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Accelerometry data in health research: challenges
and opportunities
Review and examples
Marta Karas ·Jiawei Bai ·Marcin
Strączkiewicz ·Jaroslaw Harezlak ·
Nancy W. Glynn ·Tamara Harris ·
Vadim Zipunnikov ·Ciprian
Crainiceanu ·Jacek K. Urbanek
Received: date / Accepted: date
Marta Karas
Department of Biostatistics
Bloomberg School of Public Health
Johns Hopkins University
Tel.: +1-317-665-4551
E-mail: mkaras@jhu.edu
Jiawei Bai
Department of Biostatistics
Bloomberg School of Public Health
Johns Hopkins University
Marcin Strączkiewicz
Department of Epidemiology and Biostatistics
School of Public Health
Indiana University Bloomington
Jaroslaw Harezlak
Department of Epidemiology and Biostatistics
School of Public Health
Indiana University Bloomington
Nancy W. Glynn
Center for Aging and Population Health
Department of Epidemiology
Graduate School of Public Health
University of Pittsburgh
Tamara Harris
Laboratory of Epidemiology Demography, and Biometry
National Institute on Aging
Vadim Zipunnikov
Department of Biostatistics
Bloomberg School of Public Health
Johns Hopkins University
Ciprian Crainiceanu
Department of Biostatistics
Bloomberg School of Public Health
.CC-BY-NC-ND 4.0 International licensenot peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was. http://dx.doi.org/10.1101/276154doi: bioRxiv preprint first posted online Mar. 5, 2018;
2 Marta Karas et al.
Abstract Wearable accelerometers provide detailed, objective, and continu-
ous measurements of physical activity (PA). Recent advances in technology
and the decreasing cost of wearable devices led to an explosion in the popula-
rity of wearable technology in health research. An ever increasing number of
studies collect high-throughput, sub-second level raw acceleration data. In this
paper we discuss problems related to the collection and analysis of raw acce-
lerometry data and provide insights into potential solutions. In particular, we
describe the size and complexity of the data, the within- and between-subject
variability and the effects of sensor location on the body. We also provide a
short tutorial for dealing with sampling frequency, device calibration, data
labeling and multiple PA monitors synchronization. We illustrate these po-
ints using the Developmental Epidemiological Cohort Study (DECOS), which
collected raw accelerometry data on individuals both in a controlled and the
free-living environment.
Keywords Wearable computing ·Accelerometry ·Wearable accelerometers ·
Physical activity ·Accelerometers
1 Introduction
Wearable physical activity (PA) monitors provide detailed, continuous, and
objective measurements of individual PA in the free living environment. They
can complement or completely replace current subjective measurements col-
lected via questionnaires. Recent advances in technology and the decreasing
cost of wearable devices led to an explosion in the popularity of wearable tech-
nology in health research. Here we argue that, just like any new measurement
used in health science, there is a need to understand, reproduce, and com-
municate the measurements produced by these new devices. This can lead to
improved design of experiments, higher quality of the acquired data, and more
generalizable results. At the core of all modern PA monitors there is a small
accelerometer, a Microelectromechanical system (MEMS) that measures ac-
celerations relative to the Earth’s gravitational field. Hence, PA monitors are
often referred to as wearable accelerometers. The output of these devices is a
three-dimensional time series of accelerations expressed in gravitational units
in the frame of reference of the device. More clearly, the device has its own fra-
me of reference up-down, left-right, backward-forward. This frame is typically
different from and can change with the frame of reference of the person who
wears the device or who observes the experiment. These raw data produced by
Johns Hopkins University
Jacek K. Urbanek
Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Department of Medicine
School of Medicine
Johns Hopkins University
E-mail: jurbane2@jhu.edu
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Accelerometry data in health research: challenges and opportunities 3
accelerometers are transformed using various algorithms into PA summaries,
which have different labels (e.g. steps, calories, activity counts) and can be
aggregated at different temporal resolutions (e.g. minutes, hours, or days).
Due to battery and memory limitations, PA monitors used to return only
aggregated minute-level data in the form of proprietary activity counts (AC)
(Chen et al, 2012). The definition of ACs varies between- and within-device
manufacturers, across time, body location and between studies. Despite the-
se initial problems, they have been used effectively as a relative measure of
PA within the same study, especially when the same devices and software we-
re used and devices were calibrated (Matthews et al, 2008; Healy et al, 2011;
Schrack et al, 2014; Xiao et al, 2015). As battery and memory limitations have
been mitigated, it has become possible to collect and store high-throughput,
three-axial, sub-second level acceleration data, ranging between 10 and 200
observations per second. PA monitors have also become increasingly sophi-
sticated and are now routinely equipped with a selection of supplementary
sensors including gyroscopes, thermometers, inclinometers, pulsometers, light
intensity and skin conductance sensors. Data collected by these supplementary
sensors are beyond the scope of this paper.
The collection of raw accelerometry data opens a spectrum of new scientific
and analytic problems. For example, researchers do not need to rely on proprie-
tary aggregated measures and can use well-defined, open-source, reproducible
summaries of the data. This allows to compare and combine studies that col-
lect raw accelerometry data at the same location on the body and provides
explicit measures of activity on a recognized measurement scale. For example,
UKBiobank (Doherty et al, 2017) uses the magnitude of the 3-dimensional
vector of acceleration summarized in 5-second intervals, whereas the Women’s
Health Initiative (WHI) study has explored 1-second summaries based on stan-
dard deviations of accelerometry along each axis (Bai et al, 2016). Raw and
summarized data have also been used for recognition of activity types. A com-
mon approach is to derive accelerometry data features in a particular window
and use supervised classification approaches to predict activity type (Pober
et al, 2006; Staudenmayer et al, 2009; Attal et al, 2015). Extensive reviews of
classification techniques for activity recognition from accelerometry data are
provided by Bao and Intille (2004) and Preece et al (2009). Dictionary learning
based on raw accelerometry Bai et al (2012); He et al (2014); Xiao et al (2016)
has also been proposed in the context of fine-resolution movement prediction.
The increased granularity of the sub-second level data may contain impor-
tant additional information, but it also creates new challenges. Indeed, the
volume and structure of the data are much more complex for the raw da-
ta, especially when it is recorded for weeks at a time in free-living settings.
In this paper we discuss problems related to the collection and analysis of
sub-second level accelerometry data. To illustrate these problems, we use data
collected as a part of Developmental Epidemiological Cohort Study (DECOS)
in a controlled and in the free-living environment.
Some of these problems have been well documented in the literature. For
example, Trost et al (2005) highlighted problems associated with device se-
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4 Marta Karas et al.
lection, placement of accelerometers, epoch length, and compliance enhancing
strategies. Schrack et al (2016) discussed the limitations of using uncalibrated,
population-level data extraction algorithms in older adults. Staudenmayer et al
(2012) and Troiano et al (2014) noted that the diversity of measurements and
analytic methods for accelerometer data makes it difficult to compare results
across different studies, and advocate for standardization of measurement and
pre-processing pipelines across studies.
Currently, there is no universally accepted and standardized approach for
measuring PA using wearable accelerometers in health research. However, so-
me excellent guidelines and standardized protocols have been published. For
example, Matthews et al (2012) compiled a list of best practices for making
decisions about important choices, such as the number of monitors needed, de-
vice placement, device initialization, device tracking, and data collection. They
also provide guidance on how to report the use of PA monitors in population-
based studies. Freedson et al (2012) provided recommendations for the use
of wearable monitors for assessing PA for researchers, end users, as well as
developers of activity monitors. The authors also provide guidelines for sensor
output calibration and validation and discuss necessary steps for maximizing
the generalizability of the data analysis.
Unfortunately, harmonization of PA data between existing studies is often
impossible due to the different formulation and interpretation of activity co-
unts, body placement, and lack of universally accepted measurement. For
example, step counts produced by Fitbit cannot be compared to activity co-
unts produced by ActiGraph, as they are not even on the same scale. In fact,
is has been shown that step counts might differ substantially when measured
by different devices (Storti et al, 2008; Fortune et al, 2014). Activity counts
measured by the same device may also be different depending on the sensor
location (Fairclough et al, 2016). For example, a device located on the hip or
ankle is sensitive to ambulation, whereas a device located on the wrist will
detect both ambulation and hand movements. Moreover, some activity counts
may change substantially with the sampling frequency (Brønd and Arvidsson,
2016) even for the same device placed at a particular body location. These
problems are not likely to be resolved as long as summary data obtained via
proprietary manufacturer algorithms continue to be used. The best strategy
is to go back to the raw data and construct open-source data pre-processing
approaches that become increasingly accepted by the community. This, unfor-
tunately, is not a panacea, as pre-processing pipelines need to take into account
problems associated with device calibration, missing data, data size and com-
plexity, and measurement translation and communication.
To provide a concrete illustration of these problems and some potential
solutions, we use the Developmental Epidemiological Cohort Study (DECOS)
data, which is described in Sections 2.1- 2.2. Next we introduce the nota-
tion and statistical methods used to pre-process and summarize the data in
Section 2.3. In Section 3 we illustrate issues related to the analysis and inter-
pretation of raw accelerometry data and review some published approaches
designed to handle the complexity and heterogeneity of accelerometry data
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Accelerometry data in health research: challenges and opportunities 5
collected in the free-living environment. In Section 4 we summarize the ideas
and discuss their implication for health studies using raw accelerometry data.
2 Methods
2.1 Study participants
Forty-nine community-dwelling older adults were recruited from the Pitts-
burgh, Pennsylvania area for the Developmental Epidemiologic Cohort Study
(DECOS), part of the National Institute on Aging (NIA) Aging Research Eva-
luating Accelerometry (AREA) project (Lange-Maia et al, 2015). DECOS is
a cross-sectional study designed to examine the impact of accelerometry we-
ar location on PA and sedentary behavior assessment among healthy older
adults. Individuals were excluded from DECOS if they suffered from any of
the following conditions: hip fracture, stroke in the past 12 months, cerebral
hemorrhage in the past 6 months, heart attack, angioplasty, heart surgery in
the past 3 months, chest pain during walking in the past 30 days, current treat-
ment for shortness of breath or a lung condition, usual aching, stiffness, or pain
in their lower limbs and joints and bilateral difficulty bending or straightening
the knees fully.
2.2 Data collection
Participants were equipped with three tri-axial wearable PA monitors (Acti-
Graph GT3x+) that collected raw accelerometry data at a sampling frequency
of 80Hz (80 observations per second for each axis). Monitors were located on
the hip using an elastic belt and on both wrists using watch straps. During the
“in-the-lab” phase of the experiment all participants were asked to perform
a series of physical tasks including: lying still, standing still, washing dishes,
sitting still, dough kneading, dressing, folding towels, vacuuming, shopping,
writing, dealing cards, standing up from a chair, walking for 20 meters, wal-
king for 20 meters with arms crossed on the chest, fast walking for 20 meters,
fast walking for 20 meters with arms crossed on the chest, treadmill walking at
1.5mph for 5 minutes, walking for 40 meters and fast walking for 400 meters.
Before each task participants were given verbal instructions by a supervising
trained professional recording the times of the beginning and end of each task
with a stopwatch. During the free-living portion of the experiment, partici-
pants were equipped with accelerometers for seven consecutive days and were
told to maintain their normal, unsupervised, free-living activities. They were
instructed to take off the activity monitors only during sleep.
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6 Marta Karas et al.
2.3 Open-source summaries of accelerometry data
The raw accelerometry data are collected along three orthogonal axes in the
device-specific frame of reference. We denote the vector of raw acceleration
data by x(t) = {x1(t), x2(t), x3(t)}, where xm(t) is the acceleration measure-
ment along the m(= 1,2,3) axis at time t(for notational simplicity we drop
the subject index). The acceleration time series, x(t), are sampled at a fixed
frequency f. For example, in our application, the sampling frequency is 80 Hz,
which means that for each second along each axis there are 80 acceleration
recordings. Here we describe four open-source methods that have been used in
the literature to provide summaries of accelerometry data. All methods con-
sider non-overlapping time windows of a given length Hand reduce the 3H
measurements in the window to a single number.
Euclidean Norm Minus One (ENMO) was first introduced as a summary
metric for accelerometry data in van Hees et al (2013). It is directly based on
the Euclidean norm of x(t), defined as
r(t) = qx2
1(t) + x2
2(t) + x2
3(t).(1)
The ENMO at time tis defined as r(t)−1 when r(t)−10 and 0 otherwise,
or notationally, max [r(t)−1,0]. Further, the ENMO in a window of size His
defined as the average ENMO across the time points in that window. Formally,
ENMO(t;H) = 1
H
H−1
X
h=0
max [r(t+h)−1,0].(2)
ENMO can be quite sensitive to calibration errors when the device-specific
ENMO at rest is not close to zero. An additional calibration procedure was
introduced to mitigate the effects of calibration (van Hees et al (2014)). This
procedure performs a linear transformation on the raw data before computing
the Euclidean norm, resulting in a new version of ENMO. Calibration para-
meters amand dmare estimated for each axis m= 1,2,3, which are later used
to linearly transformed the original data to x0(t) = {x0
1(t), x0
2(t), x0
3(t)}, such
at x0
m(t) = dm+amxm(t) for m= 1,2,3.
The Vector Magnitude Count (VMC) is an aggregation statistic that is also
known as the Mean Amplitude Deviation (MAD) V¨ah¨a-Ypy¨a et al (2015).
We use the notation VMC to avoid the confusion between the two MAD
acronyms used in accelerometry literature, one for mean amplitude deviation
(V¨ah¨a-Ypy¨a et al, 2015) and one for median amplitude deviation (Mariani
et al, 2013). VMC computes the L1norm in each time window H. Denote the
average Euclidean norm in the window of length Hstarting at tas ¯r(t;H) =
PH−1
h=0 r(t+h)/H. Then VMC is defined as
VMC(t;H) = 1
H
H−1
X
h=0
|r(t+h)−¯r(t;H)|.(3)
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Accelerometry data in health research: challenges and opportunities 7
The unnormalized Activity Index (AI0) (Bai et al (2014) is a measure ba-
sed on the combination of the three within-axis standard deviations of the raw
accelerometry signal. Because AI0subtracts the local mean of the accelerome-
try signal, calibration is intrinsic and local, which allows it to adapt to cases
when the device is not calibrated, when it gets decalibrated during studies, or
when the device exhibits time-dependent decalibration. Let σm(t;H) be the
standard deviation of the acceleration along axis m= 1,2,3 in the window of
length Hstarting at t. The exact formula is
σ2
m(t;H) = 1
H
H−1
X
h=0
[xm(t+h)−µm(t;H)]2,
where µm(t;H) = 1
HPH−1
h=0 xm(t+h). Then formally,
AI0(t;H) = v
u
u
tmax (1
3"3
X
m=1
σ2
m(t;H)−¯σ2#,0),(4)
where ¯σis the systematic noise standard deviation calculated using the data
collected during some non-moving period. The unnormalized Activity Index
(AI0) is expressed in Earth gravitational units.
The normalized Activity Index (AI, Bai et al (2016)) is strongly related to
the unnormalized Activity Index (AI0). The only difference is that the axis-
specific variances are divided by the device-specific systematic noise. More
specifically, AI is defined as follows
AI(t;H) = v
u
u
tmax (1
3"3
X
m=1
σ2
m(t;H)−¯σ2
¯σ2#,0),(5)
The downside of using AI versus AI0is that its scale is no longer in Earth
gravitational units. Instead it is expressed in multiples of noise standard de-
viation. The advantage of AI could be when the devices are not calibrated in
terms of their noise level at rest, which may induce batch effects. This, howe-
ver, seems to be a smaller problem than the internal calibration obtained by
subtracting the local mean in AI and AI0.
In the remainder of this paper, we use ENMO, VMC and AI0. We do not
use normalized Activity Index (AI) so as to keep presentations of the statistics
measurements on the same scale.
3 Statistical challenges and examples
3.1 Data volume and complexity
Figure 1 displays three time series that represent the acceleration along each
of the three orthogonal axes of an accelerometer located at the wrist. The
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8 Marta Karas et al.
top panel of Figure 1 presents 24 hours of data, with each axis data shown
in a different color. In this example, the first observation was taken at 12AM,
while the last was taken 24 hours later, also at 12AM. The middle panel in
Figure 1 displays a particular one hour interval from 8 : 40AM to 9 : 40AM
(indicated in the top panel as a dashed-line rectangle). The bottom panel di-
splays the one minute interval marked as a dashed-line rectangle in the middle
panel (from 8 : 51AM to 8 : 52AM). The signal was acquired at a sampling
frequency of fs= 80Hz. Therefore, the number of observations per subject qu-
ickly explodes. For example, a week of accelerometry data collected at 80Hz
results in 80 ∗60 ∗60 ∗24 ∗7 = 48,384,000 observations for each of the three
axes. Thus, even for a small multi-subject observational study researchers are
faced with datasets consisting of billions of observations. This enormous vo-
lume of data creates challenges at every level of the scientific investigation.
Storage and operational memory of modern computers is not unlimited and
well-optimized solutions are needed for data management. Conducting explo-
ratory data analysis, visualization, and modeling requires additional compu-
tational and methodological resources. Therefore, it is essential to implement
carefully planned protocols for collection, management and analysis of the da-
ta. In recent years several protocols and experimental design guidelines have
been proposed (Esliger et al, 2005; Cain, 2014; NHANES, 2011), though an
universally accepted approach is still elusive. This could be due to the con-
stant change of the technological and methodological landscape. For example,
the US NHANES survey protocols have changed between survey cycles 2003-
2004 (NHANES, 2006), 2005-2006 (NHANES, 2008), 2011-2012 and 2013-2014
(NHANES, 2011) both in terms of device type and body location. In the 2003-
2004 and 2005-2006 cycles, participants wore an ActiGraph 7164 on a waist
belt for 7 days during the non-sleeping time. In later cycles, the GT3X+ Ac-
tiGraph waterproof model was used on the non-dominant wrist for 7 days
without taking it off. The protocol change was reported (Troiano et al, 2014)
and was designed to improve participant compliance.
The current approach to reduce size and complexity of the raw accelerome-
ter data is to create aggregated summaries in fixed time intervals, as described
in Section 2.3. While these summaries reduce the volume of data, the potential
loss of information can be substantial. To recover some of the information, a
few methods have been proposed for recognition of activities using raw acce-
lerometry data. Some approaches focus on prediction of a group of movement
types (Lyden et al, 2014), whereas others focus on prediction of a specific
movement type (e.g. walking) (Urbanek et al, 2015). Characterizing the kine-
matics of human walking both in the lab and in the free-living environments
using accelerometry data could provide previously unavailable information on
the physical condition of individuals (Studenski et al, 2011).
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Accelerometry data in health research: challenges and opportunities 9
Figure 1 Acceleration values from three orthogonal axes of an accelerometer located on
the left wrist. Each axis data is shown in a different color. The top panel displays 24 hours
of data collected between 12AM and 12AM. The middle panel displays a one hour interval
from 8 : 40AM to 9 : 40AM (indicated in the top panel as a dashed-line rectangle). The
bottom panel displays a one minute interval from 8 : 51AM to 8 : 52AM marked as a
dashed-line rectangle in the middle panel. The signal was acquired at a sampling frequency
of fs= 80Hz.
3.2 Data heterogeneity
Interpretation of raw accelerometry data is an open and challenging problem
due to the high heterogeneity of data, both within- and between-subjects.
Within-subject variability is observed when one person performs the activity,
but the characteristics of that activity change. For example, when walking,
consecutive strides differ slightly in duration and shape due to natural stride-
to-stride variability (IJmker and Lamoth, 2012; Urbanek et al, 2017). They
can also differ substantially during the day, depending on the level fatigue of
the individual, context of walking (e.g. hiking versus shopping), and local con-
straints (e.g. running to a meeting when late versus slow walking to the kitchen
in the morning). Between-subject variability contains additional factors due
to differences in body size, musculature, will, and ability to perform certain
tasks. To further illustrate these points, the left column of Figure 2 displays
acceleration data collected on the left wrist during walking for two individuals.
The periodic character of time series is striking. However, both the duration
and amplitude of accelerometry data can vary from cycle to cycle. A more
extreme example is displayed in the right column of Figure 2, where the same
two individuals perform the getting dressed activity. Indeed, the more random
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10 Marta Karas et al.
Figure 2 Data recorded by an accelerometer located on the left wrist while walking (left
column) and getting dressed (right column), for two individuals (top and bottom row). Each
axis is shown in a different color.
character of the observations and lack of synchronization between- and within
individuals is remarkable.
These data indicate that it is important to better define the types of phy-
sical activity. Indeed, the bottom panels of Figure 2 show that data can be
very different even for what is defined as the same type of activity (e.g. get-
ting dressed). In retrospect, this should not be surprising as “getting dressed”
is a complex task that is only vaguely defined, may involve different types of
clothes, body sizes and shapes, movements that individuals use to getting dres-
sed, and order of various tasks. It should be apparent that if we want to make
any progress in this area, we need to identify well-defined sub-movements that
then translate them into research language. Clearly, in this case, the activity
“getting dressed” does not have a sharp definition, especially from the point
of view of an accelerometer. Things may be different if we had a video camera
instead of an accelerometer, but this raises other problems that exceed the
scope of the current paper.
Classifying activity types while accounting for between- and within-subject
variability is under intense methodological development. The approach discus-
sed in Bai et al (2012) and He et al (2014) uses short segments of training
accelerometry data, called “movelets”, to construct dictionaries used as re-
ference to predict activity types on new data. Dictionaries are activity- and
subject-specific to account for the individual variations in movement patterns
across subjects. Xiao et al (2016) proposed a related movelet-based method to
use labeled activity data from some subjects to predict the activity labels of
other subjects.
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Accelerometry data in health research: challenges and opportunities 11
3.3 Sensor location
The location of the accelerometer sensor on the body can also have substan-
tial effects on predicting activity types, PA volume, and PA distribution as a
function of time of the day. Indeed, the sensor collects only its own accelera-
tion, which is a proxy of the acceleration of the particular body location where
the sensor is attached. Therefore, a wrist sensor will produce different signals
from a hip or thigh sensor. To illustrate this point, Figure 3 displays the raw
accelerometry data collected simultaneously by sensors located on the hip (left
column) and left wrist (right column) while dealing cards (top panel), getting
dressed (middle panel) and walking (bottom panel). For dealing cards, an acti-
vity that requires mostly hand-movements, the signal amplitude for the wrist
sensor is much higher than for the hip sensor. For more complex, whole-body
activities, such as getting dressed, the signals corresponding to both locations
have higher amplitudes than for dealing cards. However, the amplitude of the
signal at the wrist is higher and there are no clear correlations between the hip
and wrist signals. In the case of walking, the amplitudes of the data collected
on the wrist and the hip look periodic and highly correlated. This is likely
due to the fact that both hands and legs are involved in walking, with roughly
the same frequency of movement. The slightly lower amplitudes observed at
the wrist are probably due to the more intense PA in the lower body during
walking. In our experience, an accelerometer placed at the ankle would display
even higher amplitudes of the acceleration signal.
Figure 4 provides the summary metrics introduced in Section 2.3 using
data collected during various activities performed in the controlled lab envi-
ronment. The boxplots for ENMO, VMC and AI0are displayed in the top,
middle and bottom panels, respectively, while the data for the hip and left
wrist are displayed in the left and right columns, respectively. All summary
statistics are calculated for a window size of 5 seconds during writing, washing
dishes, vacuuming, getting dressed and walking for each of 5-second intervals
and all 49 individuals. The difference between the wrist and hip data can be
observed for all summaries and activities requiring dynamic upper body mo-
vements (washing dishes, vacuuming). These differences are much lower for
low intensity hand movements (writing), though AI0seems to better capture
these differences. Also, substantial differences can be observed for moderate-
intensity whole-body activities (getting dressed), where, again, AI0seems to
be more sensitive. For walking, the difference in the distribution of all sum-
maries between the wrist and the hip is relatively small. When comparing AI0
versus ENMO versus VMC at the wrist there is a more clear differentiation
between activities. This is likely due to the fact that AI0automatically cor-
rects for possible device miss-calibration, whereas the other methods do not. It
is an open problem whether the methods perform more similarly after device
and/or signal calibration.
Summaries have been used extensively in the literature. For example, Ko-
ster et al (2016) showed that different cut-points of the vector magnitude can
be used for the classification of sedentary time in older adults using both
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12 Marta Karas et al.
Figure 3 Acceleration from three orthogonal axes of an accelerometer located on the hip
(left column) and left wrist (right column), while dealing cards (top row), getting dressed
(middle row) and walking (bottom row). Each axis data are shown in a different color.
hip-worn and wrist-worn ActiGraph accelerometers. It has also been shown
that activity recognition algorithms perform differently across body locations.
For example, Rosenberger et al (2013) reported greater sensitivity and speci-
ficity of both sedentary and moderate- to vigorous-intensity PA when using
accelerometry data collected at the hip compared to wrist. Trost et al (2014)
reported higher accuracy for hip-derived than for wrist-derived data in the
classification of specific, whole-body engaging activities. Higher accuracy of
classifying sitting was obtained with data collected from the wrist compared
to data collected from the hip. Del Din et al (2016) showed that estimated ga-
it characteristics, such as step time and length, can depend on body location
and suggested that the chest location is more appropriate than the wrist. We
conclude that the body location may lead to different results, that body loca-
tion will favor movements that directly engage that particular location, and
that translating various summaries into well defined activity categories (e.g.
walking, sedentary) requires location-specific calibration of the accelerometry
summaries.
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Accelerometry data in health research: challenges and opportunities 13
Figure 4 Boxplots of ENMO, (top panels) VMC (middle panels) and AI0(bottom panels)
statistics derived for τ= 5 seconds-length intervals of data collected from the hip (left
column) and left wrist (right column) during writing, washing dishes, vacuuming, getting
dressed and walking (x-axis), for all 49 individuals.
3.4 Device rotation
Because wearable PA monitors collect acceleration data relative to earth gra-
vity, they are sensitive not only to movement but also to their own orientation
with respect to Earth’s gravity. To better understand this, the top panels in Fi-
gure 5 display accelerometry data collected by a wrist-worn device during two
walking tasks performed by the same individual. The upper panel corresponds
to walking with both hands moving naturally, whereas the bottom panel cor-
responds to walking with arms crossed on the chest. The change in the device
orientation is manifested in the change of mean values, most clearly seen in
the signals shown in green. In the free living environment changes in device
rotation are quite common and can be due to multiple sources. For example,
when walking individuals could sway their hands normally, hold them in the-
ir pockets or perform an activity (e.g. holding a smart phone), walking with
hands hanging loose or with hands in the pockets. Additionally, the device can
rotate around the wrist or move higher or lower on the hand, resulting in an
altered distribution of the observed signal.
To prevent a device from rotating, it can be directly attached to the skin
with adhesive pads or affixed indirectly with a waistband clip or elastic belt
(Matthews et al, 2012). Indeed, it has been recommended that devices should
be fitted as tightly to the body as possible (Boerema et al, 2014). However,
even with these precautions, belts can loosen up, resulting in device orien-
tation changes (O’Neill et al, 2017). Devices that adhere to the skin might
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14 Marta Karas et al.
Figure 5 Acceleration values from three orthogonal axes of an accelerometer located on the
left wrist, collected during two walking tasks performed by the same individual. Each axis
data is shown in a different color. The upper panel corresponds to walking with both hands
moving naturally, whereas the bottom panel corresponds to walking with arms crossed on
the chest.
be attached upside-down or placed in a slightly different position when deta-
ched and reattached. Moreover, for devices that have it, the orientation chart
can be obscured, which can result in improper device orientation (Edwardson
et al, 2016). We consider that all these precautions should be carefully im-
plemented and adapted to the specific problem that one tries to address. In
addition, it is important to understand the extent of the problem in specific
applications and, when possible, attempt to correct it. Several methods were
proposed to address this problem by rotating the observed three-dimensional
vector to the common, reference, orientation (Xiao et al, 2016; Yurtman and
Barshan, 2017). When one uses summary metrics that are robust to device
orientation, this problem is less important. For example, ENMO, VMC and
AI are all rotation invariant.
3.5 Sampling frequency
Sampling frequency fs(expressed in Hz) is the parameter describing how often
accelerometry data are collected by the device. In modern wearable accelero-
meters sampling frequency usually ranges between 10 to 200 Hz, though it
could be set as high as 1000 Hz for specialized applications, such as preci-
se human movement tracking during sport activities (Dominguez-Vega et al,
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Accelerometry data in health research: challenges and opportunities 15
Figure 6 Boxplots of ENMO, (top panels) VMC (middle panels) and AI0(bottom panels)
for 5 second time windows. Data is shown for all 49 individuals in the study and were
collected from the left wrist during writing, washing dishes, vacuuming, getting dressed and
walking (x-axis). Data were collected with the original sampling frequency fs= 80 Hz and
then decimated to simulate sampling frequencies of 40, 20 and 10 Hz.
2015). One of the hidden problems is that the summaries produced by vario-
us devices can depend on the sampling frequency of the device. This could
have substantial implications if, for example, in a study the sampling frequ-
ency is varied between- and within-individuals and/or devices. For example,
according to ActiGraph, LLC, the manufacturer of ActiGraph PA monitors,
the observed activity counts depend on the sampling frequency (ActiGraph,
2016).
Figure 6 illustrates the boxplots of ENMO (top panel), VMC (middle pa-
nel) and AI0(bottom panel) calculated for all 49 participants during writing,
washing dishes, vacuuming, getting dressed and walking in 5-second time in-
tervals. Data were collected by the device located on the left wrist with the
original sampling frequency fs= 80 Hz. Additionally, data has been decimated
to simulate sampling frequencies of 40, 20 and 10 Hz. The median summary
values are reported in Table 1. Interestingly, all open source summaries are
relatively stable as a function of frequency, with stronger decreases at 10 Hz.
For the AI0statistic, the change is most pronounced for walking, where the
median AI0decreases by 19.0% from 80 to 10 Hz. For the other activities the
reduction is much smaller in the 1 to 7% range. These smaller differences in
open source measures are encouraging. Indeed, Brønd and Arvidsson (2016)
investigated the effects of sampling frequency on ActiGraph activity counts.
They compared results obtained during walking and running with the default
30 Hz sampling frequency with 40 and 100 Hz sampling frequencies. For fast
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16 Marta Karas et al.
Table 1 Median values of ENMO, VMC and AI0statistics derived for τ= 5 seconds-length
intervals of data collected from the left wrist during writing, washing dishes, vacuuming,
getting dressed and walking, for all 49 individuals. Results are obtained for original sampling
frequency fs= 80Hz (3rd column) and simulated sampling frequencies fs= 40,20,10 H z
(4-6th columns).
Statistic Activity 80Hz 40Hz 20Hz 10Hz
ENMO Writing 0.015 0.015 0.016 0.016
ENMO Washing Dishes 0.014 0.014 0.014 0.014
ENMO Vacuuming 0.031 0.031 0.031 0.028
ENMO Getting Dressed 0.040 0.040 0.040 0.036
ENMO Walking 0.195 0.195 0.191 0.176
VMC Writing 0.003 0.002 0.002 0.002
VMC Washing Dishes 0.007 0.006 0.006 0.004
VMC Vacuuming 0.023 0.022 0.022 0.019
VMC Getting Dressed 0.034 0.033 0.033 0.029
VMC Walking 0.198 0.197 0.193 0.175
AI0Writing 0.007 0.007 0.007 0.007
AI0Washing Dishes 0.026 0.027 0.027 0.026
AI0Vacuuming 0.071 0.071 0.070 0.066
AI0Getting Dressed 0.089 0.089 0.088 0.083
AI0Walking 0.193 0.192 0.183 0.156
run activity, they reported approx. 6,800 counts per minute (cpm) mean for
default 30 Hz frequency, and an increase of mean cpm as high as 24% for 40
Hz and 18% for 100 Hz frequency.
The Table 3 in Appendix A) provides the medians, 25-th, and 75-th per-
centile for the same five activities, but broken down by subject for 5 different
subjects. Results are only shown for the hip accelerometer, though similar re-
sults are available for wrist accelerometers. The ranking of activity intensities
by medians across subjects is the same, but the medians for individual sub-
jects are quite variable even for the same activity and summary metric. For
reference, at the hip, AI0is roughly around 0 milli g for writing, between 1
and 2 milli g for washing dishes, 3 and 14 milli g for vacuuming, 5 and 10
milli g for getting dressed, and 20 to 100 milli g for walking. Here we used
only the minimum of the first and maximum of the third quartiles across the
five subjects to create these ranges. These measures are averages per second
during the 5 second intervals and not totals. If one would like to transform
these numbers into totals per minute then the values need to be multiplied by
60; similar for other intervals.
3.6 Measurement bias and batch effects
Measurement bias is the difference between the measured accelerations and
their true values. Estimation of both bias and measurement error of acce-
lerometry data requires a dedicated experimental setup utilizing calibrated
vibration exciters. The device is exposed to a known acceleration and the
measured acceleration time series is compared to this known acceleration, as
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Accelerometry data in health research: challenges and opportunities 17
described in Bassett et al (2012). Authors noted that newer devices, such Ac-
tiGraph GT1M, undergo initial unit calibration during production and are
supposed to be calibrated for as long as they are used. However, the calibra-
tion standards of the different manufacturers may be different. Therefore, we
recommend doing some basic calibration checks before utilizing the device in
a study.
Even when dynamic calibration is conducted, bias in static measurements
can still exist. Ideally, an accelerometer resting on a flat surface, with one me-
asurement axis oriented perpendicularly to the ground, should measure con-
stant acceleration of 1gfor that axis and 0gfor the other two orthogonal axes.
In practice, measurements may deviate slightly due to their imprecision or to
the quality of assembly, which may, for example, misalign the accelerometer
axes with the monitors’ casing. In theory, the vector magnitude (Eq. (1)) for
resting state (no movement) is equal to 1g, as the earth’s gravity is the only
force acting on the accelerometer. In practice, however, the vector magnitude
at rest can be slightly different from 1g. To quantify this calibration bias, we
calculated a vector magnitude r(t) averages from 5-second time windows, de-
noted r(t)τ=5, for the acceleration signal collected from the hip during sitting
still activity, for all 49 subjects. We report the percentiles of this distribution
in Table 2. Ideally, if no bias was present in the data, r(t)τ=5 values should all
be equal to 1. The median is 1.007 indicating very close agreement with what
we expect. However, the 5 and 95 percentiles were 0.964 and 1.047, indicating
that 10% of the devices have a deviation of 5% or more from 1g at rest.
Table 2 Percentiles of r(t)τ=5, vector magnitude r(t) averages from 5-second time windows,
for the acceleration signal collected from the hip during sitting still activity, for all 49
subjects.
Percentile 5 25 50 75 95
r(t)τ=5 [g] 0.964 0.991 1.007 1.016 1.047
The Activity Index (Bai et al, 2016) was designed to be robust to bias by
subtracting the local mean around each axis and to measurement error by con-
structing the mean relative to the variability at rest. An additional calibration
procedure was also introduced for ENMO to mitigate the effects of calibration
bias (van Hees et al (2014)). This procedure performs a linear transformation
on the raw data before computing the Euclidean norm, resulting in a calibrated
version of ENMO.
3.7 Data labeling
Classification of physical activity types requires gold standard labels for activi-
ty, which can be obtained through direct observation or by inspection of video
recordings. Obtaining gold standard labels is a labor intensive process, which
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18 Marta Karas et al.
Figure 7 Acceleration data from three orthogonal axes at the hip collected around the time
when a participant performed a 400-meter-walk activity. The dashed-line red box indicates
the portion of the 400-meter-walk period identified by a human observer.
often restricts the process to “in-the-lab” experiments or to a few subjects.
Even gold standard labels are of different quality, depending on the accura-
cy and resolution at which the activity type is predicted. For example, when
one is interested in predicting standing up from a chair, the duration of the
activity is in the 1 to 4 second range. This makes accurate labeling even for a
human observer extremely difficult. If one is interested in predicting whether
the person walked or not in a particular 1 minute interval, the labels will be
less accurate and will simply indicate whether the person has walked in a par-
ticular interval and approximately around what time stamp and for how long.
However, even these labels can be substantially mis-aligned. This can be due
to multiple factors including imperfect synchronization of clocks, time elapsed
between the beginning and recording of the task, basic observer or data en-
try error. As an example, Figure 7 displays a portion of the acceleration data
recorded at the hip for one subject. The dashed-line box is the portion of 400-
meter-walk period labeled by the human observer. There is a clear 45 second
shift in the label relative to the actual activity. In such cases using the original
label without inspection would lead to inferior prediction algorithms and wa-
ste of resources during the modeling phase. We chose to manually inspect all
“in-the-lab” data for each subject and re-label walking as periods that closely
correspond to the sustained harmonic walking (SHW). The overlap between
the labels provided by the human observer and the labels improved by human
inspection of the data was below 80% in 18 out of 49 subjects.
The most effective approach to proper labeling is synchronization of accele-
rometry data with video-recordings of the experiment (Bussmann et al, 1998).
This method has been successfully used in many “in-the-lab” experiments
(Godfrey et al, 2015; Del Din et al, 2016). However, using video-recordings
for labeling free-living data is harder and subject to privacy considerations.
Indeed, it is possible to equip participants with body-worn cameras, but vi-
deo data de-identification can be quite challenging as it might contain family
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Accelerometry data in health research: challenges and opportunities 19
members, car plates, and addresses. In spite of these limitations, body-worn
cameras have been used to label PA collected in the free-living environment.
For example, Ellis et al (2016) used video data to train a PA classifier and
Hickey et al (2017) used video data to train a walking prediction algorithm.
In Hickey’s experiment, body-worn cameras were facing down to record only
the feet movement.
Another, less labor intensive, approach for precise labeling of raw accele-
rometry data is to use landmarks introduced by the individual wearing the
device. For example, in the case of wrist-worn devices, participants can clap
their hands before and after each tasks. Claps result in high-amplitude, short-
time spikes in the observed data that can be used to estimate timestamps for
each task. For other body locations, participants can vigorously tap the device
to generate proper landmarks in the data. This approach was successfully used
in Straczkiewicz et al (2016). Another approach is to use the device-specific
own event-markers to place labeling landmarks. Some modern PA monitors
have built-in event marker buttons (e.g. Actiwatch Spectrum Plus and Pro).
These event-markers generate binary indicators at the same granularity as
that of the observed accelerations. When pressed, they return a value of 1
until pressed again. Initially, they were intended to mark major everyday ac-
tivities (e.g. sleep) and critical events (e.g. falls), but they can be used for
labeling data, as well. Unfortunately, the utility of event markers is limited by
the compliance of participants (Chen et al, 2014; Boudebesse et al, 2015).
3.8 Synchronization of multiple PA monitors
Many studies collect data using multiple PA sensors. Synchronizing data across
different monitors allows to combine information about specific human move-
ments at multiple locations on the body (Bao and Intille, 2004; Cleland et al,
2013; He et al, 2014; Altini et al, 2015). Most devices can be set up to initialize
their measurement collection at a given time (e.g. at midnight) and/or can be
initialized manually. In practice, even if such approaches are used, measure-
ments might still be desynchronized between devices. We identify two main
reasons for device desynchronization.
First, most operating systems used in personal computers are not real-time
operational systems. Therefore, time of execution of any command can not be
precisely determined (see details in Stallings (2008)). That may result in sub-
second level differences in measurements start times on multiple PA monitors.
Second, the internal drift of device clocks can lead to inaccurate stamping
of the time interval (Bennett et al, 2015). Such drifts are usually small (a
few seconds per day) and can typically be ignored. However, when combining
sub-second level data from multiple sensors in the free-living environment,
the effects of the drift can have substantial side effects. To illustrate these
problems, Figure 8 displays 20 seconds of data collected in the free-living
environment by two monitors located on the left (top panels) and the right
wrist (bottom panels). The two sensors were synchronized at the beginning of
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20 Marta Karas et al.
Figure 8 Acceleration values representing 20 seconds of data collected in the free-living
environment using two monitors located on the left wrist (top panels) and the right wrist
(bottom panels). The two sensors were synchronized at the beginning of the experiment.
The left and right column provide data collected on the first and seventh day of observation,
respectively.
the experiment. The left and right column provide data collected on the first
and seventh day of observation, respectively. The dotted vertical lines mark
the end of a high-amplitude activity for each device. Although visually, data
from the two devices appears to be correlated during both days, a shift in the
two recordings is apparent on both days. On day 1 the time-shift is around
2.5 seconds, which is probably due to imperfect timing of device initialization.
On day 7 the time shift is about 4 seconds, with the additional 1.5 seconds
probably due to drift in device clocks. This drift need not be in the same
direction or of the same magnitude for all devices. Such de-synchronization
would have minor implications for PA summaries at the minute level collected
over a 7 to 14 days period, but they can lead to substantial differences when
one is interested in analyzing sub-second level data.
The time shift introduced during device synchronization and initialization
can be addressed using video recordings or landmarks. Lab experiments ra-
rely last more than a few hours, and the effects of time drift can often be
ignored. However, for data collected ‘in the free-living environment, the effects
of time drift are cumulative, which can raise substantial challenges for data
analysis. A possible solution could be to use devices designed specifically for
parallel measurements. For example, GaitUp (GaitUp, 2017) is a system for
synchronous measurement of feet movement. Alternatively, one can perform
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Accelerometry data in health research: challenges and opportunities 21
landmark-based synchronization for every time-interval in the data (e.g. every
day).
4 Discussion
We have presented challenges related to the collection and analysis of raw,
sub-second level accelerometry data. The increased granularity of observa-
tions when moving from the minute to the sub-second resolution leads to a
large increase both in the volume and complexity of the data. This makes raw
data harder to use than summarized data, but also holds promise of unlocking
additional information glossed over by taking minute-, hour-, or day-level sum-
maries. For example, describing gait parameters during the course of the day
in the free-living environment and characterizing their potential association
with health outcomes cannot be done without using sub-second level data.
Raw accelerometry data requires specialized visualization and analytic me-
thods. This is fertile ground both for scientific researchers, as additional in-
formation is likely embedded in the raw signals, and for data scientists, as
new methods and insights are becoming increasingly necessary. To start ad-
dressing this complexity we make a few points that are worth remembering:
1) activity counts are summaries of the raw data, which can depend on the
device manufacturer, software version, and body location; 2) open source sum-
mary statistics are increasingly available, though more research is needed to
understand their relative performance; 3) raw and summarized PA data can
vary substantially with the device location, between- and within-individuals;
4) proper location choice might yield data signatures tailored to a particular
study purpose; 5) device orientation can change over the course of an experi-
ment and needs to be standardized both within- and between-individuals and
devices; 6) sampling frequency can affect both raw accelerometry and sum-
marized measurements; 7) device calibration, bias removal, and measurement
error quantification can lead to higher quality data; 8) proper labeling of data
is very important for training activity classifiers at the sub-second level, espe-
cially for short activities; and 9) synchronizing multiple devices must be done
carefully and needs to be accounted for during the design of the experiment
phase.
In spite of these challenges, the number of publications focused on raw ac-
celerometry is continuously increasing, especially in the area of activity type
classification. This is due in part to the increased popularity of these devices,
their convenient design, and reduced cost. The application of raw accelerome-
try data in epidemiological studies is still in its infancy, though some important
steps forward have been made. We anticipate that, as the interest changes to
understanding the details of human movement kinematics in the free-living
environment, the focus on raw data will become stronger. The number of stu-
dies that both collect and disseminate raw activity data will probably provide
a huge boost to raw accelerometry data research. For example, the UK Bio-
.CC-BY-NC-ND 4.0 International licensenot peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was. http://dx.doi.org/10.1101/276154doi: bioRxiv preprint first posted online Mar. 5, 2018;
22 Marta Karas et al.
bank PA dataset is currently the largest of its kind. It was collected using the
open-hardware AX3 acceleration sensor (Doherty et al, 2017).
In closing, we offer a few practical suggestions for the scientists who would
like to conduct their own activity studies: 1) discuss your plans with a team
that has expertise in activity research; 2) avoid the pitfalls of accelerometry
research by incorporating robust, fault-tolerant designs of experiments; 3) if
possible, use established protocols for data collection and pre-processing; 4)
record and store the raw accelerometry data in addition to summaries, such as
activity counts; 5) conduct a lab study and record the activity summaries for a
well-defined group of activities in 10 to 100 individuals who are representative
of the population to be studied.
5 Acknowledgements
The authors would like to acknowledge Annemarie Koster, PhD and Paolo
Caserotti, PhD for designing the DECOS experiments.
6 Funding
This research was supported by Pittsburgh Claude D. Pepper Older Ameri-
cans Independence Center, Research Registry, and Developmental Pilot Grant
(PI: Glynn) NIH P30 AG024826 and NIH P30 AG024827. National Institu-
te on Aging Professional Services Contract HHSN271201100605P. NIA Aging
Training Grant (PI: AB Newman) T32-AG-000181. The project was suppor-
ted, in part, by the Intramural Research Program of the National Institute on
Aging.
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Accelerometry data in health research: challenges and opportunities 29
A Appendix
.CC-BY-NC-ND 4.0 International licensenot peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was. http://dx.doi.org/10.1101/276154doi: bioRxiv preprint first posted online Mar. 5, 2018;
30 Marta Karas et al.
Table 3 Summary of the four statistics: ENMO, VMC, AI0and AI for five selected subjects
and all subjects: median, 25-th percentile and 75-th percentile (percentiles are reported
in brackets), obtained from accelerometry data collected at the hip during five activities:
writing, washing dishes, vacuuming, getting dressed and walking.
id Writing Washing Dishes Vacuuming Getting Dressed Walking
ENMO
Sub. 1 0.021 0.033 0.037 0.035 0.189
(0.019,0.023) (0.032,0.033) (0.035,0.039) (0.032,0.038) (0.161,0.204)
Sub. 2 0.084 0.029 0.031 0.055 0.147
(0.083,0.085) (0.028,0.030) (0.027,0.047) (0.052,0.058) (0.122,0.158)
Sub. 3 0.024 0.037 0.039 0.064 0.175
(0.022,0.024) (0.037,0.038) (0.037,0.043) (0.059,0.071) (0.157,0.198)
Sub. 4 0.005 0.008 0.043 0.041 0.181
(0.003,0.006) (0.006,0.009) (0.028,0.089) (0.024,0.051) (0.154,0.192)
Sub. 5 0.017 0.019 0.038 0.035 0.297
(0.014,0.023) (0.018,0.019) (0.030,0.066) (0.031,0.044) (0.263,0.318)
All 0.015 0.014 0.031 0.040 0.195
Sub. (0.007,0.025) (0.009,0.025) (0.020,0.047) (0.031,0.055) (0.143,0.257)
VMC
Sub. 1 0.004 0.006 0.020 0.021 0.194
(0.002,0.005) (0.006,0.007) (0.015,0.023) (0.017,0.025) (0.166,0.206)
Sub. 2 0.003 0.005 0.018 0.022 0.154
(0.003,0.003) (0.004,0.005) (0.014,0.034) (0.021,0.025) (0.13,0.166)
Sub. 3 0.002 0.006 0.015 0.058 0.182
(0.000,0.003) (0.005,0.007) (0.012,0.026) (0.049,0.068) (0.164,0.205)
Sub. 4 0.003 0.008 0.043 0.041 0.186
(0.000,0.003) (0.006,0.008) (0.028,0.092) (0.024,0.051) (0.158,0.196)
Sub. 5 0.002 0.009 0.030 0.032 0.303
(0.000,0.003) (0.008,0.010) (0.024,0.065) (0.027,0.037) (0.271,0.323)
All 0.003 0.007 0.022 0.034 0.198
Sub. (0.000,0.004) (0.005,0.009) (0.014,0.041) (0.025,0.050) (0.147,0.258)
AI0
Sub. 1 0.000 0.001 0.005 0.006 0.042
(0.000,0.002) (0.001,0.002) (0.003,0.007) (0.005,0.007) (0.033,0.047)
Sub. 2 0.000 0.000 0.005 0.017 0.024
(0.000,0.000) (0.000,0.001) (0.003,0.009) (0.013,0.019) (0.021,0.027)
Sub. 3 0.000 0.001 0.003 0.009 0.034
(0.000,0.001) (0.001,0.002) (0.002,0.006) (0.008,0.009) (0.028,0.040)
Sub. 4 0.000 0.001 0.018 0.014 0.037
(0.000,0.000) (0.001,0.003) (0.007,0.024) (0.010,0.017) (0.033,0.041)
Sub. 5 0.000 0.001 0.009 0.006 0.093
(0.000,0.000) (0.001,0.002) (0.005,0.014) (0.005,0.010) (0.081,0.103)
All 0.000 0.001 0.006 0.009 0.040
Sub. (0.000,0.000) (0.000,0.002) (0.003,0.010) (0.006,0.013) (0.024,0.062)
AI
Sub. 1 5.745 14.505 37.066 28.311 128.847
(2.504,7.369) (12.166,16.730) (33.375,41.246) (24.978,37.332) (113.873,135.39)
Sub. 2 1.124 8.421 44.291 24.230 97.084
(0.536,2.210) (7.398,9.537) (39.960,49.576) (21.487,39.287) (88.253,103.289)
Sub. 3 0.000 10.437 55.963 27.359 111.914
(0.000,2.442) (7.720,15.131) (51.028,59.763) (21.271,33.922) (102.208,121.594)
Sub. 4 0.000 11.002 51.713 59.428 117.736
(0.000,2.598) (9.077,13.150) (40.562,61.589) (34.030,83.187) (109.104,122.844)
Sub. 5 0.000 12.948 39.288 41.695 177.989
(0.000,0.544) (11.625,15.230) (34.278,45.534) (30.223,61.612) (161.927,184.464)
All 0.000 11.396 44.566 32.03 122.077
Sub. (0.000,2.294) (7.407,15.713) (35.171,56.015) (20.833,46.736) (95.299,149.542)
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