Measuring the impact of apnea and obesity on circadian activity patterns using functional linear modeling of actigraphy data

Wang Jia, Xian Hong, Licis Amy, Deych Elena, Ding Jimin, Mcleland Jennifer, Toedebusch Cristina, Li Tao, Duntley Stephen, Shannon, Shannon William

Description

Actigraphy provides a way to objectively measure activity in human subjects. This paper describes a novel family of statistical methods that can be used to analyze this data in a more comprehensive way. Methods A statistical method for testing differences in activity patterns measured by actigraphy across subgroups using functional data analysis is described. For illustration this method is used to statistically assess the impact of apnea-hypopnea index (apnea) and body mass index (BMI) on circadian activity patterns measured using actigraphy in 395 participants from 18 to 80 years old, referred to the Washington University Sleep Medicine Center for general sleep medicine care. Mathematical descriptions of the methods and results from their application to real data are presented. Results Activity patterns were recorded by an Actical device (Philips Respironics Inc.) every minute for at least seven days. Functional linear modeling was used to detect the association between circadian activity patterns and apnea and BMI. Results indicate that participants in high apnea group have statistically lower activity during the day, and that BMI in our study population does not significantly impact circadian patterns. Conclusions Compared with analysis using summary measures (e.g., average activity over 24 hours, total sleep time), Functional Data Analysis (FDA) is a novel statistical framework that more efficiently analyzes information from actigraphy data. FDA has the potential to reposition the focus of actigraphy data from general sleep assessment to rigorous analyses of circadian activity rhythms.

Sujets

• Apnéa
• Bmi
• Functional data analysis

Informations

• Publié par: biomed
• Publié le: 01 janvier 2011
• Nombre de lectures: 11
• Langue: English

Extrait

Wang
etal
.
JournalofCircadianRhythms
2011,
9
:11
http://www.jcircadianrhythms.com/content/9/1/11

RESEARCH

OpenAccess

Measuringtheimpactofapneaandobesityon
circadianactivitypatternsusingfunctionallinear
modelingofactigraphydata
JiaWang
1
,HongXian
1,2
,AmyLicis
3
,ElenaDeych
1
,JiminDing
4
,JenniferMcLeland
3
,CristinaToedebusch
3
,TaoLi
1
,
StephenDuntley
3
andWilliamShannon
1*

Abstract
Background:
Actigraphyprovidesawaytoobjectivelymeasureactivityinhumansubjects.Thispaperdescribesa
novelfamilyofstatisticalmethodsthatcanbeusedtoanalyzethisdatainamorecomprehensiveway.
Methods:
Astatisticalmethodfortestingdifferencesinactivitypatternsmeasuredbyactigraphyacrosssubgroups
usingfunctionaldataanalysisisdescribed.Forillustrationthismethodisusedtostatisticallyassesstheimpactof
apnea-hypopneaindex(apnea)andbodymassindex(BMI)oncircadianactivitypatternsmeasuredusing
actigraphyin395participantsfrom18to80yearsold,referredtotheWashingtonUniversitySleepMedicine
Centerforgeneralsleepmedicinecare.Mathematicaldescriptionsofthemethodsandresultsfromtheir
applicationtorealdataarepresented.
Results:
ActivitypatternswererecordedbyanActicaldevice(PhilipsRespironicsInc.)everyminuteforatleast
sevendays.Functionallinearmodelingwasusedtodetecttheassociationbetweencircadianactivitypatternsand
apneaandBMI.Resultsindicatethatparticipantsinhighapneagrouphavestatisticallyloweractivityduringthe
day,andthatBMIinourstudypopulationdoesnotsignificantlyimpactcircadianpatterns.
Conclusions:
Comparedwithanalysisusingsummarymeasures(e.g.,averageactivityover24hours,totalsleep
time),FunctionalDataAnalysis(FDA)isanovelstatisticalframeworkthatmoreefficientlyanalyzesinformationfrom
actigraphydata.FDAhasthepotentialtorepositionthefocusofactigraphydatafromgeneralsleepassessmentto
rigorousanalysesofcircadianactivityrhythms.
Keywords:
Apnea,BMI,circadianactivitypatterns,FunctionalDataAnalysis

1.Introduction
todaytimeactivityortotalactivity,[7,8]standarddevia-
Activitymeasuredbywristactigraphyhasbeenshowntionofsleeponsettime,[9]andintra-dailyvariability
tobeavalidmarkerofentrainedPolysomnography[10].Morecomplexmodelingofactigraphyincludes
(PSG)sleepphaseandisstronglycorrelatedwithspectralanalysis,[7]cosinoranalysis[7]andwaveform
entrainedendogenouscircadianphase[1].Actigraphyeductioncalculatedasan
“
averagewaveform
”
forsome
dataisrecordeddensely,suchaseveryminuteoreveryperiod[11].
15seconds,foreachpatientovermultipledays.ThisInthispaperweproposeanovelstatisticalframework,
dataisgenerallyanalyzedbyreducingthetimeseriesFunctionalLinearModeling(FLM),asubsetofFunc-
activityvaluestosummarystatisticssuchassleep/waketionalDataAnalysis(FDA),foranalyzingactigraphy
ratios,[2,3]totalsleeptime,[2,4]sleepefficiency,[5,6]datatoextractandanalyzecircadianactivityinforma-
wakeaftersleeponset,[2,3,6]ratioofnighttimeactivitytionthroughdirectanalysisofrawactivityvalues[12].
FLMextendsstandardlinearregressiontotheanalysis
*Correspondence:[e-mail]
offunctions,whichinthiscaserepresentcircadian
1
Dept.ofMedicine,WashingtonUniversitySchoolofMedicine,(660South
activitypatterns.FLMisperformedby1)convertinga
EuclidAvenue),St.Louis,(63110),USA
subject
’
srawactigraphydatatoafunctionalform(i.e.,
Fulllistofauthorinformationisavailableattheendofthearticle
©2011Wangetal;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons
AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproductionin
anymedium,providedtheoriginalworkisproperlycited.

Wang
etal
.
JournalofCircadianRhythms
2011,
9
:11
http://www.jcircadianrhythms.com/content/9/1/11

continuouscurveovertime),and2)analyzingsetsof
functionstoseeiftheydifferstatisticallyacrossgroups.
OurFLM-basedanalysisshowswhereandwithwhat
levelthedifferencebetweengroupsoccursalongthe
time,whichprovidesvaluablereferenceforclinicalana-
lysisandtreatments,anddistinguishesourmethods
fromexistingcircadiananalysisworks(see[13]fora
review).Moreover,weadoptedanon-parametricper-
mutationFtesttodetectthedifferencebetweengroups,
whichmakestheresultsrobusttotheuncertaintyin
rawdatadistribution.UsingFLM,weshowthatthe
apnea-hypopneaindex(apnea)hasastatisticallysignifi-
cantimpactoncircadianactivitypatterns,whilebody
massindex(BMI)inthisdatasethaslittleimpact.
2.Methods
2.1ParticipantsandMeasures
Participantswererecruitedprospectivelyfromtheclinic
atWashingtonUniversityinSt.LouisSleepMedicine
Center.Thesleepcenterisamultidisciplinaryclinicata
tertiarymedicalfacility.Clinicpatientswithasuspected
diagnosisofobstructivesleepapnea(OSA),insomnia,or
restlesslegssyndrome(RLS)wereinvitedtoparticipate.
Pregnantwomen,individualsunderageof18,and
patientswhoreportworkinganeveningorovernight
shiftwereexcludedfromparticipationduetoknown
biologicallydifferentcircadianclocks.Clinicalcovariates
suchasBMI,co-morbidities,concomitantmedications,
andpresentingsleepcomplaintswerecollected.Partici-
pantsunderwentanovernightPSGwhenclinicallyindi-
cated.Thesedatawerecollectedinaccordancewiththe
standardsoftheAmericanAcademyofSleepMedicine
(AASM)andwerereviewedbyaboardcertifiedsleep
physician.PSGdatawerescoredaccordingtothe
AASMManualfortheScoringofSleepandAssociated
Events.Thisongoingstudyhasbeenapprovedbythe
WashingtonUniversitySchoolofMedicineInstitutional
ReviewBoard.
ActivitywasmeasuredusingActicaldevices(Philips
RespironicsInc.)whichwerepositionedonthenon-domi-
nantwristofsubjectsattheinitialsleepcentervisitand
settomeasureactivityeveryminutefor7days.Three
hundredandninetyfivepatientshavebeenrecruited,of
which305haveapneaand/orBMImeasured.Thissub-
groupcomesfromalargerNIHfundedstudycurrently
recruitingacrosssectionof750patientsreferredtothe
WashingtonUniversitySleepMedicineCenterforthepur-
poseofdevelopingandvalidatingfunctionaldataanalysis
methodsforactigraphydata(HL092347).
2.2.FunctionalDataAnalysis(FDA)
FDAisanemergingfieldinstatisticsthatextendsclassi-
calstatisticalmethodsforanalyzingsetsofnumbers
(scalarsforunivariateanalyses,andvectorsfor

Page2of10

multivariateanalyses)toanalyzingsetsoffunctions[13]
[15].FDAisasubsetofthelargerfieldcalled
‘
object
dataanalysis
’
or
‘
objectorienteddataanalysis
’
thatuses
statisticalmethodstoanalyzedatathatareinnon-
numericformsuchasimages,graphs(e.g.,trees),or
functions[14,15].Thegoalofobjectorienteddataana-
lysisistoanalyzeobjectsintheirnaturalform(e.g.,
functions,graphs)toextractmoreinformationthan
generallycanbeextractedwhentheobjectsarecon-
vertedintosimplersummarymeasures(e.g.,average
activitylevel,totalsleeptime)wherestandardstatistical
methodscanbeapplied.
2.2.1Functionalsmoothing
Functionaldataanalysis(FDA)beginsbyreplacingdis-
creteactivityvaluesmeasuredateachtimeunit(e.g.,
minute)byafunctiontomodelthedataandreduce
variability.Thefunctionrepresentstheexpectedactivity
valueateachtimepointmeasured.Sincetheactigraphy
hasequidistantdata,toallowflexibilityinrepresenting
thedataasafunction,aFourierexpansionmodelis
used,thoughanysmoothingmethodcouldbeused.Let
y
kj
bethediscreteactivitycountforpatientkattime
point
t
kj
,thenthemodel
y
kj
=
Activity
k
(
t
kj
)+
ε
k
(
t
kj
)
(1)
representsactivity,where
k
=1,2,...
,N
,
N
istotalnum-
berofpatients,
j
=1,2,...,
T
k
,
T
k
isthetotalnumberof
timepointsforpatient
k
.Inourdataset,observation
timesareminutesfrommidnighttomidnightin24
hours,soallsubjectshavethesamenumberofmeasure-
ments
T
k
.
Weconverttherawactigraphydatatoafunctional
formusingabasisfunctionexpansionfor
Activity
k
(
t
j
)
Activity
k
(
t
j
)=
a
1
k

1
(
t
j
)+
a
2
k

2
(
t
j
)
2()+
···
+
a
nk

n
(
t
j
)
where
{
a
ik
}
in
=1
arescalarcoefficientsforpatientkand
{

i
(
·
)
}
in
=1
arebasisfunctions.Possiblebasisfunctions
includepolynomials(
f
(
t
)=
a
1
t
+
a
2
t
2
+...+
a
n
t
n
),Four-
(
f
(
t
)=
a
1
+
a
2
sin(
ω
t
)+
a
3
cos(
ω
t
)+
ierbasis,splines,
a
4
sin(2
ω
t
)+
a
5
cos(2
ω
t
)+
···
+
a
n
ϕ
n
)
andwavelets.
Experimentalresults(unpublished)showmostbasis
functionsworkequallywellandwehavefoundaFour-
ierexpansionwithn=9basisfunctionscapturethe
majortrendofactivitypatternwithreducednoise.Let

1
(
t
)=1,

2
(
t
)=cos(
ω
t
),

3