there is general consensus that physical activity is important for preserving functional capacities of older adults and for positively influencing quality of life [ 7 , 12 ] . to measure physical activity in studies , a variety of direct ( e.g. , pedometer ) or indirect ( e.g. , questionnaires ) methods
the measurement methods differ with regard to their quality , criteria validity and retest reliability , costs and acceptance by study participants , and depend closely on the feasibility within the study design . at present , no gold standard for the assessment of physical activity has been established [ 18 , 28 ] . among direct methods to measure physical activity , accelerometry is accepted and widely applied .
an accelerometer is worn on the body ( e.g. , at the hip , ankle , or wrist ) measuring acceleration in up to three dimensions .
in so doing , information on frequency , intensity , and duration of an individual s physical activity is collected , expressed in  counts per minute 
it is assumed that the amount of cpm is associated with the intensity of physical activity [ 5 , 14 ] . to represent the average physical activity of an individual , a minimum of 3-day measurement is suggested [ 28 , 29 ] . despite the widespread use ,
direct measurement of physical activity using an accelerometer remains challenging [ 18 , 31 ] . there is - for example - no consensus on the type of accelerometer to use [ 1 , 18 , 28 ] , nor is there agreement as to the part of the body on which it should be worn , just recommendations for different target groups , e.g. , for older adults exist [ 4 , 6 , 16 , 21 ] .
older adults frequently perform physical activity with light to moderate intensity , such as housekeeping , gardening , or walking for leisure . in order to take these activities into account ,
some authors recommend the use of a wrist - worn uniaxial accelerometer [ 4 , 6 , 16 , 21 ] , since movements mainly occur in the upper body and arms ( e.g. , the wrist - worn  actiband  ab64 uniaxial accelerometer , cambridge neurotechnology ltd . , uk ) . despite the wide use of accelerometry - based measurement of physical activity in all kinds of studies , data on the retest reliability
this is true for the uniaxial wrist - worn actiband accelerometer itself , as well as for other accelerometers in general .
the only published data on the retest reliability of the actiband was found in rowe et al . .
they found a high inter - instrumental retest reliability of two actibands which were worn simultaneously during a test on a treadmill ( icc  =  0.98 ; 95  % ci : 0.910.99 ) .
however , the study was performed with ten 10 to 11-year - old boys in a laboratory environment , comparing two different actibands .
therefore , these results can not directly be adopted for the measurement of activities of daily life in community - dwelling older adults within a nonlaboratory situation .
maybe the reason for the limited data of the accelerometer - based measurement of physical activity is partly explained by the disappointing results of the analysis of retest reliability .
usually , the sum of cpm or the mean cpm , collected over a period of a few days and divided by the number of days , [ 26 , 28 , 30 ] , is used to express the average amount of physical activity of an individual .
the resulting  average counts per day  often show tremendous intra- and inter - individual variability . this variability may be partly explained by outliers of the cpm measured by the accelerometer .
these values are defined as measurement errors , since they are clearly due to methodological issues of the manufacture and can not be achieved by any kind of physical activity .
consequently , using the sum or the mean of cpm which still include the outliers can not result in high retest reliability .
unfortunately , a standardized recommendation on how to deal with outliers of accelerometry is lacking .
retest reliability might be low due to the outliers which account for the overall sum and not due the general missing possibility of reproducing the results .
, for example , defined cpm greater than 20,000 as malfunction of the accelerometer without further explanations on the cut - point they chose .
instead of defining a certain cut - point for each accelerometer , we would like to suggest a different approach .
in order to enhance the retest reliability , an alternative and more robust estimator that is less sensitive to outliers / measurement errors might be needed .
the trimmed sum is obtained by omitting a certain percentage of the most extreme observations ( e.g. , 5  % of the low and 5  % of the high end ) and taking the sum of the rest .
it is a robust measure of central tendency and is stable against abnormal extreme values ( such as measurement errors / outliers ) , which get  trimmed  away .
using the trimmed sum to express the average amount of physical activity of an individual instead of the overall sum of cpm may result in higher retest reliability .
the aim of the study was therefore to find a more robust estimator in order to account for outliers that occur by using accelerometry to measure physical activity .
this more robust estimator will then be used to test the intra - instrumental retest reliability of a wrist - worn accelerometer in a 3-day measurement of physical activity in community - dwelling older adults .
we hypothesized that using quantiles and the trimmed sum instead of the overall sum ( which includes the outliers ) of cpm will decrease the measurement error and increase the retest reliability .
the presented study was part of a validation study of a physical activity questionnaire for older adults [ 2325 ] .
participants were recruited via 13 general practitioners in north - rhine westphalia , germany during springtime .
all patients , who visited the practice for any reason and fulfilled the inclusion criteria , were asked to become a participant of the study .
the inclusion criteria were being 70  years or older , being legally competent and able to cooperate appropriately , and providing written informed consent .
the exclusion criteria were life expectancy less than 6  months , being in a wheelchair or bedridden .
m ) was computed from measured height and weight on a standard balance scale ( seca 862 ) and stadiometer ( seca 214 , both : seca , germany ) .
a sample of 123 community - dwelling older adults wore the actiband ab64 uniaxial accelerometer ( cambridge neurotechnology ltd . , uk ) continuously for 1  week ( 7  days , 24  h per day ) .
the actiband is a lightweight device ( 12  g ; size , 35    15    5  mm ) that measures and records vertical acceleration with a 1-min epoch .
the device is waterproof . in order to find a more robust estimator than the overall sum of cpm ,
the retest reliability of selected quantiles and trimmed sums was evaluated and compared to that of the overall sum of cpm .
after participants had returned the actiband to the study center , the complete data of 1  week were afterwards split into two repeated measurement values ( week set ) of 3  days each .
the first set included the cpm data from monday , tuesday , and wednesday ; and the second set included the data from thursday , friday , and saturday .
sunday was excluded . assuming that a maximum of 20  % of the cpm values at the high end of the distribution were due to outliers , these values were discarded by building two datasets each : the 80th , 85th , 90th , 95th and 99th quantiles ( q80q99 ) , and the 80 , 85 , 90 , 95 , and 99  % trimmed sums ( ts80ts99 ) . the cpm value of the , e.g. , q80 ( 80th quantile ) is the value where 80  % of the cpm values are less or equal to it and 20  % are greater than or equal to the particular cpm value .
to build the trimmed sums , only the high end of the cpm values was trimmed , since the low end contained a large number of null values ( measured during sleep or physical inactivity ) , and then summed up .
this means that the ( 1     ) trimmed sum is calculated as\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \text{t}}{{\text{s}}_{1 - \beta } } = { } \mathop \sum \limits_{i = 1}^n { w_i } \cdot { \text{cp}}{{\text{m}}_i } $ $ \end{document}where\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { w_i } = \left\ { { \matrix{{*{20}{c } } { 1 , \frac{i}{n } \leqslant 1 - \beta } \\ { 0 , \frac{i}{n } > 1 - \beta } \\ } } \right .
the special case of the overall sum (   =  0 , i.e. , nothing is trimmed ) will also be described . over the 1-week measurement period , 10,080 [ = 7    ( days )    24  ( hours )    60  ( minutes ) ] single values of cpm
  ( days )    24  ( hours )    60  ( minutes ) ] single values .
the retest reliability was assessed by using the intraclass correlation ( icc a , 1 ) .
altman plot was used as a graphic assessment of the agreement of the 2  week sets where the difference between the 2  week sets is plotted against their mean for each subject .
the 95  % limits of agreement , estimated by mean difference 1.96    standard deviation of the differences , provide an interval within which 95  % of differences between measurements by the 2-week sets are expected to lie .
the anthropometric characteristics of the 123 participants ( aged 76.5    5.1  years , 59  % female ) of the study are shown in table  1.table 1characteristics of the study participants in total and broken down by sextotal n  =  123female n  =  73 ( 59  % ) male n  =  50mean    sdminmaxmean    sdminmaxmean    sdminmaxage ( years)76.5    5.170.198.677.2    5.870.198.675.6    3.770.285.5height ( m)1.65   
0.081.471.861.60    0.061.471.781.71    0.061.541.86weight ( kg)81.2    14.550.5114.077.3    14.450.5114.086.8    12.755.0111.0body mass index ( kg    m)29.8    4.420.544.230.1    4.920.544.229.5    3.622.935.9sum cpm over 7  days619,084430,340820,977692,898426,588875,139594,925429,553708,919n number of participants , sd standard deviation , min minimum , max maximum , m meter , kg kilogrammedian25  % quantile75  % quantile characteristics of the study participants in total and broken down by sex n number of participants , sd standard deviation , min minimum , max maximum , m meter , kg kilogram the assessment of physical activity of older adults in this study showed measurement errors ( outliers ) .
this activity profile mainly shows cpm in between 0 ( inactive ) and 1,000 , whereas five single values clearly exceed the usual level .
this occurrence was similar in physical activity profiles of other participants who were randomly chosen.fig .
1listed count per minute during a 1-week period ( 10,080 in total ) and each value of the corresponding count per minute including five unreasonable high values ( measurement errors ) .
the solid vertical lines divide the 7  days of measurement from 1  day to another listed count per minute during a 1-week period ( 10,080 in total ) and each value of the corresponding count per minute including five unreasonable high values ( measurement errors ) .
the solid vertical lines divide the 7  days of measurement from 1  day to another the results of the retest reliability are summarized in table  2 .
the icc of the retest reliability of the overall sum of cpm for the 3-day measurement was icc  =  0.77 ( 95  % confidence interval [ ci ] : 0.680.83 ) . using the quantiles , the icc was between 0.22 ( 95  % ci : 0.050.39 ) and 0.91 ( 95  % ci : 0.870.93 ) .
for the trimmed sum , the icc was between 0.82 ( 95  % ci : 0.750.87 ) and 0.85 ( 95  % ci : 0.790.89 ) .
the differences in the cpm from week set 1 and week set 2 show only moderate variations in the bland 
2).table 2counts per minute of the sum , the quantile , and the trimmed sum including intraclass correlationws1 mean    sddiff ( ws1   
ws2 )    sdicc ( 95  % ci)ws2 mean    sdq80119    664    300.89 ( 0.85 ; 0.92)115    62q85158    795    330.90 ( 0.87 ; 0.93)153    74q90212    966    390.91 ( 0.87 ; 0.93)205    87q95303    1259    570.88 ( 0.83 ; 0.91)294    107q99523    2213   
3720.22 ( 0.05 ; 0.39)525    359ts8069,773    49,9381,508    28,4060.84 ( 0.78 ; 0.88)71,280    50,078ts8598,674    64,1072,304    35,6150.85 ( 0.79 ; 0.89)100,978    63,797ts90136,415    80,6003,165    44,8210.84 ( 0.78 ; 0.89)139,579    79,010ts95187,115    99,1915,156    55,1060.84 ( 0.78 ; 0.89)192,271    97,347ts99248,356    119,9966,514    70,0620.82 ( 0.75 ; 0.87)254,871    114,305overall sum273,470    127,9609,720    85,5960.77
( 0.68 ; 0.83)283,189    123,043ws1 week set 1 , ws2 week set 2 , sd standard deviation , diff difference , icc intraclass correlation , 95  % ci 95  % confidence intervalfig 2a 95  % trimmed sum of counts per minute : difference ( week set 1week set 2 ) versus average of values measured in week set 1 and week set 2 with 95  % limits of agreement ( mean , 1.96    standard deviation ) .
ws1 week set 1 consisting of monday , tuesday , wednesday ; ws2 week set 2 consisting of thursday , friday , saturday ; cpm counts per minute , solid horizontal line average of differences of ws1 and ws2 , dashed horizontal lines 95  % limits of agreement ( mean difference , 1.96    standard deviation ) counts per minute of the sum , the quantile , and the trimmed sum including intraclass correlation ws1 week set 1 , ws2 week set 2 , sd standard deviation , diff difference , icc intraclass correlation , 95  % ci 95  % confidence interval a 95  % trimmed sum of counts per minute : difference ( week set 1week set 2 ) versus average of values measured in week set 1 and week set 2 with 95  % limits of agreement ( mean , 1.96    standard deviation ) .
ws1 week set 1 consisting of monday , tuesday , wednesday ; ws2 week set 2 consisting of thursday , friday , saturday ; cpm counts per minute , solid horizontal line average of differences of ws1 and ws2 , dashed horizontal lines 95  % limits of agreement ( mean difference , 1.96    standard deviation )
the anthropometric characteristics of the 123 participants ( aged 76.5    5.1  years , 59  % female ) of the study are shown in table  1.table 1characteristics of the study participants in total and broken down by sextotal n  =  123female n  =  73 ( 59  % ) male n  =  50mean    sdminmaxmean    sdminmaxmean    sdminmaxage ( years)76.5    5.170.198.677.2    5.870.198.675.6    3.770.285.5height ( m)1.65   
0.081.471.861.60    0.061.471.781.71    0.061.541.86weight ( kg)81.2    14.550.5114.077.3    14.450.5114.086.8    12.755.0111.0body mass index ( kg    m)29.8    4.420.544.230.1    4.920.544.229.5    3.622.935.9sum cpm over 7  days619,084430,340820,977692,898426,588875,139594,925429,553708,919n number of participants , sd standard deviation , min minimum , max maximum , m meter , kg kilogrammedian25  % quantile75  % quantile characteristics of the study participants in total and broken down by sex n number of participants , sd standard deviation , min minimum , max maximum , m meter , kg kilogram
the assessment of physical activity of older adults in this study showed measurement errors ( outliers ) .
this activity profile mainly shows cpm in between 0 ( inactive ) and 1,000 , whereas five single values clearly exceed the usual level .
this occurrence was similar in physical activity profiles of other participants who were randomly chosen.fig .
1listed count per minute during a 1-week period ( 10,080 in total ) and each value of the corresponding count per minute including five unreasonable high values ( measurement errors ) .
the solid vertical lines divide the 7  days of measurement from 1  day to another listed count per minute during a 1-week period ( 10,080 in total ) and each value of the corresponding count per minute including five unreasonable high values ( measurement errors ) .
the solid vertical lines divide the 7  days of measurement from 1  day to another
the icc of the retest reliability of the overall sum of cpm for the 3-day measurement was icc  =  0.77 ( 95  % confidence interval [ ci ] : 0.680.83 ) . using the quantiles , the icc was between 0.22 ( 95  % ci : 0.050.39 ) and 0.91 ( 95  % ci : 0.870.93 ) .
for the trimmed sum , the icc was between 0.82 ( 95  % ci : 0.750.87 ) and 0.85 ( 95  % ci : 0.790.89 ) .
the differences in the cpm from week set 1 and week set 2 show only moderate variations in the bland 
2).table 2counts per minute of the sum , the quantile , and the trimmed sum including intraclass correlationws1 mean    sddiff ( ws1   
ws2 )    sdicc ( 95  % ci)ws2 mean    sdq80119    664    300.89 ( 0.85 ; 0.92)115    62q85158    795    330.90 ( 0.87 ; 0.93)153    74q90212    966    390.91 ( 0.87 ; 0.93)205    87q95303    1259    570.88 ( 0.83 ; 0.91)294    107q99523    2213    3720.22 ( 0.05 ; 0.39)525    359ts8069,773    49,9381,508    28,4060.84 ( 0.78 ; 0.88)71,280    50,078ts8598,674    64,1072,304    35,6150.85 ( 0.79 ; 0.89)100,978    63,797ts90136,415    80,6003,165    44,8210.84
( 0.78 ; 0.89)139,579    79,010ts95187,115    99,1915,156    55,1060.84 ( 0.78 ; 0.89)192,271    97,347ts99248,356    119,9966,514    70,0620.82 ( 0.75 ; 0.87)254,871    114,305overall sum273,470    127,9609,720    85,5960.77 ( 0.68 ; 0.83)283,189 
  123,043ws1 week set 1 , ws2 week set 2 , sd standard deviation , diff difference , icc intraclass correlation , 95  % ci 95  % confidence intervalfig 2a 95  % trimmed sum of counts per minute : difference ( week set 1week set 2 ) versus average of values measured in week set 1 and week set 2 with 95  % limits of agreement ( mean , 1.96    standard deviation ) .
ws1 week set 1 consisting of monday , tuesday , wednesday ; ws2 week set 2 consisting of thursday , friday , saturday ; cpm counts per minute , solid horizontal line average of differences of ws1 and ws2 , dashed horizontal lines 95  % limits of agreement ( mean difference , 1.96    standard deviation ) counts per minute of the sum , the quantile , and the trimmed sum including intraclass correlation ws1 week set 1 , ws2 week set 2 , sd standard deviation , diff difference , icc intraclass correlation , 95  % ci 95  % confidence interval a 95  % trimmed sum of counts per minute : difference ( week set 1week set 2 ) versus average of values measured in week set 1 and week set 2 with 95  % limits of agreement ( mean , 1.96    standard deviation ) .
ws1 week set 1 consisting of monday , tuesday , wednesday ; ws2 week set 2 consisting of thursday , friday , saturday ; cpm counts per minute , solid horizontal line average of differences of ws1 and ws2 , dashed horizontal lines 95  % limits of agreement ( mean difference , 1.96    standard deviation )
in order to measure physical activity within studies , accelerometry is a measurement technique which is widely applied . but this method is still afflicted with some peculiarities , e.g. , measurement errors . in order to enhance the quality of data , we proposed to use more robust estimators such as quantiles or trimmed sums as a summary measure of physical activity instead of the overall sum .
as assumed , both quantiles and trimmed sums cpm increased the retest reliability compared to the overall sum .
this was true irrespective of the chosen cut off point ( e.g. , 80 or 95  % ) above which the values were omitted ( trimmed sum ) .
we clearly showed that the retest reliability increases when using an estimator such as the ts95 .
when using a quantile to describe the physical activity , it remains unclear whether this cpm value at a predefined quantile was achieved due to one intensive physical activity ( e.g. , running quickly to get to the bus once during the 3-day measurement period ) irrespective of the remaining physical activity or if the person has a high average level of overall physical activity in general .
in contrast to the quantiles , the trimmed sum accounts for this , and the average physical activity remains in the estimator .
the trimmed sum allows a predefined ( or estimated ) error level  of the used device to be selected , and then yields a single number which reflects all activities .
additionally , the trimmed sum is proportional to the weighted / truncated mean , which allows the calculation of average activity , e.g.\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \text{average activity } } = \frac{1}{{\mathop \sum \nolimits_{i = 1}^n { w_i } } } \cdot { \text{t}}{{\text{s}}_{1 - \beta } } $ $ \end{document } summing up , the advantage of the trimmed sum is that it includes both the average level of activity and more intense effort , whereas a quantile would only measure the peak of more intense activities .
even though the ts95 did not show the highest retest reliability , it seems to be the most conservative estimator of the physical activity . virtually all measurement errors are eliminated , while all background level and intensive activities are still included . summing up
, the ts95 appears to be an appropriate measurement value for demonstrating the physical activity level of older adults . besides the introduced recommendation on dealing with outliers , we would like to compare the retest reliability of our study to others implemented on the same target group . with special regard to other manufacturers of wrist - worn accelerometers , gao and tsang   found a high retest reliability of the mean cpm in their study on 3-day measurements on 12 people (
these older participants , aged 79.8    11.2  years , wore the uniaxial actiwatch accelerometer ( mini mitter co. , inc . , bend , or , usa ) on the wrist for the same 3  days during two consecutive weeks .
found a comparably high agreement of a 7-day measurement with the actigraph uniaxial accelerometer ( gt1 m ; manufacturing technology inc ) , worn on the hip by 20 participants ( mean age about 74  years ) with pearson s r  =  0.87 .
these two studies both have a more laboratory character compared to our study , since the measurement was repeated on the same days of two consecutive weeks or a whole week after 2  months .
in contrast , we took the same week and split it into half ( sunday excluded ) . with our results on retest reliability , we were able to demonstrate that it is not compulsory to measure physical activity on the same half of the week . moreover , we also included saturdays in our analysis , even though activities on a saturday may be different to the rest of the week .
we assumed that participants would be less active on saturdays compared to monday to friday .
if this was true , our results on retest reliability would be negatively influenced and would have been even higher , if we had not included saturdays in the analysis .
accelerometry is a method widely applied to assess physical activity in studies [ 17 , 22 , 27 ] and it will often be used in the future . our recommendation of using the trimmed sum ( e.g. , 95  % ) as a conservative estimate of the physical activity level of older adults would increase the quality of data by controlling for measurement errors .
 there is general consensus that physical activity is important for preserving functional capacities of older adults and positively influencing quality of life . 
 while accelerometry is widely accepted and applied to assess physical activity in studies , several problems with this method remain ( e.g. , low retest reliability , measurement errors ) . 
 the aim of this study was to test the intra - instrumental retest reliability of a wrist - worn accelerometer in a 3-day measurement of physical activity in older adults and to compare different estimators . 
 a sample of 123 older adults ( 76.5    5.1  years , 59  % female ) wore a uniaxial accelerometer continuously for 1  week . 
 the data were split into two repeated measurement values ( week set ) of 3  days each . 
 the sum , the 8099th quantiles and the 8099th trimmed sums were built for each week set . 
 retest reliability was assessed for each estimator and graphically demonstrated by bland  altman plots . 
 the intraclass correlation of the retest reliability ranged from 0.22 to 0.91 . 
 retest reliability increases when a more robust estimator than the overall sum is used . 
 therefore , the trimmed sum can be recommended as a conservative estimate of the physical activity level of older adults . 
Introduction
Methods
Results
Participants
CPM
Retest reliability
Discussion
Perspectives