Reexamination of Accelerometer Calibration with Energy Expenditure as Criterion: VO2net Instead of MET for Age-Equivalent Physical Activity Intensity

Accelerometer calibration for physical activity (PA) intensity is commonly performed using Metabolic Equivalent of Task (MET) as criterion. However, MET is not an age-equivalent measure of PA intensity, which limits the use of MET-calibrated accelerometers for age-related PA investigations. We investigated calibration using VO2net (VO2gross − VO2stand; mL⋅min−1⋅kg−1) as criterion compared to MET (VO2gross/VO2rest) and the effect on assessment of free-living PA in children, adolescents and adults. Oxygen consumption and hip/thigh accelerometer data were collected during rest, stand and treadmill walk and run. Equivalent speed (Speedeq) was used as indicator of the absolute speed (Speedabs) performed with the same effort in individuals of different body size/age. The results showed that VO2net was higher in younger age-groups for Speedabs, but was similar in the three age-groups for Speedeq. MET was lower in younger age-groups for both Speedabs and Speedeq. The same VO2net-values respective MET-values were applied to all age-groups to develop accelerometer PA intensity cut-points. Free-living moderate-and-vigorous PA was 216, 115, 74 and 71 min/d in children, adolescents, younger and older adults with VO2net-calibration, but 140, 83, 74 and 41 min/d with MET-calibration, respectively. In conclusion, VO2net calibration of accelerometers may provide age-equivalent measures of PA intensity/effort for more accurate age-related investigations of PA in epidemiological research.


Introduction
The use of accelerometers to measure physical activity (PA) in research have expanded tremendously since the millennium shift. An essential component of PA is the intensity performed, as PA intensity is related to the health benefits achieved [1]. Therefore, it is crucial that accelerometers provide accurate measures of PA intensity, which commonly involves determining time spent in Sensors 2019, 19, 3377 3 of 14 adults produced similar accelerometer outcomes from hip recordings for the same absolute movement speed. This indicates that an accelerometer placed at the hip would capture total mechanical work in both children and adults, which would be identical at the same Speed abs [11,17]. The measurement error with the ActiGraph counts may have contributed to the confusion of the METs in the calibration of accelerometers, where children demonstrated both lower METs and lower counts than adults at the same Speed abs . In fact, children should have demonstrated lower METs but similar counts at the same Speed abs . These different outcomes would have contributed to different calibration equations and cut-points for PA intensity. While the comparability of accelerometer measures of PA intensity by age has been investigated for the hip placement, less is known about the thigh placement [17][18][19]. The thigh placement offers additional possibilities for assessment of sedentary time (sitting, standing), biking (i.e., cadence) as well as non-wear time.
Therefore, the aim of the present study was to investigate the calibration of hip and thigh accelerometers in children and adults using VO 2net (VO 2gross − VO 2stand ) as criterion for absolute PA intensity and the effect on assessment of free-living PA. With the application of a novel calibration procedure, this study may contribute to improve the assessment of PA intensity in children and to establish a measure of PA intensity equivalent by age.

Study Design
Two sub-studies were performed:

1.
A calibration study including sit, stand, walk and run on a treadmill wearing accelerometers at the hip and thigh and with measured oxygen consumption to develop accelerometer cut-points for PA intensity.

2.
Investigation of free-living PA in children, adolescents and adults comparing application of VO 2net (VO 2gross − VO 2stand ) cut-points to standard MET cut-points.

Samples
Participants in the first sub-study were 10 children 9-11 years old, 10 adolescents 14-16 years old and 10 adults 23-44 years old. They were recruited among staff and students and their children by written and verbal information at the Department of Food and Nutrition, and Sport Science in Sweden and among their friends and children [17]. All participants provided informed consent and the protocol was approved by the ethical committee at the University of Gothenburg.
The second sub-study used Swedish data collected in the European I.Family study (EC: FP7, No. 266044) [20], which is an extension of the IDEFICS study (EC: FP6, No. 016181) investigating children's health, as well as data collected in the LIV2013 study of adult's health in Sweden [21]. The I.Family sample consisted of 417 Swedish children and adolescents (50% female) with a mean (SD) age of 10.9 (2.4) years, the range being 4-16 years. The LIV2013 study consisted of 735 Swedish adults (24% female) with a mean (SD) age of 48.4 years (11.6), the range being 21-67 years. The participants in these studies have provided informed consents and the studies have been approved by the ethical committees.

Calibration Study
The calibration study was performed in the biomechanical-physiological lab at the Center for Health and Performance, Gothenburg, Sweden. The participants were asked to refrain from food intake and strenuous PA 3-4 h prior to measurements. Body weight and height were measured and one Axivity AX3 triaxial accelerometer (Axivity Ltd., Newcastle upon Tyne, UK) was attached over the right hip in an elastic belt around the waist and another at the middle of the front side of the right thigh using medical tape. The accelerometers were set to record data at a sample rate of 100 Hz and an acceleration range of ±8 g and the raw triaxial data was extracted with the OmGUI software (Axivity Ltd., Newcastle upon Tyne, UK). Oxygen consumption was measured using the stationary metabolic system Oxycon Pro (Jaeger, BD Corporation, Franklin Lakes, NJ, USA) where the participants breath through a face-mask with a turbine flow meter and expired air-sampler. Oxycon Pro has shown high accuracy when evaluated with the Douglas bag method [22]. The activities included consisted of seated rest in an armchair for 20 min to determine resting energy expenditure (REE) followed by 4 min standing, walking at 3, 4, 5 and 6 km·h −1 and running at 8 and 10 km·h −1 on a treadmill during 4 min at each speed without interruption, in order to reach steady-state [23]. VO 2 data was collected during all 20 min and respective 4 min activities.
The triaxial acceleration data were processed using our new algorithm to produce a measure of PA intensity expressed in mg, including a band-pass filter with the cut-point range of 0.29-10 Hz that was shown to include all relevant information to assess activity intensity and to minimize inclusion of noise [17,18]. However, acceleration data was down-sampled to 30 Hz and truncated to ±6 g before processing to match the corresponding ranges of the ActiGraph GT3X+ accelerometer used in the free-living measurements. VO 2 data from the 20 min of resting was filtered with a moving average filter with a window size of 2 min and the minimum value was considered the individual REE. One minute of data (accelerometer, VO 2 ) captured between duration 2:45 and 3:45 at standing and at each treadmill speed was used for calibration. VO 2net was calculated by subtracting VO 2stand from VO 2gross divided by body weight (mL·min −1 ·kg −1 ), while MET-values were calculated by the quotient of the VO 2gross and VO 2rest .
In each age-group, the relationships between Speed abs and accelerometer output (mg), Speed abs and VO 2net and Speed abs and MET were investigated, as well as the relationship between Speed eq and VO 2net and Speed eq and MET. The Speed eq was calculated as Speed eq = V 2 ·g −1 ·h −1 (V = Speed abs (m·s −1 ), g = gravity (9.81 m·s −2 ), h = body height (m)), and represent the Speed abs performed with similar kinematical effort in individuals of different body size [8,9,15]. Smoothing splines were fitted to the data from each age group, with the intercept forced to zero VO 2net or 1 MET, and zero acceleration. Based on previous biomechanical and physiological research, we made the following assumptions:

•
The three age-groups fall on the same regression line between Speed abs and hip accelerometer output, as the hip accelerometer represents total mechanical work which would be the same for the same Speed abs in the three age-groups [10,11,17].

•
The three age-groups would have less similarity in the regression line between Speed abs and thigh accelerometer output, as the mechanical work of moving the limbs is higher in shorter than taller individuals [10,11,17].

•
The three age-groups would fall on the same regression line between Speed eq and VO 2net , if VO 2net represent the same effort in the age-groups.

•
The three age-groups would fall on different regression lines between Speed eq and MET, if MET does not represent the same effort in the age-groups.

•
The three age-groups would fall on different regression lines between VO 2net and accelerometer output, if the same VO 2net in the age-groups would mean the same Speed eq and therefore the same effort, but at the same time lower Speed abs in shorter individuals and correspondingly lower mechanical work and accelerometer output.
MET cut-points at 1.5, 3.0, 6.0 and 9.0 were implemented to represent LPA, MPA, VPA and very vigorous PA (VVPA), respectively, which is in line with previous literature [12]. To calibrate accelerometer data to VO 2net , the first step was to determine the VO 2net corresponding to 3.0, 6.0 and 9.0 METs in adults by linear regression. The next step was to apply the same VO 2net cut-points (and therefore the same effort) to all three age-groups to calibrate the corresponding accelerometer mg cut-points based on fitted smoothing splines. For comparison, accelerometer mg cut-points were also determined using the traditional 1.5, 3.0, 6.0 and 9.0 METs in all three age-groups.

Free-Living Study
In both the I.Family study and the LIV2013 study the ActiGraph GT3X+ (ActiGraph, Pensacola, FL, USA) was used to collect acceleration data and was worn over the right hip in an elastic belt around the waist. The participants were instructed to wear the accelerometer for seven days and to remove it during sleep and during water-based activities. The accelerometer was set to record acceleration data at 30 Hz sampling rate with an acceleration range of ±6 g and idle sleep mode were enabled. The raw triaxial data was extracted according to available file specifications [24].
Raw triaxial data was processed using our new algorithm to produce a measure of PA intensity expressed in mg including a band-pass filter with the cut-point range of 0.29-10 Hz [17,18]. The epoch-length was set to 3 s to capture children's activities as well as intermittent activities in adults [18]. Valid days with at least 12 h were included in the analyses. Samples in which the sensor status was idle according to the idle sleep-mode were considered non-wear time. More subjects in the adult group wore the accelerometer during sleep compared to the children; therefore, the acceleration recorded between 23:00-06:00 was not included in the analysis. Our previous research has confirmed that processing of GT3X+ data and AX3 data generate similar output [16].
Accelerometer mg cut-points for LPA, MPA, VPA and VVPA from the VO 2net -based calibration and the standard MET-based calibration were applied. The participants were divided into four age-categories: Children (<13 years, n = 321 (50% female), adolescents (13-16 years, n = 96 (50% females)), younger adults (<50 years, n = 366 (75% female)) and older adults (≥50 years, n = 369 (68% female)). The time distribution in the intensity categories was compared between the age-categories with the VO 2net -based calibration versus the MET-based calibration. As the VO 2net -based calibration would imply lower Speed abs and mechanical work in children and adolescents compared to the MET-based calibration, and consequently lower accelerometer mg cut-points, we assume more free-living PA in these age groups applying the VO 2net -based accelerometer mg cut-points.
All data processing and analyses in the two sub-studies were performed in MATLAB 2018b (MathWorks, Natick, MA, USA). Figure 1 presents the relationship between Speed abs and the accelerometer output. It demonstrates that the three age-groups fall approximately on the same regression line for hip data, while children show higher values compared to the other age-groups for the thigh placement. These results confirm our assumptions of similar mechanical work captured with the hip placement and less similarity with the thigh placement. Figure 2 present the relationship between Speed abs and VO 2net and between Speed eq and VO 2net , respectively. It shows that while children have higher VO 2net than the other age-groups for the same Speed abs , there was approximately one common regression line with the Speed eq . VO 2net may therefore be considered a measure of similar effort in different age-groups according to our assumption. Figure 3 display the relationship between Speed abs and MET and between Speed eq and MET, respectively. The MET-values differ between the three age-groups for both Speed abs and Speed eq , which confirms the assumption that MET is not a measure of effort comparable between age-groups. Figure 1 presents the relationship between Speedabs and the accelerometer output. It demonstrates that the three age-groups fall approximately on the same regression line for hip data, while children show higher values compared to the other age-groups for the thigh placement. These results confirm our assumptions of similar mechanical work captured with the hip placement and less similarity with the thigh placement.   Figure 2 present the relationship between Speedabs and VO2net and between Speedeq and VO2net, respectively. It shows that while children have higher VO2net than the other age-groups for the same Speedabs, there was approximately one common regression line with the Speedeq. VO2net may therefore be considered a measure of similar effort in different age-groups according to our assumption.  Figure 3 display the relationship between Speedabs and MET and between Speedeq and MET, respectively. The MET-values differ between the three age-groups for both Speedabs and Speedeq, which confirms the assumption that MET is not a measure of effort comparable between age-groups.   Figure 2 present the relationship between Speedabs and VO2net and between Speedeq and VO2net, respectively. It shows that while children have higher VO2net than the other age-groups for the same Speedabs, there was approximately one common regression line with the Speedeq. VO2net may therefore be considered a measure of similar effort in different age-groups according to our assumption.  Figure 3 display the relationship between Speedabs and MET and between Speedeq and MET, respectively. The MET-values differ between the three age-groups for both Speedabs and Speedeq, which confirms the assumption that MET is not a measure of effort comparable between age-groups.   Figure 4 presents the relationship between MET and the corresponding VO 2net . It is the starting-point to determine the VO 2net cut-points for LPA (1.5 METs), MPA (3.0 METs), VPA (6.0 METs) and VVPA (9.0 METs) based on adult data. If the same MET-values had been applied to the children and adolescent groups, considerable higher VO 2net -values (and effort) had been used for accelerometer calibration in these age-groups.  Figure 4 presents the relationship between MET and the corresponding VO2net. It is the startingpoint to determine the VO2net cut-points for LPA (1.5 METs), MPA (3.0 METs), VPA (6.0 METs) and VVPA (9.0 METs) based on adult data. If the same MET-values had been applied to the children and adolescent groups, considerable higher VO2net-values (and effort) had been used for accelerometer calibration in these age-groups. The next step was to apply the common VO2net cut-points to all three age-groups to determine the corresponding accelerometer mg values ( Figure 5). The three age-groups achieved different regression lines, with the lowest accelerometer cut-points observed in children. Hence, when moving with the same effort, the three age-groups move at different Speedabs and consequently do different mechanical work. Still, there were some overlapping between the age-groups.  The next step was to apply the common VO 2net cut-points to all three age-groups to determine the corresponding accelerometer mg values ( Figure 5). The three age-groups achieved different regression lines, with the lowest accelerometer cut-points observed in children. Hence, when moving with the same effort, the three age-groups move at different Speed abs and consequently do different mechanical work. Still, there were some overlapping between the age-groups.  Figure 4 presents the relationship between MET and the corresponding VO2net. It is the startingpoint to determine the VO2net cut-points for LPA (1.5 METs), MPA (3.0 METs), VPA (6.0 METs) and VVPA (9.0 METs) based on adult data. If the same MET-values had been applied to the children and adolescent groups, considerable higher VO2net-values (and effort) had been used for accelerometer calibration in these age-groups. The next step was to apply the common VO2net cut-points to all three age-groups to determine the corresponding accelerometer mg values ( Figure 5). The three age-groups achieved different regression lines, with the lowest accelerometer cut-points observed in children. Hence, when moving with the same effort, the three age-groups move at different Speedabs and consequently do different mechanical work. Still, there were some overlapping between the age-groups.  In contrast, when MET-based cut-points were applied, the adults achieved the lowest accelerometer values ( Figure 6). Table 1 provides the numerical values of the VO 2net -based and the MET-based cut-points for LPA, MPA, VPA and VVPA for the two body placements in the three age-groups, expressed in mg. In contrast, when MET-based cut-points were applied, the adults achieved the lowest accelerometer values (Figure 6). Table 1 provides the numerical values of the VO2net-based and the MET-based cut-points for LPA, MPA, VPA and VVPA for the two body placements in the three agegroups, expressed in mg.

Free-Living Study
The results from the free-living study shows that when applying the VO2net calibration, there was a considerable increase in the time being physically active in children and adolescents compared with application of the standard MET calibration ( Table 2). For example, the time spent in moderate-andvigorous PA (MVPA = MPA + VPA + VVPA) accounted for 13.8% of the wear-time in children and 8.1% in adolescents with the MET calibration, but increased to 21.2% and 11.2%, respectively, with

Free-Living Study
The results from the free-living study shows that when applying the VO 2net calibration, there was a considerable increase in the time being physically active in children and adolescents compared with application of the standard MET calibration ( Table 2). For example, the time spent in moderate-and-vigorous PA (MVPA = MPA + VPA + VVPA) accounted for 13.8% of the wear-time in children and 8.1% in adolescents with the MET calibration, but increased to 21.2% and 11.2%, respectively, with the VO 2net calibration. Consequently, the difference in MVPA between children and adolescents versus adults increases. As an example, with the standard MET calibration the difference Sensors 2019, 19, 3377 9 of 14 in MVPA between children and younger adults is 6.5% units, while with the VO 2net calibration it is 13.9% units. In daily minutes, the difference corresponds to 66 min and 142 min, respectively.
As the VO 2net cut-points are determined from the MET-values for the different intensity levels in adults (i.e., 1.5, 3.0, 6.0 and 9.0), there will be no difference in the accelerometer cut-points in adults applying VO 2net calibration vs. MET calibration. Consequently, the time spent in the different intensity levels does not differ between VO 2net calibration vs. MET calibration in adults. Children include the age-range 4-12 years, adolescents 13-16 years, and the adult group was divided into younger adults (<50 years, range 21-49 years) and older adults (≥50 years, range 50-67 years).

Discussion
The novelty of this study is to propose a criterion method (VO 2net , mL·kg −1 ·min −1 ) to calibrate accelerometer PA intensity measures equivalent by age based on data collected at the hip and at the thigh. It was applied to our improved processing of acceleration data [16][17][18][19] to generate new cut-points for LPA, MPA, VPA and VVPA in children, adolescents and adults. These outcomes were supported by the finding that the relationship between Speed eq and VO 2net (VO 2gross − VO 2stand ) was similar in children, adolescents and adults, indicating that VO 2net is a measure of similar effort in the three age-groups, in contrast to the more commonly used MET in accelerometer calibration which was not a measure of PA intensity equivalent by age. When our new cut-points for PA intensity levels were applied to free-living acceleration data from the hip, the difference in PA between children, adolescents and adults increased compared to the application of the standard MET-based cut-points. The importance of the findings in this study is to allow the possibility to directly relate the PA intensity level between age-groups and thereby more accurately investigate the age-related changes in PA from childhood into adulthood and associated factors. A larger decline in PA from childhood into adults may be expected compared to what is anticipated from previous research.
Two individuals of different body size perform an activity with different movement patterns. A short individual takes shorter steps with smaller acceleration amplitude but at higher frequency, while the taller individual takes longer steps with larger acceleration amplitude but at lower frequency [10,11,17]. Biomechanical theory demonstrates that the total mass-specific mechanical work is the same in short and tall individuals moving at the same Speed abs , but that the shorter individual generates more internal work related to the higher frequency of moving the limbs while the taller individual generates more external work related to the movement of the center of mass [10,11]. Consequently, one would expect an accelerometer placed at the hip to generate higher values in the taller individual while the opposite would occur with the placement on the thigh. Interestingly, our results ( Figure 1A) show that the hip placement generates similar accelerometer output for the same Speed abs in children, adolescents and adults, indicating that all the acceleration signals captured represent total mechanical work. Hence, an accelerometer placed at the hip can be used to compare the total mechanical work performed between age-groups. Instead, the thigh placement generated higher accelerometer output in the children compared to the other groups ( Figure 1B), indicating that this placement captures more internal work which is not comparable between age-groups. In contrast to the results herein, the original ActiGraph counts from hip recordings are lower in children than in adults for the same Speed abs [25,26], while the opposite occur with the Euclidian Norm Minus One (ENMO) accelerometer output [27]. Consequently, none of these methods provide measures of mechanical work equivalent by age. In the case of the ActiGraph counts, this age difference is caused by a well-defined processing error [16]. In the case of the ENMO accelerometer output, it may be a processing error less clearly defined. With the ENMO method, all negative accelerations are set to zero after subtracting 1 g from the vector magnitude [27]. This means that acceleration signals generated with larger amplitude but at lower frequency (as in adults) will be excluded to larger extent compared to acceleration signals with a lower amplitude but at a higher frequency (as in children). In contrast, the ActiGraph counts and the accelerometer method developed in our research group are aggregations of both positive and negative accelerations.
Even if an accelerometer placed at the hip would capture total mechanical work at the same Speed abs , the activity is performed with different effort and energy cost in children compared to adults ( Figure 2A) [8,9], and therefore has different physiological loads/health effects on the body. Consequently, an accelerometer output needs to be calibrated against a criterion measure of equivalent effort/load by age. The MET was developed to provide a criterion measure of absolute PA intensity. Our study showed that the MET was not equivalent by age as different values were achieved in children, adolescents and adults for the same Speed abs and Speed eq (Figure 3). If we compare the results in Figures 5 and 6, we clearly see the consequence of applying the MET-based accelerometer calibration: Higher accelerometer cut-points are set for younger individuals to reach MPA, VPA and VVPA, when they are actually performing the activity at these PA intensity levels with a higher degree of effort according to the Speed eq ( Figure 3B) and with a higher energy cost according to the VO 2net (Figure 4) compared to the older individuals. This calibration error will contribute to the underestimation of the PA in children relative to adults.
Alternative criterion measures of PA intensity equivalent by age have been investigated, for example mass-specific VO 2gross (mL·kg −1 ·min −1 ), VO 2net (VO 2gross − VO 2rest , mL·kg −1 ·min −1 ) and VO2 allom (mL·kg −0.75 ·min −1 ) [14]. None of the measures was optimal for the PA intensity range. The allometric scaling seems to work well for ambulatory activities and the MVPA intensity range [14] and has previously been proposed as an accurate criterion measures for accelerometer calibration [28]. We based our choice of VO 2net (VO 2gross − VO 2stand , mL·kg −1 ·min −1 ) on that this measure captures the dynamic movement only and therefore matches the dynamic acceleration captured by an accelerometer. Although, previous research has shown a remaining difference by age when this measure was related to Speed eq . For example, at Speed eq = 0.3, the VO 2net was about 230 and 200 mL·kg −1 ·km −1 in children and adults, respectively [8]. We also observed some fluctuations in the difference between the age-groups across Speed eq range ( Figure 2B), but the relevance of these small differences and those found in the study by McCann et al. [8] is unclear and requires further investigations. We still find our results to provide a strong indication of VO 2net as a criterion measure of PA activity intensity equivalent by age and suitable for accelerometer calibrations.
A limitation with the VO 2net measure is that there are no established PA intensity cut-points as for the MET measure (i.e., 3.0 and 6.0 METs). We based our calibration procedure on the adult MET-values and cut-points for LPA, MPA, VPA and VVPA (Figure 4), as the MET as a measure of absolute PA intensity was initially developed in adults [29], and translated them to the corresponding VO 2net . The same VO 2net cut-points were thereafter applied to all three age-groups to represent PA intensity levels equivalent by age and used for the accelerometer calibration ( Figure 5). As children, adolescents and adults produce the same total mechanical work at the same Speed abs [10,11], which is captured by an accelerometer at the hip ( Figure 1A), and as VO 2net differs between these age-groups at the same Speed abs (Figure 2A) due to different efforts related to step frequency [10,11] but is similar at the same Speed eq (Figure 2B), these age-groups will present different regression lines between VO 2net and the accelerometer output and consequently also different accelerometer cut-points (children < adolescents < adults). The somewhat smaller difference in the VO 2net -acceleration regression lines between the age-groups with the thigh placement ( Figure 5) is explained by differences in the accelerometer output, which is supported by the biomechanical literature showing that smaller individuals produce more internal work [10,11] and consequently more thigh acceleration. Our calibration procedure requires knowledge about speed of movement. An alternative procedure embraced in calibration and validation studies, is to let the participants perform walking and running at a self-selected pace not involving the measurement of movement speed [13]. It is possible that the self-selected paces correspond to the same Speed eq in different age-groups. The accelerometer calibration research field has postulated that a variety of activity types (including intermittent) should be included in calibration protocols to provide calibration algorithms representative of people's daily activity pattern [30], not only walking and running. Still, that protocol would include activities where the steady-state is not easily attained in order to accurately assess the oxygen consumption of an activity [23], which is the case for protocols including only continuous walking and running as in the present study.
The contribution of our study can be exemplified based on two large epidemiological studies where the PA has been compared between children and adults. Cross-sectional analyses of accelerometer data from the National Health and Nutrition Examination Survey (NHANES) have shown that boys and girls 6-11 years old spend 95 and 75 min daily in MVPA, respectively, while men and women 40-49 years old attained 35 and 19 min, respectively [2]. Longitudinal analyses of accelerometer data in the European Youth Heart Study between ages 9 and 15 years old demonstrated a decline in MVPA from 100 to 52 min daily in Swedish boys and from 73 to 44 min daily in Swedish girls [4]. In another sample in this study, there was a decline between ages 15 and 21 years old from 68 to 58 min daily in Swedish males and from 46 to 40 min daily in Swedish females. These studies used MET-based accelerometer cut-points for MPA and VPA, applying similar (3.0 and 6.0 METs) or higher (4.0, 7.0 vs. 3.0, 6.0 METs) MET-values in children compared to adults. Consequently, higher demands were required from the children to reach MPA or VPA than in the adults. Further, the acceleration data was processed to the original ActiGraph counts with its limitations to assess PA intensity [16][17][18][19]. In addition, the aggregation of the acceleration data was performed into 60 s epochs, which would be insensitive to the movement pattern of children [1]. The application of our improved processing of accelerometer data [17,18] and calibration procedure presented herein together with the use of 3 s epochs would have demonstrated a larger decline in MVPA from childhood into adulthood. Consequently, there may have been an underestimation of the change in the risk of future cardiometabolic disease in those studies.
A further complication with the widely adopted 3.0 MET cut-point is that it may have been set too low to accurately represent MPA in the general population. The American College of Sports Medicine Position Stand classify 4.8-7.1 METs and 4.0-5.9 METs as MPA in young respective middle-aged adults [31]. Further, 3.0 METs was already reached at comfortable walking by all age-groups in the present study as well as in other studies of children and adults [6,7,13,14]. Consequently, people would be considered physically active too easily. This issue requires further discussion to be settled, but a higher cut-point for MPA might be considered in investigations of the general population.
The present study has several strengths and limitations. Raw acceleration data were processed with algorithms improving assessment of PA intensity [17,18]. Further, short 3 s epochs were applied to improve assessment of children's PA pattern [1] as well as intermittent PA. Calibration of activity intensity cut-points was performed on a treadmill with four minutes at each speed. Previous studies with other accelerometers have showed inconsistent results concerning the impact of setting (treadmill vs. ground) on accelerometer output [32,33]. Calibration performed with walking and running on a treadmill may not be applicable to other types of activities. As we have commented on earlier in the discussion section, using oxygen consumption as criterion measure of PA intensity requires steady-state of oxygen consumption data [23]. Still, the steady-state requirement may be a challenge as a large part of free-living PA does not fulfill it. The present calibration included less data points in the VPA range (see Figure 5) compared to the MPA and VVPA ranges which may affect the precision of resultant regression lines and cut-points. The calibration sample age-range of 9-44 years did not fully represent the free-living sample age-range of 4-67 years, which may affect the results of the free-living stub-study.

Conclusions
We propose VO 2net (VO 2gross − VO 2stand , mL·kg −1 ·min −1 ), instead of MET (VO 2gross /VO 2rest ), to be a criterion measure for accelerometer calibration in children, adolescents and adults. This conclusion is based on the finding that these age-groups showed similar relationship between Speed eq and VO 2net , and consequently VO 2net may be considered a measure of absolute PA intensity equivalent by age. The same similarity between the age-groups was not found for the relationship between Speed eq and MET. New VO 2net -based accelerometer cut-points were developed and when they were applied to free-living data, the difference in PA between children, adolescents and adults was increased compared to applying MET-based accelerometer cut-points. The implications of these findings are that PA can now be directly compared between age-groups in epidemiological research to investigate changes in PA behaviors from childhood into adulthood and associated factors related to risk for cardiometabolic disease. We contribute with new accelerometer cut-points for absolute PA intensity for the hip and thigh placement in children, adolescents and adults (Table 1), to be applicable to accelerometer output generated from raw triaxial acceleration data [17,18]. The algorithms for processing the raw acceleration data are available by request to the authors. Still, this is a small and explorative study and further research is needed to evaluate the robustness of the VO 2net calibration method proposed.