A diagnostic tool for population models using non-compartmental analysis: The ncappc package for R

computermethods andprograms in biomedicine 127 (2016)83–93

j ou rn a l h om epa ge :w w w . i n t l . e l s e v i e r h e a l th . c o m / j o u r n a l s / c m p b

A

diagnostic

tool

for

population

models

using

non-compartmental

analysis:

The

ncappc

package

for

R

Chayan

Acharya

_,

_Andrew

_C.

_Hooker

_,

_Gülbeyaz

_Yıldız

_Türkyılmaz

_,

Siv

Jönsson

_,

_Mats

_O.

_Karlsson

a_{DepartmentofPharmaceuticalBiosciences,UppsalaUniversity,P.O.Box591,SE-75124Uppsala,Sweden} b_{EgeUniversity,FacultyofPharmacy,DepartmentofBiopharmaceuticsandPharmacokinetics,35100 ˙Izmir,Turkey}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received13July2015 Receivedinrevisedform 7December2015 Accepted7January2016

Keywords:

Non-compartmentalanalysis(NCA) PK

NONMEM

Posteriorpredictivecheck Simulation-baseddiagnostic

a

b

s

t

r

a

c

t

Backgroundandobjective:Non-compartmentalanalysis(NCA)calculatespharmacokinetic (PK)metricsrelatedtothesystemicexposuretoadrugfollowingadministration,e.g.area undertheconcentration–timecurveandpeakconcentration.Wedevelopedanewpackage inR,calledncappc,toperform(i)aNCAand(ii)simulation-basedposteriorpredictivechecks (ppc)forapopulationPK(PopPK)modelusingNCAmetrics.

Methods:ThencafeatureofncappcpackageestimatestheNCAmetricsbyNCA.Theppc fea-tureofncappcestimatestheNCAmetricsfrommultiplesetsofsimulatedconcentration–time data andcomparesthemwith thoseestimatedfromtheobserveddata.Thediagnostic analysisisperformedatthepopulationaswellastheindividuallevel.Thedistribution ofthesimulatedpopulationmeansofeachNCAmetriciscomparedwiththe correspond-ingobservedpopulationmean.Theindividuallevelcomparisonisperformedbasedonthe deviationofthemeanofanyNCAmetricbasedonsimulationsforanindividualfromthe correspondingNCAmetricobtainedfromtheobserveddata.Thencappcpackagealsoreports thenormalizedpredictiondistributionerror(NPDE)ofthesimulatedNCAmetricsforeach individualandtheirdistributionwithinapopulation.

Results:Thencappcproducestwodefaultoutputsdependingonthetypeofanalysis per-formed,i.e.,NCAandPopPKdiagnosis.ThePopPKdiagnosisfeatureofncappcproduces 8 setsofgraphicaloutputstoassesstheability ofapopulation modelto simulatethe concentration–timeprofileofadrugandtherebyevaluate modeladequacy.Inaddition, tabularoutputsaregeneratedshowingthevaluesoftheNCAmetricsestimatedfromthe observedandthesimulateddata,alongwiththedeviation,NPDE,regressionparameters usedtoestimatetheeliminationrateconstantandtherelatedpopulationstatistics.

Conclusions:Thencappcpackageisaversatileandflexibletool-setwritteninRthat success-fullyestimatesNCAmetricsfromconcentration–timedataandproducesacomprehensive setofgraphicalandtabularoutputtosummarizethediagnosticresultsincludingthemodel specific outliers.The outputis easytointerpretandto useinevaluationof a popula-tionPKmodel.ncappcisfreelyavailableonCRAN(http://cran.r-project.org/web/packages/ ncappc/index.html/)andGitHub(https://github.com/cacha0227/ncappc/).

©2016TheAuthors.PublishedbyElsevierIrelandLtd.Thisisanopenaccessarticleunder theCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

∗ _{Correspondingauthor.Tel.:+46184714304.}

E-mailaddress:chayan.acharya@farmbio.uu.se(C.Acharya).

http://dx.doi.org/10.1016/j.cmpb.2016.01.013

0169-2607/©2016 TheAuthors. Published byElsevier Ireland Ltd. Thisis an open accessarticle underthe CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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1.

Introduction

Theprincipal objective ofthe pharmacokinetics(PK) stud-ies is to understand the kinetics of a drug molecule in terms ofabsorption,distribution, metabolismand elimina-tion (ADME). PK data analysis can primarily be classified into non-compartmental analysis (NCA) and model-based analysis,wherethelattercanrangefromcompartment mod-els tophysiology-based models[1]. TheNCA benefitsfrom fewerassumptions,comparedtomodel-basedapproaches.In NCA,the area under the curve (AUC), peak observeddrug concentration(Cmax),timeofpeakconcentration(Tmax),

ter-minaleliminationrateconstant(Lambdaz),terminalhalf-life (HLLambdaz)andothermetricsareestimatedtodetermine thesystemicexposureofadrugfollowingadministration.NCA istypicallyanessentialpartofPKanalysisinthefieldofdrug discoveryandinrichlysampledclinicalPKstudies.Regulatory decisionsregarding bioequivalence studies are oftenbased oncomparisonsofAUCandCmax,inparticular.Additionally,

NCAmay alsobeusedas adiagnostictooltoevaluatethe performanceofanycompartmentalpopulation pharmacoki-netic(PopPK)modelsbycomparingtheNCAmetricsobtained fromsimulatedconcentration–timedatatothesamemetrics obtainedfromtheobservedconcentration–timeprofile.This canprovideinformationonthemodelsabilitytoprovide ade-quate description of exposure measures that are typically judgedasimportantforrichlysampledconcentration–time profiles.

Anumberofsoftwaretools(suchasKinetica[2],WinNonlin

[3],PKmoduleinR[4],Scientist[5],PKSolver[6])areavailable thatcanperformNCA.Asanovelty,wehaveextendedtheuse ofNCAasapharmacometricmodeldiagnostictoolemploying theprinciplesofaposteriorpredictivecheck[7]withtheNCA metricsasteststatistics.Inthisarticlewereporta simulation-baseddiagnosticpackage,calledncappc,writteninR[8]that (i)providesasimpleandflexiblemethodtoestimatetheNCA metricsfromtheobserveddataand(ii)comparesthemwith thesamemetricestimatedfrommultipledatasetssimulated usingthePopPKmodeltobediagnosed.Thusncappchelpsto bridgethegapbetweenNCAandpopulationmodelanalyses.

ncappcpackagecanpotentiallyfacilitatetheearlystageofthe drugdiscoveryprocessbyevaluatingtheperformanceofthe relatedPopPKmodelandidentifythemodelspecificoutliers.

2.

Methods

2.1. Implementationandtheusageofthencappc package

ThencappcpackageisimplementedinRandacceptsasetof inputarguments,resultingincertainprocessingofdataand outputproduction.Table1depictsthelistofacceptable argu-mentswithdefaultvaluesofthe arguments.Thenamesof mostoftheNCAmetricsestimatedbythencappcfunctionare consistentwiththoseusedinWinNonlin[3].Acomparisonof NCAmetricsobtainedbythencappcpackageandWinNonlin showednodiscrepanciesandtheresultscanbefoundinthe Supplementarymaterial-I.

obsFile and simFile arguments,used in ncappc, represent the observed and the simulated data. The default values of these two arguments are “ncaoriginal.npctab.dta” and “nca simulation.1.npctab.dta”,respectively.ToperformNCA,

obsFileargumentshouldbeadjustedtothecorrectnameofthe observeddatafile.IfsimFileargumentisNULLandtheworking directorydoesnotcontain“ncasimulation.1.npctab.dta”,only

ncafeatureofthispackagewillbeexecuted.Thenameofthe simulationoutputfile,structuredasiscommonintablefiles ofmanysoftwareincludingNONMEM[9]issuppliedviasimFile

argumenttousetheppcfeatureofthepackage.Allother argu-mentsareoptionalandtheirdefaultvaluemaybeadjusted accordingtothedescriptiongiveninTable1.

There are three arguments(namely str1Nm,str2Nm and

str3Nm)inncappcthatcanbeusedtostratifythestudy popula-tion.Forasinglelayerofstratificationanyofthesearguments canbeused.Iftheyareusedincombination,thepopulationis stratifiedintonestedlayers,wherestr1Nm,str2Nmandstr3Nm

representthe1st,2ndand3rdlevelsofstratification, respec-tively.

Ifnounitsaresuppliedforthedose,timeorconcentration,

ncappclabelsthe NCAmetricswithappropriate dimension-ality in terms of mass (M), length (L) and time (T). Fig. 1

displaystheworkflowofthisfunction.IfthesimFileargument is omitted only NCA on observeddata is performedwhile inclusionofthesimFileargumentresultsinbothNCA calcu-lationsand theppc-baseddiagnostics.Detailsofthe output generatedbyncappcpackagearedescribedinthe Supplemen-tarymaterial-II.Inbrief,theNCAfeatureproducestwosets of figures displaying the concentration vs. time profilefor eachindividualwithinacertainpopulationgroupandthe his-togramoffourNCAmetrics(AUClast,AUCINFobs,Cmax and

Tmax)estimatedfromtheobserveddata(seethe

Supplemen-tarymaterial-Iforthedefinitions).Additionally,twotablesare producedrepresentingtheestimatedindividualvaluesofthe NCAmetricsobtainedfromtheobserveddataandthevalues ofvarious populationstatistics ofeach oftheNCA metrics estimatedfromtheobserveddata,respectively.Pleaseseethe Supplementarymaterial-II forthedescriptionofthe output tablesandfiguresgeneratedbyncappc.

Inthe presenceofthe simulateddata obtainedusingof the concerned PopPK model,ncappc functionestimates the same setofNCAmetrics fromeach setofthesimulations. Next, the function performsthe individual and population level diagnostic testsand producesacomplete reportwith thegraphicalandtabularoutputsreportingtheindividualand populationleveldiagnosticresultsinvolvingsimulationmean, deviationfromtheobservedvalueandNormalizedPrediction DistributionError(NPDE)valuesofeachNCAmetric.Alltables producedbyncappcareintab-separatedtextformatandcanbe easilyloadedingenericdatavisualizationsoftwarelikeExcel, R,etc.

2.2. Simulation-basedPopPKmodelevaluationin ncappcpackage

Theobjectiveofthisfeatureofthencappcpackageistoperform aPopPKmodelevaluationusingsimulation-baseddiagnostics bycomparingtheNCAmetricsestimatedfromthesimulated datawiththesamemetricsestimatedfromtheobserveddata.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 2 7 ( 2 0 1 6 ) 83–93

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Table1–Descriptionandexpectedvaluesofthencappcarguments.

Name Description Exampleofpossiblevalues Default

obsFile Observedconcentration–timedatafromaninternaldataframe oranexternaltablewithcomma,taborspaceasseparator

Filenameordataframe “ncaoriginal.npctab.dta” simFile Simulatedconcentration–timedatainNONMEMformatfrom

aninternaldataframeoranexternaltable

Filenameordataframe “ncasimulation.1.npctab.dta”

str1Nm Columnnamefor1stlevelpopulationstratifier Columnname NULL

str1 StratificationIDofthememberswithin1stlevelstratification c(1,2) NULL

str2Nm Columnnamefor2ndlevelpopulationstratifier Columnname NULL

str2 StratificationIDofthememberswithin2ndlevelstratification c(1,2) NULL

str3Nm Columnnamefor3rdlevelpopulationstratifier Columnname NULL

str3 StratificationIDofthememberswithin3rdlevelstratification c(1,2) NULL

concUnit Unitoftheconcentration “ng/mL” “M.Lˆ-3”

timeUnit Unitofthetime “h” “T”

doseUnit Unitofthedose “g” “M”

doseNormUnit Normalizationfactorfordose “kg” NULL

obsLog Concentrationinobserveddatainlogarithmic Logical(TRUEorFALSE) FALSE

simLog Concentrationinsimulateddatainlogarithmic Logical(TRUEorFALSE) FALSE

psnOut ObserveddataisanoutputfromPsN(inNONMEMoutput format)

Logical(TRUEorFALSE) FALSE

idNmObs ColumnnameforIDinobserveddata Columnname “ID”

timeNmObs Columnnamefortimeinobserveddata Columnname “TIME”

concNmObs Columnnameforconcentrationinobserveddata Columnname “DV”

idNmSim ColumnnameforIDinsimulateddata Columnname “ID”

timeNmSim Columnnamefortimeinsimulateddata Columnname “TIME”

concNmSim Columnnameforconcentrationinsimulateddata Columnname “DV”

AUCTimeRange RangeoftimetocomputeAUC Lowerandupperlimitoftime(e.g.

c(0,24))

NULL

backExtrp OptiontobackextrapolatetopredictinitialconcentrationC0 Logical(TRUEorFALSE) FALSE

LambdaTimeRange RangeoftimetocomputeLambdaz Lowerandupperlimitoftime(e.g.

c(15,24))

NULL

LambdaExclude TimepointstobeexcludedfromLambdazcalculation Numeric(e.g.c(20,24)) NULL

doseAmtNm Columnnamefordoseamount Columnname AMT

adminType Doseadministrationtype “iv-bolus”,“iv-infusion”,

“extravascular”

“extravascular”

doseType Steadystateornon-steadystateofdose “ns”or“ss” “ns”

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Name Description Exampleofpossiblevalues Default

Tau Steadystatedosinginterval Numeric NULL

TI Infusionduration Numeric NULL

method ComputationalmethodtoestimateAUCandAUMC “linear”,“log”,“linear-log” “linear-log”

blqNm ColumnnameforBLQdata Columnname NULL

blqExcl BLQcolumnvaluestobeexcluded Numericorlogical(e.g.1,c(1,2),

“>=1”)

1

evid UseEVIDcolumntofilterdata Logical(TRUEorFALSE) TRUE

evidIncl EVIDvaluestobeincluded Numeric(e.g.0) 0

mdv UseMDVcolumntofilterdata Logical(TRUEorFALSE) FALSE

filterNm Columnnametofilterdata Columnname NULL

filterExcl Filteridentifiersusedtoexcludedata Numericorlogicalcondition(e.g.

1,c(1,2),“>=1”)

NULL

negConcExcl Excludenegativeconcentrations Logical(TRUEorFALSE) FALSE

param NCAmetricsusedfordiagnostics c(“AUClast”,“AUClowerupper”,

“AUCINFobs”,“AUCINFpred”, “AUMClast”,“Cmax”,“Tmax”, “HLLambdaz”)

c(“AUClast”,“Cmax”)

timeFormat Dataformatfortime Number,H:M,H:M:S “number”

dateColNm Nameofthedatecolumn Columnnamefordate NULL

dateFormat Formatofthedate D-M-Y,M-D-Y,Y-M-D,D/M/Y,

M/D/Y,Y/M/D

NULL

spread Measureofthespreadofsimulateddata “ppi”(95%parametricprediction

interval)or“npi”(95%

nonparametricpredictioninterval)

“npi”

tabCol OutputcolumnstobeprintedinthereportinadditiontoID, doseandpopulationstratainformation

ListofNCAmetricsinastring array

c(“AUClast”,“Cmax”,“Tmax”, “AUCINFobs”,“Vzobs”, “Cl obs”,“HL Lambda z”)

figFormat Formatoftheproducedfigures (“bmp”,“jpeg”,“tiff”,“png”) “tiff”

noPlot Suppressionofplotgeneration Logical(TRUEorFALSE) FALSE

printOut Write/printoutputonthedisk Logical(TRUEorFALSE) TRUE

studyName Nameofthestudytobeaddedasadescriptioninthereport Studydescription NULL

newdatamethod Fortestingafastermethodofreadingdata Logical(TRUEorFALSE) TRUE

overwriteSIMDATA CreatenewinformationintheSIMDATAdirectory,ortousethe informationintheSIMDATA

TRUE,FALSEorNULL NULL

outFileNm Additionaltagtothenameoftheoutputhtmlandpdfoutput filehyphenatedtothestandardncappcreportfilename

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Fig.1–Workflowofncappcpackagedisplayingtwodifferentlogicalpathsofthepackagebasedontheavailabilityofthe simulationoutputdataset.SeeSupplementarymaterial-IIfordetaileddescriptionoftablesandfiguresgenerated.

AsNONMEM[9]isthemostwidelyusedsoftwareinnon-linear mixed-effect modeling ofPK/PD data, currently the model evaluationpartofthencappc packageisbasedonthe sim-ulationoutputobtainedfromNONMEM, butothersoftware cangenerate the same typeofoutput to beusedas input forthisroutine.ThePopPKmodeltobeevaluatedisusedto simulateksetsoftheplasmaconcentrationvs.timeprofile usingNONMEM,wherekisapositiveinteger.ncappcproduces

ksetsofNCAmetricsforeachindividualfromthesimulated data.Thispackageallowstheusertoemployanycombination ofthefollowingeightNCAmetricsforthemodelevaluation tests: AUClast, AUClowerupper, AUCINFobs, AUCINFpred, AUMClast, Cmax, Tmax, HLLambdaz (see the

Supplemen-tarymaterial-I forthe definitions).Asadefult, ncappcuses AUClastandCmaxformodelevaluationtests.TheNCAmetrics

obtainedfromtheobservedandthesimulateddataare sub-jectedtothefollowingsetofdiagnosticteststoevaluatethe performanceofthePopPKmodel.

2.2.1. Populationleveldiagnostics

2.2.1.1. Comparisonofthepopulationmeans. Acompleteset ofNCAmetricsareestimatedforeachindividualfromeach setofsimulateddata.ThepopulationmeanofeachoftheNCA metricsiscalculatedforeverysinglesetofthesimulateddata. Theprobabilitydistributionofthepopulationmeansofeach NCAmetricestimatedfromthesimulateddataiscompared graphicallywiththe populationmeanofthecorresponding NCAmetricestimatedfromtheobserveddata.Inthepresence ofstratifiedpopulation,thepopulationmeansarecalculated foreachstratumseparatelyforthecomparison.Dependingon thevalueofthespreadargumenttothefunction,thespread

ofthe simulateddistribution can bequantified as: (i) 95% parametricpredictioninterval(ppi)or(ii)95%nonparametric

prediction interval (npi). For derivationof prediction inter-vals,seeSupplementarymaterial-I.Asapreliminarygraphical analysis, thisfunction detectsif theNCA metricestimated fromtheobserveddatalieswithin95%ppiornpiofthe dis-tributionofthepopulationmeanoftheNCAmetricestimated fromthesimulateddata.

2.2.1.2. PopulationNPDEsofNCAmetrics.Basedonthe simu-lateddatasetstheNPDEoftheNCAmetricsforeachindividual iscomputedusingthemethodreportedbyCometsetal.[10]. ThepopulationmeanandSD(includingimprecision)ofthe NPDEsarecomparedwiththeexpectedvalues(i.e.mean0, SD1)inforestplots.TheprobabilitydensityoftheNPDE val-uesfortheentirepopulationisproducedandcomparedwith respecttothenormaldistributionwithmean0andvariance1.

2.2.2. Individualleveldiagnostics

2.2.2.1. Deviationfromtheobserveddataandidentificationof outliers. Asapartoftheindividualleveldiagnosis,deviation ofthesimulation-based mean ofthe NCAmetrics foreach individual from the corresponding NCA metrics estimated from the observed data are calculated by subtracting the individualsimulation-based meanoftheNCAmetricsfrom the same estimated from the observed data. The valueof the deviationis scaled by the spread ofthe corresponding simulateddistribution (measured eitheras95% ppior 95% npi).Incaseofppi,thedeviationisdividedbythedistanceof thesimulationmeantothe95%ppiboundary;incaseof95% npi,thedeviationisdividedbythedistanceofthesimulation meantothe95%npiboundarynearertotheobservedvalue. SuchdeviationiscalculatedforeachoftheNCAmetricsused formodeldiagnosis.Anegativevalueofthedeviationsignifies over-prediction of the corresponding NCA metric, while a

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Table2–DatasummaryofMoxonidinePKstudy. GroupID(DGRP)a _OccasionID (VISI)a Dailydose (␮g)a No.of individualsa No.of outliersb Selectedoutliers IDandNCA metricsb 7 3 200 24 0

7 8 200 21 2 ID402-Cmax,ID802-AUClast

8 3 200 26 0

8 8 400 25 2 ID606-AUClast,ID906-AUClast 9 3 200 24 1 ID322-AUClast,ID322-Cmax

9 8 600 24 0

a _{Obtainedfromtheinputdata.} b _{Obtainedfromtheresultsofncappc.}

positivevalueofthedeviationsignifiesunder-prediction of the same.Anindividual yielding the absolutevalueofthe scaled deviation >1, corresponding to the individual lying outsideofthecorresponding 95%predictioninterval ofthe model,foranyoftheNCAmetricsusedformodeldiagnosisis consideredasanoutlierforthespecificmodel.Foranoutlier theprobabilitydistributionoftheNCAmetriccomparedwith thecorrespondingobservedvaluesarereportedgraphically.

2.2.2.2. Individual NPDE of NCA metrics.The NPDE values fortheNCA metricsforeach individual are calculatedand reported.TheoreticallytheNPDEvaluesshouldbedistributed normallywithameanof0andSDof1.Thedistributionofthe individualNPDEvaluesforeachNCAmetricisplottedforeach populationstratumtodetectanytrendormodelbias.

3.

Results

3.1. CasestudywithMoxonidine

Moxonidineisacentrallyactingantihypertensivedrugused forthetreatmentofmildtomoderatehypertension.Herewe presentacasestudytoillustratethepackageofncappcpackage usingthedataobtainedfromthepopulationpharmacokinetic studyreportedbyKarlssonetal.[11].Thebasicinformation regardingtheMoxonidinePKdatasetisshowninTable2.In thisstudy74patientswereincludedintheactivetreatment group and treated with extravascular dose of Moxonidine. Patientsreceivingtheactivetreatmentweredividedintothree populationgroupsortreatmentarms(DGRP7,8and9)and eacharmreceivedMoxonidineintwodifferentoccasions(VISI

Fig.2–Concentrationvs.timeprofileoftheindividualsinDGRP7andVISI3obtainedformtheobserveddata.Theleft panelsrepresenttherawdata,whiletherightpanelsrepresentthesemi-logarithmicformoftheconcentrationdata.Eachof thelinesrepresentsindividualdata.

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Fig.3–PopulationhistogramoffourselectedNCAmetrics(AUClast,AUCINFobs,Cmax,Tmax)estimatedfromtheobserved dataforDGRP7forVISI3.Thesolidanddashedblueverticallinesrepresentthepopulationmeanandthespreadofthe observeddata.Thespreadisdefinedby2.5thand97.5thpercentileboundariesoftheNCAmetricsobtainedfromthe observeddata.

3and8).TheindividualsinDGRP7received200␮gofdailydose forbothoccasions(VISI3andVISI8);theindividualsinDGRP 8received200␮gdailydoseatthefirstoccasion(VISI3)and then400␮gdailydoseatthesecondoccasion(VISI8)andthe individualsinDGRP9received200␮gdailydoseand600␮g dailydose ofMoxonidineinVISI3andVISI8,respectively. Pharmacokineticsamplingwasperformedatbothoccasions foreach subject.Aone-compartmentallinearPopPKmodel withfirst-orderabsorptionwithlagtimewasusedtosimulate theconcentrationvs.timeprofile1000timesforeach indi-vidual.TheNCAmetricswereestimatedfrombothobserved andsimulateddatasets.AUClastandCmaxmetricswereused

forthe diagnostictests.Fig.2presentstheplasma concen-trationprofileoftheindividualsobtainedfromtheobserved data.Fig.3representsthepopulationdistributionoffourNCA metrics(AUClast,AUCINFobs,CmaxandTmax)estimatedfrom

theobserveddata.Thesolidanddashedblueverticallines rep-resentthepopulationmeanandthespreadoftheNCAmetrics estimatedfrom theobserveddata.Thespreadisdefinedby the2.5thand97.5thpercentileboundariesoftheNCAmetrics obtainedfromtheobserveddata.

3.1.1. Comparisonofpopulationmeans(populationlevel analysis)

Fig.4representsthehistogramofthepopulationmeanofthe NCAmetricsestimatedfromthesetofsimulateddata.The

spreadofthedistributionofthesimulatedNCAmetricswas measuredbythe95%npi,calculatedfromthedistributionof thepopulationmeansestimatedfromeachsetofsimulated data.

3.1.1.1. Evaluationofreport. Thegraphicalreportofthe dis-tributionoftheestimatedpopulationmeanscomparedtothe observedpopulationoftheNCAmetricsisusedtodetermine the generalperformance ofthe PopPK modelto reproduce the drugexposureprofileforthe entirepopulation. In gen-eral,ifthe95%npiofthedistributionofthesimulatedNCA metricsusedforthediagnosticsfailtoencompassthe pop-ulation mean ofthe corresponding NCAmetrics estimated fromtheobserveddata,thePopPKmodelmayberevisitedfor improvement.Inthiscase,thegivenPopPKmodelisableto satisfytheconditionwithrespecttoAUClastandCmax.

3.1.2. Deviationofsimulatedmeanfromobservedvalue (individuallevelanalysis)

Fig.5representsthedeviationofthemeanofeachofthetwo NCAmetricsforeachindividualwithinDGRP7andVISI3 esti-matedfromthe1000setsofsimulateddatafromthevalue ofthe samemetric estimatedfromthe observeddata.The rawvaluesofthedeviationswerescaledbydividingthemby thedistancebetweenthesimulationmeanandthe95%npi boundarynearertotheobservedvalue.

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Fig.4–HistogramofthepopulationmeanoftheAUClastandCmaxobtainedfromthesimulateddatafromthesimulations fortheindividualsinDGRP7forVISI3.TheredandbluesolidverticallinesrepresentthepopulationmeanoftheNCA metricobtainedfromtheobserveddata(mean(obs))andthemeanofthepopulationmeansofthesameNCAmetric obtainedfromthesimulations(mean(meanSim)),respectively.Thebluedashedverticallinesrepresentthespreador95% nonparametricpredictionintervalboundariesforthepopulationmeanoftheNCAmetricsobtainedfromthesimulateddata.

3.1.2.1. Evaluationofreport. Thevaluesofthescaled devia-tion foreach individual withinaspecifictreatmentarmor populationgroupare usedtodetectmodelmisspecification andindividualoutliers.Anyindividualyieldingtheabsolute

valueofthescaleddeviationgreaterthan1islabeledasan outlierbyncappcforthePopPK model.Thetotalnumberof identified outliers in the case ofMoxonidine data set was 5 out of 74 individuals and across 2 different metrics

Fig.5–DeviationofthemeanoftheNCAmetricsforeachindividualinDGRP7andVISI3estimatedfromthesimulated dataobtainedfromthesimulations(meanSim)fromthecorrespondingvaluesestimatedfromtheobserveddata(Obs).The deviationisscaledbythespreadofthesimulateddata,whichis,inthiscase,definedbythedistancebetweenthemeanof thePKsimulatedmetricvalueandthe95%nonparametricpredictionintervalboundaryofthesimulatedmetricdistribution proximaltotheobservedvalue(Deviation=(ObsmeanSim)/distancebetweenmeanSimandthe95%nonparametric predictionintervalboundarynearertotheObs).

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Fig.6–Theindividual402inDGRP7forVISI8isidentifiedasaninthisexampleforthecorrespondingPopPKmodel.This individualislabeledasoutlierasthevalueoftheCmaxobtainedfromtheobserveddataisoutsidethe95%npiofthe distributionoftheCmaxvaluesobtainedfromthesimulateddataset.Theredandbluesolidverticallinesrepresentthe observedmetricvalueandthemeanofthesimulatedmetricvaluesforthatindividual,respectively.Thedashedblue verticallinesrepresentthe95%npiforthedistributionofthesimulatedmetricvalues.

(Cmax andAUClast)and 2profiles persubject. Last column

inTable2liststhe IDnumbers andthecorrespondingNCA metric of the individuals who are assigned as outliers for theircorrespondingpopulationgroupsunderthegivenPopPK

model.Fig.6illustratetheprobabilitydistributionoftheNCA metricsofoneoftheseoutliers(ID-402DGRP-7VISI-8)where theabsolutevalueofthescaleddeviationofCmaxwasgreater

than1.

Fig.7–ForestplotdisplayingthepopulationmeanandstandarddeviationoftheNPDEvaluesstratifiedontreatmentarms anddosegroups.TheredandgreendotsrepresentthemeanandthestandarddeviationoftheNPDE,respectivelywhilethe horizontallinesrepresentthecorresponding95%confidenceintervals.Thevaluesofthepopulationmeanandstandard deviationalongwiththecorresponding95%confidenceintervalsareshowninthefigure.

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Fig.8–NPDEtypeanalysisforeachindividualinDGRP7andVISI3.NPDEvalueswerecalculatedfromthecorresponding observedandsimulatedvaluesoftheNCAmetrics.ThenegativevalueoftheNPDEsignifiesover-predictionofthe correspondingNCAmetrics,whileapositivevalueoftheNPDEsignifiesunder-predictionofthesame.

3.1.3. NPDEofNCAmetrics(bothpopulationand individuallevelanalysis)

TheNPDEvaluesofallNCAmetricsusedindiagnosticsfor eachindividualarereported. Thepopulationmeanandthe standarddeviationoftheNPDE valuesfortheNCAmetrics arealsocalculatedandshowninaforestplot(Fig.7)along withthecorresponding95%confidenceintervals.For deriva-tion ofconfidence intervals,see Supplementary material-I.

Fig.8representstheNPDEvaluesofAUClastandCmaxforeach

individualinDGRP7andVISI3.Fig.9representsthe probabil-itydistributionoftheNPDEvaluesforallindividualswithina specifictreatmentarmandoccasiongroupDGRP7andVISI3.

3.1.3.1. Evaluation of report. The forest plot (Fig. 6) shows thatthemeanNPDEvaluesofAUClastandCmaxofall

treat-mentarmsandoccasions.ForanacceptablePopPKmodel,the

Fig.9–HistogramoftheNPDEvaluesofallindividualsfortheNCAmetricsinDGRP7andVISI3.Theredsolidvertical representsthemeanoftheidealNPDEornormaldistribution(mean=0,SD=1).Thebluesolidverticallinesrepresentthe meanoftheestimatedNPDEdistributionforthecorrespondingpopulation.Thedashedblueverticallinesrepresentthe standarddeviationofthedistributionoftheNPDE.

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populationmeanandSDalong withtheirconfidence inter-valshouldencompass0and1,respectively.Thepopulation modelsuccessfullyproducesthe95%confidenceintervalsof themeanoftheNPDEvaluesencompassing0,however,the 95%confidenceintervalsoftheSDoftheNPDEsofAUClastin DGRP8forVISI3andthesameofCmaxinDGRP8forVISI8

failtoencompass1.Thisindicatesadiscrepancybetweenthe PopPKmodelandtheobserveddataforthesemetricsinthese treatmentgroups.Nonetheless,Figs.8and9donotshowany systematictrendoferrorsforAUClastandCmax.

Theresultsoftheabovementionedsetofpopulationlevel and individual level diagnostic testsfor thestudied PopPK modelaresystematicallyreportedbythencappcpackageand itproducesacompletereportinHTMLandPDFformat.The resultsofthediagnostictestscanbeusedtoidentifymodel misspecificationsatthepopulationlevel; theresultsofthe

ncappccanalsobeusedtoidentifyspecificindividuals,which aremisfits totheconcerned PopPK modelortothe defini-tionofthepopulationstrata.Theconclusionsdrawnbased onthediagnosticswillbedependentontheintendeduseof themodelandalsowhichspecificmodelaspectthatthis diag-nosticisusedfor.Thus,theconsequenceofthediagnosticsfor thefurthermodeldevelopmentwillvarybetweenprojectand criteria.Anacceptablediscrepancymayneedtobedefinedfor eachcase.Forexample,ifthemainpurposeofthemodelis todescribethegeneraltendencyinthedata,thepopulation leveldiagnosticswillbeofmostimportance.

4.

Conclusion

Thencappcpackageisaversatileandflexibletool-setwrittenin RthatsuccessfullyestimatestheNCAmetricsrelatedtoNCA fromtheobservedandasetofsimulatedconcentration–time data.Itproducesacomprehensivesetofgraphicaland tab-ularoutputtosummarizetheresultsofthediagnostictests includingthemodelspecificoutliers.Theoutputiseasy to interpretandtouseinevaluationofapopulationmodel.This programalsoproducesacompletereportinPDFandHTML format.ncappcisfreelyavailableonCRANandGitHubatthe followingURL,respectively.

CRAN: http://cran.r-project.org/web/packages/ncappc/ index.html/.

GitHub:https://github.com/cacha0227/ncappc/.

Acknowledgements

Theresearchleading tothese resultshasreceived support from the Innovative MedicinesInitiative Joint Undertaking under grant agreement n◦ 115156, resources of which are

composed of financial contributions from the European Union’sSeventhFrameworkProgramme(FP7/2007–2013)and EFPIAcompanies’inkindcontribution.TheDDMoReproject isalsofinanciallysupportedbycontributionsfromAcademic andSMEpartners.Theauthorswouldalsoliketo acknowl-edge The Scientificand Technological Research Councilof Turkey(TÜB˙ITAK)forsupportingpostdoctoralresearchof Gül-beyazYıldızTürkyılmazandEgeUniversity,CenterforDrug Research&DevelopmentandPharmacokineticApplications (ARGEFAR), ˙Izmir,Turkeyforprovidinguswiththelicenseof WinNonlin.

Appendix

A.

Supplementary

data

Supplementarydataassociatedwiththisarticlecanbefound, in the online version, at http://dx.doi.org/10.1016/j.cmpb. 2016.01.013.

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