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APPLIED SCIENCES: Physical Fitness and Performance

Predictive Validity of Three ActiGraph Energy Expenditure Equations for Children


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Medicine & Science in Sports & Exercise: February 2006 - Volume 38 - Issue 2 - p 380-387
doi: 10.1249/01.mss.0000183848.25845.e0
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Adequate participation in physical activity during childhood and adolescence is considered essential for good health and normal growth and development (28,29). Available evidence indicates that, among youth, regular physical activity is inversely related to an array of negative health outcomes, including obesity, elevated blood lipids, hypertension, and cigarette smoking, whereas it is positively related to favorable health outcomes such as increased cardiorespiratory fitness, elevated high-density lipoprotein (HDL) cholesterol, increased bone mass, and improved psychological well-being (4,28,29). Moreover, because several of the health outcomes related to physical activity tend to track from childhood into adulthood (27), adequate participation in physical activity during childhood and adolescence may be of critical importance in the primary prevention of chronic disease.

With promotion of regular physical activity a public health priority, it is critically important that researchers and practitioners have access to precise, yet practical instruments to measure physical activity behavior in children and adolescents. Valid and reliable measures of physical activity are a necessity in studies designed to (a) determine the association between physical activity and health outcomes, (b) document the frequency and distribution of physical activity in defined population groups, (c) determine the amount or dose of physical activity required to influence specific health parameters, (d) identify the psychosocial and environmental factors that influence physical activity behavior, and (e) evaluate the effectiveness of health promotion programs to increase habitual physical activity in individuals, groups, and whole communities.

To date, a variety of methods have been used to measure physical activity in children and adolescents. These include self-report questionnaires, direct observation, doubly labeled water, heart rate monitoring, and motion sensors such as accelerometers and pedometers (10,16). Because of the limitation of self-report methods in young children (e.g., <10 yr) and the high cost and subject burden associated with direct observation, doubly labeled water, and heart rate monitoring, accelerometry has become the method of choice for objectively measuring physical activity in free-living children and adolescents (10,23). Although a number of accelerometer makes and models are commercially available, one product in particular, the ActiGraph, formerly known as Computer Science and Applications (CSA) and Manufacturing Technology Inc. (MTI), (ActiGraph, LLC, Fort Walton Beach, FL), has received a substantial amount of research attention and is currently the accelerometer of choice in numerous studies involving children and adolescents.

Despite the widespread use of the ActiGraph, considerable uncertainty exists about how to convert its output (counts per unit of time) into units of energy expenditure (EE) or estimates of physical activity intensity (23). Energy expenditure prediction equations developed for adults (7,11,21) are not valid for children and adolescents because they do not take into account (a) developmental differences in resting metabolic rate (RMR), and (b) the poorer economy of movement exhibited by children and adolescents relative to adults (15,18,23,30). In recognition of these important differences, at least the following three youth-specific ActiGraph-based EE prediction equations have been independently developed and published in the peer reviewed scientific literature.

Trost et al. (26):

Freedson child (24,25):

Puyau et al. (17):

These equations take into account the physiological differences between children and adults. It is important, however, to note that all three equations were developed in controlled laboratory settings and, to our knowledge, have not been simultaneously cross-validated in an independent sample of children and adolescents under field-based conditions, where overground EE is influenced by environmental conditions, footwear, and surface. Additionally, because the design features of the original calibration studies differed considerably with respect to age range studied, speed of locomotion, and types of activities examined, it is important to evaluate the generalizability of each equation using a standardized protocol. Accordingly, this study evaluated the validity of three independently developed ActiGraph equations for predicting EE and physical activity intensity during overground walking and running in children and adolescents.



The sample consisted of 45 children and adolescents between the ages of 10 and 18 yr. This age range was selected because original calibration studies included children and adolescents between the ages of 6 and 18 yr. Moreover, an age diverse sample was necessary to determine how well each equation controlled for age-related difference in RMR and economy of movement. Participants were recruited through flyers posted around the University of Wollongong campus and by word of mouth. All participants were residents of Wollongong, Australia. The sample was evenly distributed across the age range and contained approximately the same number of boys and girls. All participants were physically active but were not involved in any systematic training program. Before participation in the study, written assent and written informed consent was obtained from each participant and his or her primary guardian, respectively. The study was approved by the University of Queensland and the University of Wollongong human research ethics committees. Descriptive characteristics are presented in Table 1.

Descriptive characteristics of the participants.


Each participant performed the following tasks for 5 min: walking at a normal pace; walking at a brisk pace; running at an easy pace; and running at a fast pace. The intensity of each task was self-selected. All trials were completed on a flat oval indoor track. Before and after each activity trial, each participant was required to sit quietly for 5 min as a rest period. The speed and distance of each walking and running trial was recorded using standardized procedures. To assist with motivation and pacing, a research assistant jogged with the participants during the running tasks. During each trial, verbal feedback was provided to the participant if the research assistant felt that the pace was inappropriate. Average walking and running speed, oxygen consumption (V̇O2), heart rate, and average accelerometer counts for the four activity trials are reported in Table 2.

Descriptive data for the four activity trials (means ± SD).


Indirect calorimetry.

Oxygen uptake during the walking and running trials was measured using the Cosmed K4b (2) (Rome, Italy), a lightweight (925 g) portable indirect calorimetry system specifically designed to measure energy expenditure in nonlaboratory settings. A flexible facemask (Hans Rudolf, Kansas City, MO) held in place by a nylon head harness covered the participant's nose and mouth. The mask was attached to a bidirectional digital turbine flowmeter to measure the volume of inspired and expired air. A sample line running from the turbine to the analyzer unit delivered expired air for the determination of O2 and CO2 content. The Cosmed K4b (2) has been shown to provide valid measures of oxygen uptake over a range of exercise intensities in adults (5,13). The Cosmed K4b (2) has been used extensively in studies involving children and adolescents (9,19,22). One unpublished validation study involving children and adolescents reported a small positive bias for the Cosmed compared with a standard laboratory metabolic cart. Across the entire range of exercise intensity examined, differences, however, were <6% (9).

Before each test, the Cosmed was calibrated according to manufacturer's guidelines. After warming up the unit for 30 min, the CO2 and O2 analyzers were calibrated against room air as well as a reference gas of known composition (5.20% CO2, 16.00% O2, and 78.80% N). To compensate for the time lag between the sampling and expiration of air, a delay calibration was completed. This procedure required participants to expire and inspire in time with an auditory cadence provided by the Cosmed unit. Following this step, the turbine was calibrated using a 3-L Hans-Rudolf syringe. To facilitate computation of derived values, relative humidity, barometric pressure, ambient temperature, and participant body mass were all measured and entered directly into the Cosmed analyzer unit.


The ActiGraph is a uniaxial accelerometer designed to detect vertical accelerations ranging in magnitude from 0.05 to 2.00 g with a frequency response of 0.25-2.50 Hz. These parameters allow for the detection of normal human motion and will reject high-frequency vibrations encountered during activities such as operation of a lawn mower. The filtered acceleration signal is digitized, rectified, and integrated over a user-specified epoch interval. At the end of each epoch, the summed value or "activity count" is stored in memory and the integrator is reset. For the current study, 5-s epochs were used. Before commencement of each trial, the ActiGraph was initialized according to manufacturer specifications, placed in a nylon pouch, attached to a flexible elastic belt that was fastened snuggly around the waist of the participant. The ActiGraph was positioned on the right midaxilla line at the level of the iliac crest.

Data Reduction

Before each test, the ActiGraph and Cosmed unit were synchronized to an external timepiece. Following download of the data from the respective instruments, an Excel spreadsheet was used to calculate steady-state V̇O2 and mean counts per minute during the last 2 min of each activity trial. For each participant, the attainment of steady state was confirmed by inspection of recorded HR and V̇O2 values. Tolerance levels were ±5 bpm and ±10% for V̇O2 and HR, respectively. Mean V̇O2 was converted into units of EE (kcal·min−1 and kcal·kg−1·min−1) using the constant 1 L O2 = 4.825 kcal (12). MET values were calculated by dividing mean V̇O2 by RMR. RMR was predicted from the participant's sex, age, weight, and height using Schofield's equation for children aged 10-18 yr (20). Activity EE (AEE) for each condition was computed as mean EE − predicted RMR. Mean counts per minute were converted into units of EE using the Trost (kcal·min−1), Freedson (METs) and Puyau (kcal·kg−1·min−1) prediction equations, respectively. Because the most appropriate method for reporting physical activity intensity in children and adolescents has not been determined, we did not attempt to standardize outcomes to a single unit of measurement.

To evaluate the ability of each equation to classify physical activity intensity, measured and predicted units of EE were classified as either light-, moderate-, or vigorous-intensity physical activity. For measured and predicted AEE, the intensity classification scheme described by Puyau et al. (18) was adopted. Light activity was defined as ≥0.015 kcal·kg−1·min−1 and <0.04 kcal·kg−1·min−1. Moderate activity was defined as ≥0.04 kcal·kg−1·min−1 and <0.10 kcal·kg−1·min−1. Vigorous activity was defined as ≥0.10 kcal·kg−1·min−1. These thresholds were selected because they closely approximated the conventional MET levels associated with light, moderate, and vigorous physical activity. To evaluate the classification accuracy of the Trost equation, measured and predicted kilocalorie-per-minute values were converted to AEE (kcal·kg−1·min−1) by dividing kilocalories per minute by body mass and subtracting predicted RMR. The resultant AEE scores were classified using the Puyau classification scheme. For measured and predicted METs, the intensity classification scheme described by Freedson et al. (7) was adopted. Light activity was defined as ≥1.5 METs and <3 METs. Moderate physical activity was defined as ≥3 METs and <6 METs. Vigorous activity was defined as ≥6 METs.

Data Analyses

Differences between observed and predicted values were evaluated using dependent t-tests. The predictive accuracy of each equation was compared by calculating the pure error and coefficient of variation (CV) for each activity trial and the four activity trials combined. Pure error, which is used to measure the performance of a predictive equation on cross-validation, was calculated as the square root of the sum of squared differences between the observed and the predicted values divided by the number of observations. The pure error and the standard error of estimate (SEE) are conceptually similar, but differ slightly numerically. The smaller the pure error, the greater the accuracy of the equation when applied to an independent sample (8). The CV is the pure error estimate standardized to the mean of the observed variable and allows direct comparison of the predictive validity of equations with different units of measurement. In addition, Bland-Altman plots were used to determine systematic bias and the 95% limits of agreement for each equation (1,3). Pearson correlations between mean EE and individual error scores were used to examine if bias was systematic over the range of activity intensities examined. The ability to correctly classify moderate- and vigorous-intensity physical activity was evaluated by calculating percent agreement, sensitivity, specificity, and area under the receiver operating characteristic (ROC) curve (33). Significance was set at an alpha level of 0.05


Differences between observed and predicted values for the Trost, Freedson, and Puyau equations are displayed in Figures 1A, B, and C, respectively. The Trost equation significantly overestimated mean EE (kcal·min−1) during normal (23.3%) and brisk walking (13.3%) and significantly underestimated mean EE during fast running (−12.3%). Predicted METs during slow running were not significantly different from observed kilocalories per minute (−0.9%). The Freedson equation significantly overestimated mean EE (METs) during normal walking (29.4%), brisk walking (23.5%), and slow running (15.9%). Predicted METs were not significantly different from observed METs during fast running (4.5%). For the Puyau equation, mean AEE was not significantly different from observed AEE during normal walking (0.6%). Observed mean AEE, however, was significantly underestimated during brisk walking (−13.3%), slow running (−29.3%), and fast running (−37.7%). Pure error and CV statistics for the three prediction equations are summarized in Table 3 to allow the errors in the equations to be directly compared. Notably, all three prediction equations exhibited a substantial degree of error, with CV statistics ranging from 20 to 45%. The Puyau equation exhibited the lowest CV during normal walking; the Trost equation demonstrated the lowest CV during brisk walking and slow running, whereas the Freedson equation exhibited the lowest CV during fast running. Pure error statistics for all three equations increased with activity intensity and exceeded the SEE reported in the original calibration studies.

Pure error and coefficient of variation (CV) statistics.
Measured vs predicted energy expenditure values for the Trost (A), Freedson Child (B), and Puyau (C) accelerometer prediction equations. # Statistically significant difference (P < 0.05).

Bland-Altman plots for the Trost, Freedson, and Puyau equations are displayed in Figures 2, 3, and 4, respectively. Because plots of the absolute differences and individual means revealed evidence of heteroscedasticity, mean bias and 95% limits of agreement were calculated using log-transformed data and presented as dimensionless ratios (1,3). Across the four trials, the mean bias on a ratio scale (observed ÷ predicted) for the Trost, Freedson, and Puyau equations was 0.98, 0.87, and 1.33, respectively. Thus, the difference between measured and predicted EE for the Trost, Freedson, and Puyau equations was, on average, −2, −13, and +33%, respectively. The corresponding 95% ratio limits of agreement were 0.45-1.52, 0.38-1.36, and 0.44-2.22, respectively. Thus, for any individual in the population, EE values predicted by the Trost, Freedson, and Puyau equations may differ from measured EE values by −55 to +52%, −62 to +36%, and −56 to +122%, respectively. For all three equations, difference ratios were positively correlated with activity intensity, with the correlation being much stronger for the Puyau equation (r =0.61) than the Trost (r = 0.41) and Freedson equations (r = 0.30).

Bland-Altman plot depicting mean bias and ratio limits of agreement (measured ÷÷ predicted) for the Trost equation.
Bland-Altman plot depicting mean bias and ratio limits of agreement (measured ÷÷ predicted) for the Freedson child equation.
Bland-Altman plot depicting mean bias and ratio limits of agreement (measured ÷÷ predicted) for the Puyau equation.

Percent agreement, sensitivity, specificity, and area under the ROC curve for the three equations are displayed in Table 4. For the purpose of categorizing counts as either light-, moderate-, or vigorous-intensity physical activity, the Trost equation (83.9% agreement) demonstrated better agreement than the Freedson (75.6%) and Puyau equations (71.1%). All three equations exhibited reasonable levels of sensitivity and specificity with respect to detecting moderate and vigorous physical activity, with sensitivity and specificity varying according to each equation's propensity to over- or underestimate EE.

Percent agreement, sensitivity (Se), specificity (Sp), and area under the receiver operating characteristic (ROC) curve (AUC) for each equation by intensity level.

The area under the ROC curve provides a measure of classification accuracy that jointly considers sensitivity and specificity (33). The curve plots the false-positive rate (1 - specificity) on the x-axis and the true positive rate (sensitivity) on the y-axis. An area of 1 represents perfect classification, whereas an area of 0.5 represents a complete absence of classification accuracy. Values of ≥0.90 are considered excellent, 0.80-0.90 good, 0.70-0.80 fair, and <70 poor (14). Classification accuracy for moderate- and vigorous-intensity physical activity was evaluated separately using all the available data. For moderate intensity, measured and predicted values were coded as moderate ("1"; ≥3 METs and <6 METs; ≥0.04 kcal·kg−1·min−1 and <0.10 kcal·kg−1·min−1) or otherwise (coded "0"). Similarly, for vigorous intensity, measured and predicted values were coded as vigorous ("1"; ≥6 METs; ≥0.10 kcal·kg−1·min−1) or otherwise (coded "0"). Applying the rubric described above, the Trost equation demonstrated excellent classification accuracy (0.92) for vigorous activity and good classification accuracy (0.84) for moderate activity. The Freedson equation demonstrated good classification accuracy (0.82) for vigorous activity and fair classification accuracy (0.76) for moderate activity. The Puyau equation demonstrated fair to good classification accuracy (0.80) for vigorous activity and fair classification accuracy (0.73) for vigorous activity.


This is the first study to simultaneously evaluate the validity of three prediction equations for converting ActiGraph counts into units of EE in children and adolescents. Predicted and measured units of EE were compared under field conditions using modes of physical activity readily detected by accelerometry (i.e., walking and running). In addition, the ability of each equation to correctly classify physical activity intensity was evaluated. Although each equation exhibited acceptable group-level precision in at least one activity trial, the greater tendency for each equation to under- or overestimate EE suggests that they are inappropriate for estimating EE on a minute-by-minute basis. In contrast, the equations exhibited fair to excellent classification accuracy with respect to activity intensity and, therefore, may be useful for estimating daily participation in sustained moderate and vigorous physical activity.

Ideally, an accelerometer prediction equation should accurately predict EE over a range of activity types and intensities. In the present study, none of the equations accurately predicted mean EE during each of the four activity trials. Nevertheless, each equation accurately predicted mean EE in at least one activity trial. The Puyau equation accurately predicted EE during slow walking. The Trost equation accurately predicted EE during slow running. The Freedson equation accurately predicted EE during fast running. Notably, none of the three equations accurately predicted EE during brisk walking. These findings indicate that additional calibration studies are needed before the ActiGraph can be used to estimate the energy cost of specific activities or daily EE in children and adolescents. The fact that EE during slow walking, slow running, and fast running was most accurately predicted by a different equation, clearly demonstrates that the design features of a calibration study (age range, setting, speed of locomotion, types of activities) has a significant impact on the range and generalizability of a prediction algorithm.

The Trost and the Freedson equations, which were developed using treadmill walking and running, significantly overestimated EE during normal and brisk-paced walking. This finding is in agreement with the results of field-based studies evaluating the validity of treadmill-based ActiGraph prediction equations in adults. Yngve et al. (32) contrasted measured and ActiGraph predicted METs during overground walking in a sample of young adults. The treadmill-based Freedson equation for adults (7) [METs = 1.439008 + (0.000795 × counts per minute)] overestimated MET level during normal (4.3 km·h−1) and brisk overground walking (5.8 km·h−1) by 22.6 and 25.6%, respectively. Similarly, Bassett et al. (2) reported the adult Freedson equation to overestimate MET level during slow (4.7 km·h−1) and brisk (6.0 km·h−1) overground walking by 17.1 and 16.0%, respectively.

The propensity for treadmill-based prediction equations to overestimate EE during overground walking can be attributed, at least in part, to differences in gait mechanics during treadmill locomotion. Compared with overground walking at the same velocity, stride length, vertical displacement, and vertical ground reaction forces are significantly reduced during treadmill walking, whereas stride rate is significantly increased (6,31). It is plausible that such differences would contribute to a systematically lower count accumulation for treadmill versus overground walking at a given walking velocity, resulting in an artificial "left shift" in the linear regression line relating activity counts per minute (x-axis) to energy expenditure (y-axis) (lower activity counts for a given level of EE). Consequently, substituting the higher activity counts recorded during overground walking into a treadmill-based prediction equation will result in an overestimation of EE. In support of this assertion, adult studies have reported activity counts during treadmill walking to be significantly lower than counts recorded during overground walking at the same velocity (32). Moreover, prediction equations derived from treadmill-based locomotion tend to exhibit higher Y-intercepts and flatter slopes than equations based on overground locomotion (11,32). Our observation that the Trost and Freedson equations performed better during the overground running trials, suggests that the biomechanical differences contributing to the lower ActiGraph counts during treadmill-based walking are either diminished or less important during running. Future accelerometer calibration studies should explore this possibility.

The Puyau equation predicted mean AEE during slow walking within 1 kcal·kg−1·min−1. During brisk walking and both running trials, however, the Puyau equation under estimated AEE by a substantial margin (13.3-37.7%). The tendency for this equation to underestimate AEE during moderate to vigorous physical activity may, in part, be related to the inclusion of "lifestyle activities" in the original calibration study. In contrast with the treadmill-based equations of Trost and Freedson, the Puyau calibration study included a wide range of lifestyle activities such as arts and crafts, video games, martial arts, ball games, jumping rope, and soccer. Investigators often include lifestyle activities in calibration studies with hopes that it will improve the accuracy of the accelerometer-based prediction equations in field settings. It is possible, however, that the inclusion of such activities in calibration studies may compromise the prediction of EE during walking and running. Specifically, the inclusion of predominantly nonambulatory activities with low activity counts and moderate-to-high levels of EE, leads to a partial "clockwise rotation" of the activity counts-EE calibration curve, such that its slope is flatter and its Y-intercept is substantial larger. Consequently, EE during light- to moderate-intensity activities is overestimated, whereas EE during moderate- to vigorous-intensity activities is underestimated. Evidence of this systematic pattern can be found in the Bland-Altman plot for the Puyau equation. Notably, Bassett et al. (2) reported similar findings for the lifestyle activity prediction equation developed by Hendelman et al. (11).

Accelerometer prediction equations have been used to classify activity counts as either moderate- or vigorous-intensity activity. Importantly, the broad classification of physical activity intensity allows researchers and practitioners to evaluate compliance with public health guidelines for physical activity. In the present study, all three equations exhibited good to excellent predictive accuracy for vigorous physical activity. The ability of the three equations to differentiate moderate activity from vigorous or light physical activity, however, ranged from fair to good. Of the three equations, the Trost equation exhibited the highest classification accuracy, whereas the Puyau equation exhibited the lowest. The practical implications of these differences can best be illustrated by contrasting the summative activity estimates provided by the two equations. Over the four activity trials, the participants, on average, completed 8.8 min of moderate and 9.8 min of vigorous activity. Based on the average counts per minute for each trial, the Trost equation estimated the duration of moderate and vigorous activity to be 9.1 and 10.6 min, respectively. In contrast, the Puyau equation estimated the duration of moderate and vigorous activity to be 12.4 and 6.7 min, respectively.

Because the summative activity estimates provided by the Trost and Puyau equations were based on AEE thresholds, it is difficult to directly compare the MET-based estimates provided by the Freedson equation. Notably, the traditional MET-based intensity cut points for moderate and vigorous physical activity (3 and 6 METs) will only coincide with the AEE cut points (0.04 and 0.10 kcal·kg−1·min−1) when RMR equals 0.02 kcal·kg−1·min−1. For participants with RMR >0.02 kcal·kg−1·min−1, AEE values of 0.04 kcal·kg−1·min−1 or slightly greater will be less than 3 METs [(0.025 + 0.045)/0.025 = 2.8 METs]. Alternatively, for participants with RMR <0.020 kcal·kg−1·min−1, AEE values of <0.04 kcal·kg−1·min−1 will be >3 METs [(0.018 + 0.038)/0.018 = 3.1 METs]. Acknowledging this discrepancy, participants under a MET-based classification scheme completed, on average, 8.4 min of moderate and 9.9 min of vigorous activity. In comparison, the Freedson equation estimated the average duration of moderate and vigorous activity to be 7.8 and 12.1 min, respectively.

Identification of the most accurate prediction equation would allow the field to move toward a uniform approach to ActiGraph data reduction. A standardized approach to data reduction would allow direct comparison of results across individual studies and also provide the opportunity to conduct valuable cross-cultural epidemiological studies. Based on the results of this study, we were unable to label one prediction equation as being clearly superior to others. Nevertheless, the higher classification accuracy exhibited by the Trost and Freedson equations relative to the Puyau equation suggests that these two equations may be the most useful of the three for estimating physical activity intensity in free-living children and adolescents. Our findings, however, should be interpreted with caution because our study only examined EE during sustained walking and running. Furthermore, because kilocalorie-per-minute values predicted by the Trost equation were converted to AEE using measured body mass and individually predicted RMR, the classification accuracy results for the Trost equation may be inflated.

In conclusion, previously published ActiGraph prediction equations developed specifically for children and adolescents do not accurately predict EE during overground walking and running. The Trost and Freedson equations, however, may be useful for classifying activity counts as either moderate- or vigorous-intensity activity. Given the widespread use of the ActiGraph in pediatric studies around the globe, additional calibration studies are urgently needed to develop more precise prediction equations for free-living children and adolescents. Future studies should also evaluate the predictive validity of the Trost, Freedson, and Puyau equations using a combination of ambulatory and nonambulatory activities.

The results of the present study do no constitute endorsement by the authors or ACSM of the products described in this paper.


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