Review of Prediction Models to Estimate Activity-Related Energy Expenditure in Children and Adolescents

Table 1

Prediction models ordered by accelerometer.

Accelerometer	Activities	Criterion	Prediction models & Statistics
Actical (Mini Mitter Co., Inc., Bend, OR), (formerly known as Actiwatch).; Omnidirectional: senses motions in all directions but is most sensitive within a single plane. Detects low frequency (0.5–3.2 Hz) G-forces (0.05–2.0 Hz) common to human movement and generates an analogue voltage signal, that is, filtered and amplified before being digitized by an A-to-D converter at 32 Hz. The digitized values are then summed over user-specified time intervals (epoch) between 0.25 and 1 min. The actual numbers stored by the Actical are proportional to the magnitude and duration of the sensed accelerations and, thus, roughly correspond to changes in physical activity energy expenditure.; When mounted to the hip, most sensitive to vertical movements of the torso.; Water resistant, lightweight (17 g), small (2.8×2.7×1.0 cm^3).	Flat walking, graded walking, and running on a treadmill.	Indirect calorimetry	Corder et al. [13]; AEE (J⋅kg−1⋅min^−1) = 0.2AC + 168.7 → 𝑅^2=0.67, SEE 105; Flat walking: mean difference (J⋅kg^−1⋅min^−1) −65±23, 95% CI −78, −52; Graded walking: mean difference (J⋅kg^−1⋅min^−1) 72±35, 95% CI 52, 91; Running: Mean difference (J⋅kg^−1⋅min^−1) 18±69, 95% CI −26, 62; Flat and graded walking significantly different from measured values.
	- Three sitting activities: handwriting, card sorting, and Video game playing.; - Three simulated house cleaning activities: floor sweeping, carpet vacuuming, table dusting. and; - Locomotion activities: slow and moderate treadmill walking, treadmill jogging, OR self-paced slow walking, self-paced fast walking (indoor track).	Indirect calorimetry	Heil et al. [9], 1𝑅 = single regression modelling, 2𝑅 = double regression modelling; Include sitting and cleaning activities; Ankle 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.02304 + (3.750E-5) × AC → 𝑅^2 =.60, SEE = 0.020, 𝑃<.001; Hip 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.01667 + (5.103E-5) × AC → 𝑅^2 =.75, SEE = 0.014, 𝑃<.001; Wrist 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.01149 + (3.236E-5) × AC → 𝑅^2 =.59, SEE = 0.020, 𝑃<.001; Include all activities; Ankle 1𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.03403 + (1.179E-5) × AC → 𝑅^2 =.45, SEE=0.028, 𝑃<.001; Hip 1𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.03411 + (1.270E-5) × AC → 𝑅^2 =.61, SEE=0.024, 𝑃<.001; Wrist 1𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.02299 + (1.902E-5) × AC → 𝑅^2 =.67, SEE=0.022, 𝑃<.001; Include walking and jogging activities; Hip 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.03534 + (1.135E-5) × AC → 𝑅^2, SEE = 0.018, 𝑃<.001; Include walking activities only; Ankle 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = −0.02268 + (1.939E-5) × AC→ 𝑅^2 =.60, SEE = 0.015, 𝑃<.001; Wrist 2𝑅: AEE (kcal⋅kg^−1⋅min^−1) = 0.03115 + (1.581E-5) × AC → 𝑅^2 =.69, SEE = 0.019, 𝑃<.001
	Playing Nintendo, using a computer, cleaning, aerobic exercise, ball toss, treadmill walking, and running.	Room respiration calorimetry 4 h, Indirect calorimetry 1 h.	Puyau et al. [10]; Hip: AEE (kcal⋅kg^−1⋅min^−1)=0.00423+0.00031*Actical^0,653→ 𝑅^2 0.811, SEE 0.0110 Counts, age, and gender were included in the model; inclusion of height gave no significant improvement.
ActiGraph (model 7164, formerly known as Computer Science and Applications CSA activity monitor. Manufacturing Technologies Inc. health Systems, Shalimar, FL); Uniaxial.; Is sensitive to movements in the 0.51–3.6 Hz range. Hip- and ankle-mounted. When mounted to the hip, most sensitive to vertical movements of the torso.; The acceleration signal is represented by an analog voltage that is sampled and digitized by an eight-bit analog-to-digital converter at a rate of 10 times per second.	Flat walking, graded walking, and running on a treadmill.	Indirect calorimetry	Corder et al. [13]; Hip: AEE (J⋅kg^−1⋅min^−1) = 0.17 counts + 201.1 → 𝑅^2 = 0.5, SEE 123; Flat walking: mean difference (J⋅kg^−1⋅min^−1) −88 ± 14, 95% CI −97, 80; Graded walking: mean difference (J⋅kg^−1⋅min^−1) 66±26, 95% CI 51,82; Running: Mean difference (J⋅kg^−1⋅min^−1) 139±60, 95% CI 101, 177; All significantly different from measured values.; Ankle: AEE (J⋅kg^−1⋅min^−1) = 0.89 counts + 39.4 gender – 1.4 height + 361.9 → 𝑅^2 = 0.37, SEE 144; Flat walking: mean difference (J⋅kg^−1⋅min^−1) −104±39, 95% CI −126, −82; Graded walking: mean difference (J⋅kg^−1⋅min^−1) 77±48, 95% CI 51, 103; Running: Mean difference (J⋅kg^−1⋅min^−1) 176±233, 95% CI 28, 324; All significantly different from measured values.; Age was not included in the models because of lack of heterogeneity in the sample.
	Six activities, each activity lasted 5 minutes: Lying, sitting, slow walking, brisk walking, jogging, hopscotch.; (Step test calibration 8 minutes).	Indirect calorimetry	Corder et al. [14] validation of priori models and one new model derived.; Corder et al. [13], hip: AEE (J⋅kg^−1⋅min^−1) = 0.054 × AC[counts per minute] + 169 → 𝑅^2 = 0.81, RMSE = 161.8; Mean bias: −44.8; 95% CI: −54.1, −35.5; Derivation activities: flat and graded treadmill walking and flat running; Puyau et al. [17], hip: AEE (J⋅kg^−1⋅min^−1) = 0.042 × AC[counts per minute] + 76.6 → 𝑅^2 = 0.84, RMSE = 245.3; Mean bias: −151.6; 95% CI: −160.4, −142.8; Derivation activities: various sedentary, light, moderate, and vigorous activities; Trost et al. [19], hip: AEE (J⋅kg^−1⋅min^−1) = 3.35 × AC[counts per minute] + 334.8 × weight [kg] − 9334 → 𝑅^2 = 0.85, RMSE = 126.0; Mean bias: 5.5; 95% CI: −3.6, 14.6; Derivation activities: flat treadmill activity at 3.2, 6.4, and 9.6 km^−1; Corder et al. [14], hip: AEE (J⋅kg^−1⋅min^−1) = 0.1 × AC[counts per minute] − 2.29 × height [cm] + 353 → 𝑅^2 = 0.87, RMSE 118.0; Mean bias −1,9; 95% CI −11.4, 7,6; Derivation activities: lying, sitting, slow and brisk walking, jogging and hopscotch
	Free-living; Two school weeks, 14 consecutive days, the children wore the monitor during daytime following their normal living. Exceptions were during water activities such as swimming and bathing.	Doubly labelled water	Ekelund et al. [15]; Centre of gravity/lower back: AEE (kcal⋅d^−1) = (Activity counts × 1.042) − (Gender × 243.4) + 238 → Adjusted 𝑅^2 = 0.45, SEE 149; The mean difference between measured and predicted AEE was −45 kcal⋅d^−1 (𝑃=.58), and the 95% limits of agreement were −485 kcal⋅d^−1 to 395 kcal⋅d^−1.
	Sedentary: Nintendo, arts and crafts, playtime 1; Light activities: aerobic warm-up, walk 1; Moderate activities: Tae Bo exercises, playtime 2, walk 2 Vigorous activity: jogging.	Room respiration calorimetry	Puyau et al. [17]; Hip: AEE (kcal/kg/min) = 0.0183 + 0.000010 (counts) → SEE 0.0172 → 𝑟^2 (adj) 75%; Fibula head: AEE (kcal/kg/min) = 0.0142 + 0.000007 (counts) → SEE 0.0154 →𝑟^2 (adj) 82%; Predicting AEE from the combination of the counts from the hip and leg increased the 𝑟^2 (adj) to 86%.; Regression of AEE on counts was independent of gender and age, thus only counts were included in the model.
	Field conditions; flat oval indoor track. Normal walking, brisk walking, easy running, fast running.; The intensity of each task was self-selected.	Indirect calorimetry	Trost et al. [11] validation of Puyau et al. 2002; Puyau et al. [17], hip: AEE (kcal⋅kg^−1⋅min^−1) = 0.0183 + 0.000010 (counts per minute)𝑡-tests for difference in means of measured AEE (indirect calorimetry) and predicted AEE by Puyau equation: Normal walking: 0.6% not significantly different (pure error 0.014 kcal⋅kg^−1⋅min^−1); Brisk walking −13.3% significantly different (pure error 0.025 kcal⋅kg^−1⋅min^−1); Slow running −29.3% significantly different (pure error 0.054 kcal⋅kg^−1⋅min^−1); Fast running −37.7% significantly different (pure error 0.078 kcal⋅kg^−1⋅min^−1); Overall mean pure error was 0.049 kcal⋅kg^−1⋅min^−1; Mean bias on ratio scale is 1.33, difference between measured and predicted AEE was +33%. The corresponding 95% ratio limits of agreement were 0.44–2.22
Actiheart (Cambridge Neurotechnology, Cambridge, UK).; Combined HR and movement sensor is able to measure acceleration, HR, HR variability, and ECG magnitude.; Acceleration is measured by a piezoelectric element with a frequency range of 1–7 Hz (3 dB).; One electrode is placed at the base of the child’s sternum and the other horizontally to the child’s left side.; The main component is 7 mm thick with a diameter of 33 mm. A wire of approximately 100 mm length runs to the clip (5×11×22 mm^3). The total weight is 8 g.	Flat walking, graded walking, and running on a treadmill (protocol).	Indirect calorimetry	Corder et al. [13]; Actiheart Activity, chest: AEE (J⋅kg^−1⋅min^−1) = 0.22 counts + 29.3 gender + 144.3 → 𝑅^2 = 0.69, SEE 101; Flat walking: mean difference (J⋅kg^−1⋅min^−1) −74±32, 95% CI −91,−56; Graded walking: mean difference (J⋅kg^−1⋅min^−1) 56±32, 95% CI 38, 74; Running: Mean difference (J⋅kg^−1⋅min^−1) −86±116, 95% CI −159, −12; All significantly different from measured values.; Actiheart Combined, chest: AEE (J⋅kg^−1⋅min^−1) = 4.4 HRAR + 0.08 counts − 2.7 gender + 1.1 (gender × HRAR) + 15.1; (HRAR: Heart Rate Above Rest) → 𝑅^2 = 0.86, SEE 69 (69 J⋅kg^−1⋅min^−1); Flat walking: mean difference (J⋅kg^−1⋅min^−1) −11±27, 95% CI −55, −15; Graded walking: mean difference (J⋅kg^−1⋅min^−1) −38±48, 95% CI −29, 26; Running: mean difference (J⋅kg^−1⋅min^−1) 10±102, 95% CI −105, −6; Graded walking significantly different from measured values.; (Age was not included in the models because of lack of heterogeneity in the sample).
	Six activities, each activity lasted 5 minutes: Lying, sitting, slow walking, brisk walking, jogging, hopscotch.; (Step test calibration 8 minutes).	Indirect calorimetry	Corder et al. [14] validation of priori models and new models derived.; Corder et al. [13], chest: HR + ACC model: AEE (J⋅kg^−1⋅min^−1) = 5.6 × HRaS [bpm] + 1.37 × gender^∗HRaS + 0.1 × AC[counts per minute] − 44 × gender − 129; (HRaS: Heart Rate above Sleep) → 𝑅^2 = 0.90 RMSE = 118.0; Mean bias: 18.7; 95% CI: 8.1, 29.3 Derivation activities: flat and graded treadmill walking and flat running; Corder et al.[13]/Branched, chest: HR equation: AEE (J⋅kg^−1⋅min^−1) = 6.2 × HRaS [bpm] – 27 × gender + 1.2 × gender^∗HRaS − 139; AC equation: AEE (J⋅kg^−1⋅min^−1) = 0.22 × AC[counts per minute] + 29 × gender + 144; 𝑅^2 = 0.90, RMSE = 115.6; Mean bias: −43,4; 95% CI: −52.2, −34.6; Derivation activities: flat and graded treadmill walking and flat running; (First branch threshold is 25 activity counts per minute, the second depends on the HRaS); Corder et al. [14], chest: AEE (J⋅kg^−1⋅min^−1) = 5.17x HRaS [bpm] + 0.61 × gender^∗HRaS + 0.07 × AC[counts per minute] −0.6 × gender − 74 → 𝑅^2 = 0.90, RMSE = 100.1; Mean bias −2.5; 95% CI: −12.2, 7.2; Derivation activities: lying, sitting, slow and brisk walking, jogging and hopscotch; Corder et al. [14], chest: AEE (J⋅kg^−1⋅min^−1) = 3.95 × HRaS[bpm] + 0.26 × gender^∗HRaS + 0.07 × AC[counts per minute] + 8 × gender + 0.68 × 𝛼-step + 1.31 ×  𝛽-step^∗ HRaS −49; 𝑅^2 = 0.91, RMSE = 97.3; Mean bias: −2.3; 95%CI: −11.4, 6.8; Derivation activities: Lying, sitting, slow and brisk walking, jogging and hopscotch (with step calibration)
Actiwatch (model AW16; Mini-Mitter, Bend Or).; Omnidirectional accelerometer built from a cantilevered rectangular piezoelectric bimorph plate and seismic mass, which is sensitive to movement in all directions, but most sensitive in the direction parallel with the longest dimension of the case. Is designed to detect a wide range of limb movements related to sleep/wake behavior. Sensitive to movements in the 0.5- to 7-Hz frequency range. Firmware detects the peak value of 32 samples in a 1-s window and adds this to the accumulated value for that epoch.; Waterproof.	Sedentary: Nintendo, arts and crafts, playtime 1; Light activities: aerobic warm-up, walk 1; Moderate activities: Tae Bo exercises, playtime 2, walk 2 Vigorous activity: Jogging.	Room respiration calorimetry	Puyau et al. [17]; Hip: AEE (J⋅kg^−1⋅min^−1) = 0.0144 + 0.000038 hip (counts) → SEE 0.0147 → 𝑟^2(adj) 81%; Fibula head: AEE (J⋅kg^−1⋅min^−1) = 0.0143 + 0.000020 leg (counts) → SEE 0.0195 → 𝑟^2(adj) 71%; Predicting AEE from the combination of the counts from the hip and leg increased the 𝑟^2(adj) to 84%.; Regression of AEE on counts was independent of gender and age, thus only counts were included in the model.
	Playing Nintendo, using a computer, cleaning, aerobic exercise, ball toss, treadmill walking and running.	Room respiration calorimetry 4 h, Indirect calorimetry 1 h.	Puyau [10]; Hip: AEE (kcal⋅kg^−1⋅min^−1) = 0.00441 + 0.00032^∗Actiwatch^0,724 → 𝑟^2 0.79, SEE 0.0117; Counts, age and height were included in the model, inclusion of gender gave no significant improvement.
Caltrac accelerometer (Muscle Dynamics Fitness, Madison, Wis, USA).; Measures the degree and intensity of movement in the vertical plane.	Free-living; Three days, including one weekend day. The subjects began wearing the Caltrac upon waking in the morning and continued until just before going to sleep at night. The Caltrac was taken off for activities involving water, such as swimming or bathing.	Doubly labelled water	Johnson et al. [16]; Hip: AEE (kcal⋅d) = 63.97+ (284.962 × gender) − (17.671 × race) + (12.876 × FM) − (6.18 × FFM) → 𝑅^2 = 0.28, 𝑃=.06, SSE±315; Race: Caucasian = 0, Mohawk = 1; When the three-day mean AC was forced into the model, the amount of variation in AEE was explained, did not increase significantly 𝑅^2 = 0.29, 𝑃=.12, SSE = ±321
RT3 accelerometer (Stayhealthy, Monrovia, CA). The instrument measures the acceleration in three dimensions: anterior-posterior (x), medio-lateral (y), and vertical (z) directions. Activity counts is the square root of the sum of the squared accelerations of each direction.	Indoor: laying down, sitting relaxed, writing, standing relaxed, sitting and standing (alternating every 5 s), cycling, stepping up and down, walking. The speed of treadmill was predetermined so that most children could complete jogging on the treadmill.; Outdoor: picking up tennis balls, and then standing up, catching and passing a basketball, kicking a soccer ball, shooting a basketball while walking, walking relaxed nonlinearity, jogging lightly, and jogging fast.	Indirect calorimetry	Sun et al. [18]; The RT3 was placed at the waist/midline thigh.; Indoor activities: AEE (kcal⋅min^−1) = 0.0006359 (counts⋅min^−1) −0.0006427 (body weight) + 0.733; (Activity counts is the square root of the sum of the squared accelerations of each direction); 𝑟=.95 (𝑅^2 =.90), 𝑃=.001.; B&A: mean error 0.94 kcal⋅min^−1, 95% confidence interval = (−1.83,2.77) kcal⋅min^−1.; Outdoor activities: AEE (kcal⋅min^−1) = 0.00030397 (counts⋅min^−1) + 0.00586272 (body weight) + 0.58; 𝑟=.78 (𝑅^2 =.61), 𝑃<.001.; B&A: mean error −1.66 kcal⋅min^−1, 95% confidence interval (−3.2, 1.57) kcal⋅min^−1.

Abbreviations: AC: Accelerometer Counts, adj.: adjusted, AEE: Activity related Energy Expenditure, B&A: Bland & Altman, bpm: beats per minute, CI: Confidence Interval, FFM: Fat Free Mass, FM: Fat Mass, g: gram, h: hour, Hz: hertz, J: Joule, kcal: Kilocalorie, kg: kilogram, min: minute, r= correlation coefficient, RMSE: Root Mean Squared Error, SEE: Standard Error of the Estimate, SSE: Sum of Squared Errors.