and time spent in PA categories, data from time sleeping in the whole-room indirect calorimeter were excluded from analysis. However, a 24-h study was important to collect stable SEE in individuals.

As in previous reports (31), the equation-predicted EE were expressed in METs, which was the PAEE normalized to individual measured REE (35). This approach is considered more accurate than using a constant factor of 3.5 mL of oxygen per body mass per minute (4) proposed by Jette et al. (17).

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Statistical Analysis

Descriptive statistics were calculated as the mean with SD and the total range or median with interquartile range (IQR) for continuous variables. For categorical variables, percentage (N) was presented. Predicted PAL and the time spent in the four PA intensity ranges (specified in METs) calculated from all the equations were compared with measured values by the room calorimeter. All analyses included wear time for all waking hours. As the standard criteria, the calorimetry MET values were calculated on a minute-by-minute basis as the ratio of measured EE to SEE. The Kruskal–Wallis test was used to compare PAL data among the normal, overweight, and obese. The Wilcoxon signed-rank test was used to compare the predicted PAL with the actual PAL for each device and each equation. The predicted and actual time spent in each intensity category was compared using Wilcoxon signed-rank test. The PAL difference for sex, ethnicity, and obesity status were compared using the Mann–Whitney U test. To account for multiple testing, a Type I error rate of P < 0.001 was used for statistical significance. We analyzed the association of BMI with PAL difference (equation minus calorimeter) for each device/equation using ordinary least squares, adjusting for age, ethnicity, and sex. We used restricted cubic splines to model the nonlinear effect of BMI and age. Interactions between age and BMI and sex and BMI were also included to account for the BMI effect differences at different ages and between male and female. Residual plot and q-q (quantile–quantile) plot were used to check the model assumptions. All statistical analyses were performed using open source R statistical software (version 2.13.0, Vienna, Austria).

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Difference in PAL predicted with each regression equation and the measurement using the calorimeter is represented in Figure 1. The median PAL measured by room calorimeter during waking was 1.92 (IQR, 1.80 to 2.01), with a mean testing duration of 13.3 h (SD = 0.3 h). All equation estimates significantly differed from the room calorimeter measures at P < 0.001, except RT3 (P = 0.008). PAL was underpredicted by the AC1, AC2, and AG3 equations and overpredicted by the AG1 and AG2 equations. Discrepancies between actual and estimated PAL ranged from 0.05 to 0.68. The AG1 and AG2 equations overpredicted PAL by 0.58 (95% confidence interval (CI), 0.49–0.68) and 0.32 (95% CI, 0.25–0.39) respectively; whereas the AC2 equation underpredicted PAL by 0.46 (95% CI, 0.42–0.50). The AG3 and RT3 equations were the closest approximations to the calorimeter measurement, underpredicting PAL by 0.10 (95% CI, 0.05–0.19) and 0.14 (95% CI, 0.08–0.20), respectively. The above variations in PAL results were similar between ethnicity (white vs black) and sex (female vs male). However, the median differences in estimating PAL by models were consistently higher in the overweight and obese compared with normal BMI youth (Table 3, Supplemental Fig. 1,





For further investigation of the PAL variations seen between obese, overweight, and normal BMI youth, the analysis of PAL difference between calorimeter and individual predictive equation was also investigated using BMI as a continuous variable while adjusting for age, sex, and ethnicity. Higher BMI was associated with increased PAL difference for AG1 (P < 0.001) and AG2 (P < 0.001) and neared significance associated for RT3 (P = 0.002) (Fig. 2, Supplemental Table 1, A similar pattern was demonstrated when percentage body fat was investigated as a continuous variable instead of BMI, except for RT3 (P = 0.027) (Supplemental Table 1, However, because the results of these two variables were similar and BMI is much easier to obtain in population studies, it was chosen as the continuous variable for reporting of results.



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Time spent in PA intensity categories

During the awake periods in the calorimeter, participants spent approximately 40% of their time in sedentary activities (1–1.5 METs), 50% in light (1.5–3 METs), 8% in moderate (3–6 METs), and 2% in vigorous (>6 METs) PAL categories. There were significant differences between the calorimeter measurements and most accelerometer predictions for the sedentary and light categories (P < 0.001). AC1 and AC2 overpredicted and AG1 and AG2 underpredicted the time spent in sedentary behaviors by 35% or more. Only two equations fell within 35% of the calorimeter measure of time spent in sedentary behavior, AG3 (7% underestimated) and RT3 (18% overestimated). Similar differences were observed for light activities, with the AG3 equation overpredicted the calorimeter measure by 12% and the RT3 underpredicted it by 20%. The remaining five equations under- or overpredicted the calorimeter reading for time spent in the light PAL category by 34% or more. Most equation predictions differed from the calorimeter estimate of time spent in moderate and vigorous PA categories, ranging from 1% overestimation to 5% underestimation for moderate PA and from −1% to 1% for vigorous PA (Fig. 3).



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Our study was designed to quantify the accuracy of 1 day of PAEE predicted from three commonly used accelerometers in a large group of heterogeneous youth using the gold standard reference of a room calorimeter. Using simple regression algorithms, we found the ActiGraph (AG3) and RT3 closely predicted the overall PAL (within 4.2% and 6.8%, respectively) as a group. When adjusting for age, sex, and ethnicity, the Actical (AC1 and AC2) and ActiGraph (AG3) were not influenced by BMI. However, we also demonstrated a gap between some hip-worn accelerometer predictive and regression equations compared with both criterion measurement and each other, which poses a potential difficulty for interstudy (e.g., accelerometers) and intrastudy (e.g., adiposity) comparisons.

The predictive equations used in this present study included commonly used regressions validated in children and adolescents (15,43), with variable inclusion or exclusion of several components (weight, age, and stature). However, the development of these equations was largely achieved with small cohorts composed of limited numbers of obese youth. For the five predictive equations with published methods and results (the StayHealthy RT3 proprietary equation being excluded), only one study had a cohort size greater than 35 (the AG2 equation was derived from a study involving 74 adolescent females) (14,28,29,34,40). In addition, at least one equation (AG1) was derived from a cohort that did not include any obese youth (28). The variability in cohort composition (ethnicity, age, and sex) and testing methods (different activities and exercise intensities) between studies likely also present variables that would contribute to the variances observed among predictive equations. Our present study is strengthened by a relatively large sample size of 131 youth with a heterogeneous composition according to age, ethnicity, sex, and BMI. In addition, approximately 13 h of continuous waking energy expenditure data per subject measured by reference standard room calorimeter (37) were collected on each individual for comparison with accelerometer-predicted EE.

Summary statistics for time spent in PA intensity categories is a commonly used measure for assessing whether an individual has met daily PA recommendations (18). Among equations, AG1 and RT3 were the most accurate in estimating moderate activity, whereas AC2, AG2, and RT3 were the most accurate in estimating vigorous activity (within 2% of the calorimeter data). However, all equations were substantially less accurate in predicting sedentary and light activity. The AG3 equation, which underestimated sedentary activity by 7% and overestimated light activity by 12%, was most accurate in estimating mean proportion of time spent in activity intensities. However, this equation also produced the largest degree of individual variability, suggesting low individual accuracy. This can be explained, at least in part, by the lack of a body mass component in the equation. The AG2 equation, with a similar structure, provides lower individual variability. The RT3 equation overpredicted EE of sedentary activity by 18% and underpredicted light activity by 20%. The AG1 equation significantly overestimated the percentage of time spent in the moderate activity category. Several participants had more than 20% of time categorized as moderate activity, which was significantly higher than measured time. The AG2, AC1, and AC2 equations under- or overestimated sedentary and light activity similarly (Fig. 3).

There are limitations of this study that should be considered. First, because of our relatively large sample size (as regards both the number of participants and duration of data collection), even small mean differences on an individual’s basis may be detected as statistically significant within the entire study population. This is particularly evident in the data for time spent in moderate and vigorous activities. Despite the small percentage of time spent in either of these activity categories, several differences were statistically significant. We have attempted to address absolute and relative differences between the predictions of each equation and the calorimeter measurements regardless of their statistical significance. However, the translation of these statistically significant findings to clinically significant applicability remains undefined. Even if absolute differences appear minimal, overprediction of PAL or intensity classification might falsely predict that threshold values have been achieved. Second, our analysis of BMI as a continuous variable was limited by its skewed distribution, which is characteristic for obese children and adolescents. A large percentage of participants were at or near the 99th percentile of BMI adjusted for sex and age, which prompted our use of unadjusted BMI when analyzed as a continuous measure. For categorical measures of BMI (nonobese vs obese), age- and sex-adjusted BMI percentiles were used. However, in both methods, the results were similar, with BMI representing a statistically significant modifier for AG2 and AG2 equation PAL estimation. Researchers should use care to consider the clinical significance of the discrepancies reported here within the context of their own work. Lastly, a potential limitation and source of error is the use of >3 METs as the lower cut point for moderate PA. Traditionally, this has been the accepted cut point in children and adolescents based on several validation studies (10,28,38). However, recent studies have suggested that this lower cut point is not valid in children and instead should be >4 METs (24,38).

Results of this study suggest the accelerometers examined were generally limited in their ability to distinguish between sedentary and light activities but performed reasonably well at detecting moderate and vigorous activities, which was an unexpected finding. Trost et al. (39) recently examined five predictive equations for the ActiGraph monitor (one of which were also used in our study) and demonstrated the most consistent accuracy for sedentary behaviors. Although inclusion of other predictive equations might provide different results, our findings for sedentary and light activities were present regardless of the particular device or predictive equation used. Potential etiologies for these findings of sedentary and light activities are the duration of observation and variations in times spent in either sedentary or light activities. According to the indirect calorimetry data, percentage sedentary activity time was 41% (IQR, 31% to 51%) and percentage light activity time was 50% (IQR, 42% to 59%). This wide variation was also demonstrated in the accelerometer data, which resulted in much broader ranges than that in data for percentage time spent in either moderate or vigorous activities. A practical significance of these findings is that the current standard approach (hip worn, 1-min epoch, and simple regression) should be used cautiously in clinical trials and intervention studies targeted on sedentary behaviors (e.g., screen time in youth) but might be adequate for measuring compliance with moderate to vigorous PA recommendations. However, researchers should exercise caution when using these equations to characterize an individual’s general PA profile. On the basis of our results, we suggest that to increase accuracy of PAEE and PA pattern prediction from currently available accelerometers in youth across a wide range of BMI, it is necessary to develop new approaches, equations, or correction factors.

In conclusion, we found that ActiGraph (AG3) and RT3 closely predicted overall PAL (within 4.2% and 6.8%, respectively) as a group. When adjusting for age, sex, and ethnicity, Actical (AC1 and AC2) and ActiGraph (AG3) were not influenced by BMI. The presented data suggest that there is a gap between some hip-worn accelerometer predictive and regression equations compared with both criterion measurement and each other. These differences pose a potential difficulty in both interstudy (e.g., accelerometers) and intrastudy (e.g., BMI, adiposity) comparisons.

This work was supported by grants from the National Institutes of Health, RO1HL082988, Vanderbilt CTSA grant UL1 RR024975, and Vanderbilt Diabetes Research and Training Center supported by the National Institutes of Health grant DK20593.

We would like to thank Marissa Avolio, Stephane Daphnis, Cindy Dorminy, Kristen Jensevar, Natalie Meade, and Elizabeth Provenzano for their contributions to the acquisition of the data for this study.

The authors report no conflict of interest.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

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