Table Of ContentPART
A
Interpretation
of Breath
Analysis Data
CHAPTER
1
Mathematical and Statistical
Approaches for Interpreting
Biomarker Compounds in
Exhaled Human Breath
JoachimD.PleilandJonR.Sobus
NationalExposureResearchLaboratory,OfficeofResearchandDevelopment,
USEnvironmentalProtectionAgency,ResearchTrianglePark,NC27711,USA
1.1 INTRODUCTION
Thevariousinstrumentaltechniques,humanstudies,anddiagnosticteststhatproduce
datafromsamplesofexhaledbreathhaveonethingincommon:theyallneedtobe
putintoacontextwhereinaposedquestioncanactuallybeanswered.Exhaledbreath
containsnumerouscompounds;justthevolatileorganicfractionalonehasbeenesti-
matedtorepresentinexcessof500differentchemicalspecies.Inaddition,theaerosol
fractioncontainsproteins,signalingmolecules,dissolvedinorganiccompounds,and
evenbacteriaandvirusesaddingtothecomplexityofthetotalsample.
Nosingletechniquecandetecteverythinginbreath,infact,eventhemostbroadly
designedbreathmeasurementsresultinsuitesofcompoundsrestrictedbythemethods
used.Forexample,reactiveoxygenspeciesmaybeobservedusingreal-timesensors
orreal-timemassspectrometry(MS),butnotbygaschromatography-MS(GC-MS),
whereas GC-MS can discriminate among a variety of hydrocarbons, alcohols, and
ketones that may overlap completely in a real-time MS instrument without benefit
ofchromatographicseparation.Furthermore,thefractionofthebreath(gas-phaseor
aerosolphase)alsodetermineswhatmeasurementscanbemade;forexampleproteins
andsignalingmoleculescouldbedetectedinexhaledbreathcondensateviaenzyme-
linkedimmunosorbentassay(ELISA),nuclearmagneticresonance(NMR),orliquid
chromatography(LC)MS,butnotwithanygas-phaseinstrumentssuchasthosebased
onopticalspectroscopyorgaschromatography.
Thefirstissuethatthedataanalystfacesisthatalldataheorshesees,regardless
howcomplexordetailed,isnotcomprehensivebutalwaysstratified(restricted)bythe
chemistry, instrumentation, and thermodynamics of the choices made for sampling
andanalysis.Thesecondissueisthatasuiteofcompounds measuredinanygiven
sampledoesnotrepresentanindependentsetofvariables;sub-groupsofbiomarker
compoundsoftenhaveappreciablecovariancereflectingsimilarmetabolicpathways
orexogenoussources.Thethirdissuerelatestovariability;anygivensampleisunique
anditcanneverbetakenforgrantedthattheconstituentsofthebreatharethesame
betweenpeoplenorwithinonepersonovertime.Finally,anyindividualcompound
VolatileBiomarkers.http://dx.doi.org/10.1016/B978-0-44-462613-4.00001-5 3
2013PublishedbyElsevierB.V.
4 CHAPTER 1 Mathematical and Statistical Approaches
inbreathcanhaveawiderangeofconcentrationsthatareallconsidered“normal”or
“unremarkable”intheapparentlyhealthygeneralpopulation.Thishasimplications
for assessing health or exposure status based on just a few data points; under such
constraints,theanalystcanonlyinterpretameasurementasastatisticalprobability
thattheconcentrationisprobative.
1.2 DATA INTERPRETATION
Inthischapter,wedescribeaseriesofmathematicalandstatisticalapproachesgeared
specifically to the interpretation of volatile organics in exhaled breath that can be
implementedtoaddressthefourissuesoutlinedabove.Althoughallmethodsinteract,
wehaveassignedthemtofivecategoriesforthepurposesofthisdiscussionasfollows:
1. Datavisualizationandsummarystatistics.
2. Variableindependenceandclustering.
3. Populationstatisticsandvariancecomponents.
4. Stochasticmodelsandmeta-data.
5. Dynamicmodelsandlongitudinaldata.
Eachoftheseapproachescanprovidedistinctinformationaboutabreathdataset,
generallyincreasingindetailintheorderlisted.Wenotethatthebroaderinterpreta-
tionsgleanedfromcategories1–3feedthemodelingprocessesin4and5.Wefurther
note that not all of these procedures need to be performed; often it is sufficient to
answeraquestionwithasimpleanalysisbasedonagraphorasummarytable.Inthe
following,wedescribethesecategoriesandshowhowtheycanprogressivelytella
storyaboutacquireddata.Weassumethatmultiplecompoundshavebeenmeasured
acrossanumberofpeople,subjectsmaybegroupedascasesandcontrols,hostfactor
meta-data have been collected, and measurements may have been repeated, either
withorwithoutinterventionortreatment.
1.2.1 Data visualization and summary statistics
The first step in any analysis of newly acquired data is to get a “feel” for how the
experimentturnedout.Generally,wemakegraphsandcalculateaverages,standard
deviations, data ranges, etc. We have found that it is very helpful to get all of the
data into some form of visual representation, either as bar graphs, cluster plots, or
heatmaps,dependingoncomplexityofthedatastructure.Forexample,inarecent
publication, we described measurements of a series of polar volatile organic com-
pounds (PVOCs) in exhaled breath condensate (EBC) made during an intervention
study of diesel exhaust exposure.1 Human subjects (3 males and 6 females) were
eachexposedfor2htoadilutedieselexhaustatmosphereandtoapurifiedairatmo-
sphereonseparateoccasions.2 Avarietyofsamples,includingEBC,werecollected
immediately before and after the exposures, and again 24h later; EBC means data
foreightofthemostprevalentcompoundswereplottedbyninesubjectsgroupedby
Pleil and Sobus 5
FIGURE1.1
Bar graph visualization of balanced exhaled breath data from an intervention study of
dieselexhaustexposure.Summarybreathdataforninesubjectsandeightcompounds.
gender(Figure1.1).Wenotedaslightgenderbiasforsomecompounds,butotherwise
the results were unremarkable and we went on to assess the data from a statistical
perspective. In a subsequent publication, however, we developed methodology for
datavisualizationusingheatmapstylegraphics.3Briefly,heatmapsarevisualrepre-
sentationsofquantitativedataontwoaxes;thex-axisreflectsindividualsamplesand
they-axisconsistsofgroupsofmeasuredparameters.Thefieldbetweentheaxesis
comprisedofanarraycontiguousboxescolorcodedtoreflectquantitation.Theterm
“heatmap”isderivedfromtheconventionthatthehigherlevelstendtowardred,the
lowerlevelstendtowardblue.
WerevisitedthedatasetfromHubbardetal.1 andfoundthatheatmapvisualiza-
tionwascapableofshowingmorepatterndetail.Thistechniquehadtoberestricted
to seven subjects with complete data to avoid blank spots on the heat map as we
lostafewsamplestofollow-up.Figure1.2showsthisalternateapproach;notethat
we now have access to results from individual subjects’ samples, for all 16 mea-
sured PVOCs, and the flexibility for grouping samples by gender and longitudi-
nal parameters. Here, the gender effect becomes obvious; males were expressing
muchhigherlevelsofmanyofthemeasuredPVOCs,especially2-methylpropanal,
1-heptanol,butanal,pentanal,1-hexanol,and3-methyl-3-pentanol.Onlyhexanaland
heptanalreversethistrend.Wefurtherseethatthereisnoapparenttreatmenteffect
orlongitudinaltimeeffect,thatis,therearenoobviouspatterndifferencesbetween
diesel exposures and air exposures, nor pre- and post-exposure data. These simple
6 CHAPTER 1 Mathematical and Statistical Approaches
FIGURE1.2
Heat map visualization of balanced exhaled breath data from an intervention study
of diesel exhaust exposure. Individual samples grouped by longitudinal time frame
(pre-exposure,post-exposure,and24hpost-exposure)aswellasbygender.
visualization approaches, coupled with summary statistics, can provide hints as to
howmoredetailedmathematicalapproachescouldbeimplementedtoquantifythese
observations.Also,wenotethatthevisualizationmethodsforcomplexdatamakethe
subsequentstatisticalcalculationsmoreaccessibletothereadership.
1.2.2 Variable independence and clustering
Oneofthemostvexingproblemsencounteredindatainterpretationproceduresisthe
determinationofactualindependenceofwhatwegenerallydenoteas“independent
variables.” Subsequent statistical evaluations rely on the notion that measurements
that are used in models are not overly correlated. For example, consider the height
and weight parameters of human subjects as host-factor data in a complex breath
experiment. We know that taller people tend to be heavier, and so there is signifi-
cantcorrelationexpected.Ifoneweretotreatheightandweightasindependentand
place them both into a model for predicting a health outcome (along with a series
of breath biomarkers), one can get completely different interpretations as to their
respectiveimportancedependinguponwhichwasenteredfirst.Thisiswhyoneoften
seesbody-massindex(BMI)usedasacompositeparameterinstead.Nowconsider
unexpectedcorrelationsamongvariables,forexample,amongcompoundsmeasured
in the exhaled breath of subjects in an intervention or case-control study. If certain
Pleil and Sobus 7
compoundsarerepeatedlybehavingthesameway,thentheirinclusioninevensimple
multivariateregressionmodelswillresultinmathematicalinstability.
Wecannotknowaprioriifdifferentanalytesaretrackingthesameoutcome,how-
ever,wecanperformvariouscorrelationtestsamongpresumedindependentvariables
toassessthedegreeofindependence.Themostfundamentalmethodisthecorrelation
matrixwhereintheregressionbetweenpairsofvariables(V,V )iscalculatedasthe
i k
Pearsoncorrelationcoefficient“r”whichhaspossiblevaluesrangingfrom−1to1.
Positiver-valuesindicatethatalargerV isassociatedwithalargerV ,whereasaneg-
i k
ativerindicatesthatalargerV isassociatedwithasmallerV .Thecloserther-value
i k
isto0,themoreindependentthetwovariables.Forexample,inastudymeasuring
height(H),weight(W),andpercentbodyfat(BF),r=0.486forWvs.H,r=0.074for
Hvs.BF,andr=0.613forWvs.BF.4Basedontheresultsofthissimplecorrelation
matrix, one would probably not include both parameters H and W, nor both W and
BF,butwouldkeepHandBFashostfactorsinaresultingmodel.
The correlation matrix approach is considered a semi-quantitative measure for
overall data independence interpretation because it treats variables two at a time;
one cannot discern directly how multiple variables, or combinations of variables,
correlate.AmoresophisticatedapproachisavailablewhereinEigenvectorprojections
arecalculatedforallvariablesinn-dimensionalspace.Usingstatisticalsoftwaresuch
as proc VARCLUS from SAS Inc. (Cary, NC, USA), it is possible to develop a
“dendrite”diagramthatcanbeusedtocreateclustersofvariablesthathavecertain
levels of co-linearity. This is similar to principle components analysis (PCA), but
rather than grouping samples, this approach groups variables. Variable clustering
servestwopurposes,itimprovesmodelstabilitybyidentifying/removingcollinearity,
andreducesthetotalnumberofvariablesforamoreparsimoniousmodel.5
Asanexample,considerthedendritediagram(dendrogram)inFigure1.3where
weshowagenericexampleofbothhostfactorandmeasurementdataclustering.5In
thiscase,weuseahypotheticaldatastructurewithsixhostfactors(gender,BMI,age,
etc.)andsevenenvironmental/biomarkervariables(e.g.concentrationmeasurements
in blood or urine). This methodology has been applied to complex environmental
dioxincongenerdata6 andtostudiesofjetfuelexposureintheUSAirForce.7
By collapsing the more highly correlated variables into clusters, we do not lose
muchexplanatory power,butimprovetheinterpretivepower ofsubsequent models
by increasing the ratio (n/m) between number of samples “n” and the number of
independentvariables“m.”Wehaveobservedthatn/m(cid:2)10isagoodruleofthumb
forassessingtheimportanceofindividualvariables.6Wecautionthatthisprocedure
requiresacertainamountofjudgmentonthepartoftheinvestigator.Thefirstissue
is choosing the variance level vs. number of clusters. This is very dependent on
the eventual n/m parameter. The second issue is how to combine information from
variablescollapsedintoclusters.Thereareanumber ofchoices thatdependonthe
natureofthevariables;intheaboveexample,weuseasimplesum,butotherstrategies
canbeemployedaswell.Forexample,givenhighlycorrelatedvariablessuchasHF3
andHF4(especiallyiftheyarenotcontinuous),onecanjustdiscardoneortheother.
8 CHAPTER 1 Mathematical and Statistical Approaches
FIGURE1.3
Example dendrogram of variable cluster analysis. Starting with a total of m=13 inde-
pendentvariables(p=6hostfactorsandq=7environmentalvariables),forming8clus-
ters(HF1,HF2,HF3+HF4,HF5+HF6,RV1,RV2,RV3+RV4+RV5+RV6,andRV7)
resultsinexplainedvarianceof∼93%.Collapsingtheclustersfurtherto2Groupsexplains
∼83%ofthevariance,butnowisdifficulttointerpret.
Formeasuredconcentrations,itissometimesbettertonormalizeeachmeasurement
toatotaltoavoidhavingaparticularvariableoverwhelmthesum.
1.2.3 Population statistics and variance components
Traditionalmathematicalanalysesofbreathbiomarkers,bothforclinicalandenviron-
mentalresearchapplications,utilizemeasurementstatistics(e.g.meanandmedian)
toevaluatedifferencesbetweengroups.Forexample,itiscommontoevaluatemea-
surements statistics to compare cases vs. controls, exposed vs. unexposed subjects,
ormalesvs.females(asshowninourearlierexampleofadieselinterventionstudy).
Furthermore,itiscommontoemploystratifieddataanalyses—thatis,analysesusing
multiplelevelsoforganization—toreducetheimpactsofconfoundingvariables.Con-
sidertheevaluationofsmokingeffectsonbreathbiomarkerlevels;onecouldperform
asingleevaluationusingallsubjects(smokersvs.non-smokers),twoevaluationsafter
stratifyingbysex(malesmokersvs.malenon-smokers;femalesmokersvs.female
non-smokers),fourevaluationsafterstratifyingbysexanddiseasestatus(malesmoker
[case]vs.malesmoker[control];malenon-smoker[case]vs.malenon-smoker[con-
trol]; female smoker [case] vs. female smoker [control]; female non-smoker [case]
vs. female non-smoker [control]), and so on. These stratified analyses can narrow
Pleil and Sobus 9
downthepotentialoriginsofanobservedeffect,butrequirelargersamplenumbers
witheachlevelofstratification.Thus,aninvestigatormustbalancethedesiredout-
come of a given analysis with costs required to achieve sufficient statistical power
andsensitivity.6
Givenadequatesamplenumbersforstratifiedgroupanalyses,itisprudenttofirst
investigatetheunderlyingdistribution(s)ofthebiomarkerdatainquestion.Ourear-
lierexamplesfordataanalysis(i.e.datavisualizationandvariableclustering)canbe
consideredqualitativeorsemi-quantitative,andgenerallyhavenoaprioriconditions
fordatastructure.Hypothesistestingontheotherhand,isentirelyquantitative,and
inmanycasesreliesondistributionsofmeasurementdatabeingapproximatelyGaus-
sian,or“normal.”Simplediagnosticproceduresexistinmostsoftwarepackagesto
evaluatedatadistributions.Oftentimes,simplehistograms,normalprobabilityplots,
or quantile-quantile plots can be visually inspected to evaluate normality assump-
tions. More advanced statistical packages offer statistical tests (e.g. Shapiro-Wilk
andKolmogorov-Smirnov)toconfirmresultsfromvisualinspection.
Measurementsofanalytesinbiologicalmediaareoften“lognormally”distributed;
thatis,thedistributionoftheloggedvaluesisapproximatelynormal.Lognormaldata
canbeidentifiedbyaright-skeweddistributionoftheoriginal(non-transformed)data,
reflectingfewvaluesatexceedinglyhighlevels,andmanyvaluesnear,butnotbelow,
alowerthreshold(generallyzero).Additionalsignsoflognormallydistributeddata
include:(1)anobservedarithmeticmeanvaluethatislargerthanthemedian(reflect-
ingthedifferentialeffectsofextremelyhighvaluesonthesestatisticalparameters)and
(2)anobservedconfidenceintervalthatincludesnegativevalues(itisimpossibleto
havenegativeamountsofabiomarker).Whenoneencountersthesesigns,itisbest
to evaluate data transformation approaches before pursuing quantitative hypothesis
testing.
“Parametric”testingproceduresaregenerallyusedtoevaluatenormallydistributed
dataandlognormallydistributeddatathathavebeenlog-transformed.Commonlyused
parametrictestsincludetheStudent’st-test,thepairedt-test,andanalysisofvariance
(ANOVA).AStudent’st-testevaluatesdifferencesinbiomarkermeasurementsacross
twogroups(e.g.menvs.women);apairedt-testevaluatesdifferencesinbiomarker
measurements between paired samples from individuals (e.g. pre-intervention vs.
post-intervention);andANOVAcomparesbiomarkermeasurementsacrossmultiple
groups(e.g.childrenvs.adolescentsvs.adults).Intheeventthatbiomarkerdataarenot
Gaussian,orcannotbemathematicallytransformedtoapproximatenormality,“non-
parametric” methods exist for hypothesis testing. For example, the Mann-Whitney
test,Wilcoxontest,andKruskal-WallistestarecommonsubstitutesfortheStudent’s
t-test,pairedt-test,andANOVA,respectively.Thesetestsgenerallyapproximatethe
resultsoftheparametrictestsgivenalargeenoughsamplesize.However,theexact
datarequirements(e.g.samplenumber,sampleindependence,randomselection)for
anygiventestshouldalwaysbeconsideredpriortohypothesistesting.
The statistical tests discussed thus far generally utilize a single observation for
eachsubject.(Whilethepairedt-testusestwoobservationspersubject,thedifference
betweenthetwovalues[i.e.asinglevalue]isusedforhypothesistesting.)Therefore,
10 CHAPTER 1 Mathematical and Statistical Approaches
differentapproachestodataanalysisarerequiredwhenmultiplemeasurementsexist
for each subject. At the most basic level, it is of interest to evaluate the spread of
thedata,orthe“variance,”betweenandwithinsubjects.Todothis,thetotalvariance
acrossallmeasurementsisfirstpartitionedintothatwhichisobservedacrossrepeated
measurementsofindividualsubjects,knownas“within-person(intra-individual)vari-
ance,” and that which is observed across average levels of all subjects known as
“between-person(inter-individual)variance.”Thesebetween-andwithin-personvari-
ancecomponentscanbecalculatedusinganumberoftechniques.8 Thesimplestof
thesemethodsisanalysisofvariance(ANOVA)whichissuitableforbalanceddata
setswherethesamenumberofmeasurementsexistsforeachsubject.Morecomplex
methods,suchasrestrictedmaximumlikelihoodestimation(REML),mayberequired
whenworkingwithunbalanceddatasets;thesemethodsaretypicallyavailableonly
inmoreadvancedstatisticalsoftwarepackages.
Oncethevariancecomponentsareestablished,theybecomeinstrumentalforiden-
tifyingtheoriginsofexposureordisease,andinturn,thebestopportunitiesformitiga-
tionorintervention.Largewithin-personvarianceandsmallbetween-personvariance
indicateslittledifferencebetweensubjectsonaverage,butlargedifferencesovertime
foreachsubject.Thisresultmaypointtoatemporalevent,randomorotherwise,that
affects each subject equally. Alternatively, small within-person variance and large
between-person variance indicates little change over time, but marked differences
betweensubjects.Thisresultmaypointtoahost-specificparameter(e.g.genotype,
fitness-level) thatdictates biomarker response. Inthefirstexample, ageneral inter-
vention strategy, equally applicable to all subjects, might be suitable to reduce an
exposure or limit a biological response. In the second example, a targeted strategy
wouldlikelybenecessarytofirstidentifythecauseofelevatedbiomarkerlevelsfor
certainindividuals,andthenforintervention.
1.2.4 Stochastic models and meta-data
After identifying group-based differences in biomarkers levels, and within- and
between-subjectvariancecomponents(forrepeated-measuresstudiesonly),thenext
stepistodevelop statisticalmodelsusingstudymeta-data. Statisticalmodels serve
twofunctionsforbreathresearch:(1)theyallowinvestigatorstosimultaneouslyiden-
tifymultiplesignificantpredictorsofbreathbiomarkerlevelsand(2)theyprovidea
platformforpredictingbreathbiomarkerlevelsinotherstudieswhereonlymeta-data
exist.
Animportantdecisionformodeldevelopmentisidentifyingadependentvariable;
this is not as easy as it sounds. Often, the dependent variable is obvious by design
and represents the “outcome” for a subject; it can be binomial, that is, cancer/not
cancer,infected/notinfected,oritcanbeacontinuoushealthoutcomevariablesuch
ascholesterollevel,totalurinaryprotein,pulmonaryfunction(e.g.forcedexpiratory
volume in 1s (FEV1), forced vital capacity (FVC)), or DNA damage (e.g. sister
chromatidexchange(SCE),strandbreaks),amongothers.
Pleil and Sobus 11
However,therearemanyoccasionswhenthechoiceofthedependentvariableis
notobvious,especiallyinenvironmentalorcross-sectionalpublichealthstudiesfor
whichtheanalystwasnotconsultedinsamplingdesign.Forexample,supposeone
hasmeasuredasuiteofexogenouschemicalsandmetabolitesinexhaledbreath,and
hasacquiredmeta-dataconcerningrecentactivity,jobtype,height,weight,gender,
ethnicity,etc.,butnohealtheffectsinformationwascollectedorobserved.Whatcould
thedependentvariablebeforinterpretationpurposes?Insuchcases,thefirstquestion
tobeaddressedis:Whatdowewanttoknow?Generally,wewouldliketoexplore
the linkages between suspected exposure sources and the resulting internal dose in
humansubjects.Supposethatinthetotalityofallmeasurements,weobservebenzene,
toluene,ethyl-benzene,andxylenes(BTEX),plusmanyotherorganiccompoundsin
breath. If one of the suspected sources for all exposures is automobile exhaust, we
couldsumtheBTEXnumbersintoonecompositeparameterandusethistorepresent
the dependent variable for overall fuels exposure. This is a bit of a bootstrapping
approach, especially if we keep the individual BTEX compounds as independent
continuousvariables,butoftenthisistheonlywaytobuildastochasticmodelinthe
absenceofadesigneddependentvariable.
Giventhatwehaveanumberof“independentvariable”measurementsandrelated
meta-dataandsomeconsensusdependent(outcome)variable,thenthenextstepisto
determine which independent variables and data actually tell a story relating to the
changes intheidentified outcome variable. Thisrequires someformof amodeling
approach,andifthedataincludebothhostfactorsandcontinuousvariables,thebest
approachisageneralizedlinearmodel,ora“mixedeffects”model.8,9
Ageneralformofsuchamodelis:
(cid:2) (cid:3)
Y = β X +β X +···+β X +α +b +(cid:4) ,
hij 1 1hij 2 2hij p phij h hi hij
whereY isthevalueofsomerelevantbiologicalparameterforthejthobservation
hij
oftheithsubjectinthehthgroup; X ,X ,...,X arethevaluesofthefixed
1hij 2hij phij
effect variables such as environmental chemical concentrations (in air, water, food,
dust,etc.),andhostfactorssuchasage,healthstate,gender,geneticpolymorphisms,
ethnicity,etc.;pisthetotalnumberoffixedeffects(note:thehostfactorsmaybefixed
foralljwithinagiveni);β ,β ,…,β arethecorrespondingmodeledcoefficients
1 2 p
for the fixed effects and host factors; α is the random effect for the hth group; b
h hi
is the random effect for the ith subject from the hth group; and (cid:4) is the residual
hij
(unexplained)errorforthejthobservationoftheithsubjectfromthehthgroup.
Softwareapplicationsforthisstyleofapproacharecommerciallyavailable(e.g.
procMIXED,SAS).Uponcalculation,thecoefficientsandtheirp-valuescanbeinter-
pretedtodeterminetheeffectofincludingtheparticularfixedeffectorrandomeffect
variableinthefinalmodelforexplainingthevarianceinthebiologicalparameters’
values.Thiscanbedonewithiterativestepsofforwardadditionorreverseelimination
withtheeventualobjectivebeingaparsimoniousmodelwithoutappreciablelossof
modelingpower.Oncethefinalmodelisestablished,wecanobservewhichexposure
parameters and fixed effects are more likely to cause perturbations to the systems
biology.5
