Population pharmacokinetics

Basic information on Population pharmacokinetics, understanding bayesian theory, analysis of population pharmacokinetic data

1. POPULATION
PHARMACOKINETICS
Dr. Ramesh Bhandari
Asst. Professor,
Department of Pharmacy Practice
KLE College of Pharmacy, Belagavi

2. Dr. RameshBhandari
Population Pharmacokinetics
ALL HUMANS ARE ALIKE
TRUE ONLY AS A SPECIES
DIFFERENCE EXISTS –including
their response to the drugs

3. Dr. RameshBhandari
Population Pharmacokinetics
Research has uncovered significant
differences among different populations
in:
Rate of drug metabolism
Responses to drugs
Side effects of drugs

4. Dr. RameshBhandari
Population Pharmacokinetics
Genetic Variations of different
racial and ethnic groups
Difference in proteins encoding
Difference in drug metabolism
Sub Therapeutic/toxic levels
Dosage adjustment is needed particularly for
Narrow therapeutic Index drugs.

5. Dr. RameshBhandari
Population Pharmacokinetics
Examples of different responses of drugs among
different population groups.
CYP2C19*2 & *3 is the phenotype for poor
metabolizer.
CYP2C19*17type results in ultra metabolizing
capacity.
Approx. 15% of Japanese, 5% of the Chinese, and
5% of the Australian populations are classified as
poor metabolizer.

6. Dr. RameshBhandari
Population Pharmacokinetics
AccordingtoFDA,PopulationPharmacokineticis
“thestudyofthesourcesandcorrelatesof
variabilityindrugconcentrationsamong
individualswhoarethetargetpatientpopulation
receivingclinicallyrelevantdosesofadrugof
interest”.
Populationpharmacokinetics(PopPK)isthestudy
ofvariabilityinplasmadrugconcentrations
betweenandwithinpatientpopulationsreceiving
therapeuticdosesofadrug.

7. Dr. RameshBhandari
Population PK Approach Vs
Classical PK Approach
Traditionalpharmacokineticstudiesareusually
performedonhealthyvolunteersorhighlyselected
patients,andtheaveragebehaviourofagroup(i.e,
themeanplasmaconcentration–timeprofile)isthe
mainfocusofinterest.
PopPKexaminestherelationshipofthe
demographic,genetic,pathophysiological,
environmental,andotherdrugrelatedfactorsthat
contributetothevariabilityobservedinsafetyand
efficacyofthedrug.

8. Dr. RameshBhandari
Population PK Approach Vs
Classical PK Approach
Drug
concentration
Time
Drug
concentration
Time
Drug
concentration
Time
Classical Approach
Pop PK Approach

9. Dr. RameshBhandari
Advantages of Population
pharmacokinetics
Providesbetterunderstandingofthedose-response
relationshipamongthetargetpopulation.
Samplepopulationmimicstherealtarget
populationatlarge.
Multiplefactorsmaybestudiedinonepopulation
PKstudy.
Diversityofpatientcharacteristicsandlarger
samplesizes.
Priordoseadjustmentcanbemadeusing
PopulationPKdata.

10. Introduction to
Bayesian Theory

11. Dr. RameshBhandari
BAYESIAN THEORY
Bayesiantheorywasoriginallydevelopedtoimprove
forecastaccuracybycombiningsubjectiveprediction
withimprovementfromnewlycollecteddata.
Inthediagnosisofdisease,thephysicianmaymakea
preliminarydiagnosisbasedonsymptomsand
physicalexamination.Later,theresultsoflaboratory
testsarereceived.Theclinicianthenmakesanew
diagnosticforecastbasedonbothsetsofinformation.
Bayesiantheoryprovidesamethodtoweightheprior
information(eg,physicaldiagnosis)andnew
information(eg,resultsfromlaboratorytests)to
estimateanewprobabilityforpredictingthedisease.

12. Dr. RameshBhandari
BAYESIAN THEORY
Indevelopingadrugdosageregimen,weassessthe
patient’smedicalhistoryandthenuseaverageor
populationpharmacokineticparametersappropriate
forthepatient’sconditiontocalculatetheinitialdose.
Aftertheinitialdose,plasmaorserumdrug
concentrationsareobtainedfromthepatientthat
providenewinformationtoassesstheadequacyofthe
dosage.
Thedosingapproachofcombiningoldinformation
withnewinvolvesa“feedback”processandis,to
somedegree,inherentinmanydosingmethods
involvingsomeparameterreadjustmentwhennew
serumdrugconcentrationsbecomeknown.

13. Dr. RameshBhandari
BAYESIAN THEORY
TheadvantageoftheBayesianapproachisthe
improvementinestimatingthepatient’s
pharmacokineticparametersbasedonBayesian
probabilityversusanordinaryleast-squares-based
program.
Themethodisparticularlyusefulwhenonlyafew
bloodsamplesareavailable

14. Dr. RameshBhandari
BAYESIAN THEORY
Bayesianprobabilitytheorywhenappliedtodosingofadrug
involvesagivenpharmacokineticparameter(P)andplasmaor
serumdrugconcentration(C),asshowninEquation22.11.The
probabilityofapatientwithagivenpharmacokinetic
parameterP,takingintoaccountthemeasuredconcentration,is
Prob(P/C):
Prob(P│C) = Prob(P) . Prob(C│P)
Prob(C)
Prob(P) = Probability of the patients parameter within the assumed
population distribution
Prob(C│P)= Probability of measured concentration within the
population
Prob(C)= unconditional probability of the observed concentration

15. Dr. RameshBhandari
BAYESIAN THEORY
Problem:
Afterdiagnosingapatient,thephysiciangavethepatienta
probabilityof0.4ofhavingadisease.Thephysicianthenordereda
clinicallaboratorytest.Apositivelaboratorytestvaluehada
probabilityof0.8ofpositivelyidentifyingthediseaseinpatients
withthedisease(truepositive)andaprobabilityof0.1ofpositive
identificationofthediseaseinsubjectswithoutthedisease(false
positive).Fromthepriorinformation(physician’sdiagnosis)and
currentpatient-specificdata(laboratorytest),whatistheposterior
probabilityofthepatienthavingthediseaseusingtheBayesian
method?

16. Dr. RameshBhandari
Problem solving:
Population
Disease
Test +ve
Test -ve
No
Disease
Test +ve
Test -ve
Prob(D│+) = Prob(D) . Prob(+│D)
Prob(+)

17. ADAPTIVE METHOD
OR DOSING WITH
FEEDBACK

18. Dr. RameshBhandari
Indosingdrugswithnarrowtherapeuticratios,an
initialdoseiscalculatedbasedonmeanpopulation
pharmacokineticparameters.
Afterdosing,plasmadrugconcentrationsareobtained
fromthepatient.Asmorebloodsamplesaredrawn
fromthepatient,thecalculatedindividualizedpatient
pharmacokineticparametersbecomeincreasingly
morereliable.
Thistypeofapproachhasbeenreferredtoasadaptive
orBayesianadaptivemethodwithfeedbackwhena
specialextendedleast-squaresalgorithmisused.

19. Dr. RameshBhandari
Manyordinaryleast-squares(OLS)computer
softwarepackagesareavailabletoclinicalpracticefor
parameteranddosagecalculation.
Somesoftwarepackagesrecordmedicalhistoryand
provideadjustmentsforweight,age,andinsome
cases,diseasefactors.
AbbottbasePharmacokineticSystems(1986and
1992)isanexampleofpatientorientedsoftwarethat
recordspatientinformationanddosinghistorybased
on24-hourclocktime.
Anadaptive-typealgorithmisusedtoestimate
pharmacokineticparameters.

20. Dr. RameshBhandari
Theaveragepopulationclearanceandvolumeof
distributionofdrugsareusedforinitialestimates,and
theprogramcomputespatient-specificClandV
das
serumdrugconcentrationsareentered.
Theprogramaccountsforrenaldysfunctionbasedon
creatinineclearance,whichisestimatedfromserum
creatinineconcentrationusingtheCockroft–Gault
equation.
Thesoftwarepackageallowsspecificparameter
estimationfordigoxin,theophylline,and
aminoglycosides,althoughotherdrugscanalsobe
analysedmanually.

21. Dr. RameshBhandari
Manyleast-squares(LS)andweightedleastsquares
(WLS)algorithmsareavailableforestimatingpatient
pharmacokineticparameters.
Theircommonobjectiveinvolvesestimatingthe
parameterswithminimumbiasandgood
prediction,oftenasevaluatedbymeanpredictive
error.
TheadvantageoftheBayesianmethodistheability
toinputknowninformationintotheprogram,so
thatthesearchfortherealpharmacokineticparameter
ismoreefficientand,perhaps,moreprecise.

22. Dr. RameshBhandari
BayesianApproachwithOLSMethod:
C
i
=f(P,t
i)ℇ
i
OBJ
OLS
=σ
??????=1
????????????
??????
−??????ˆ
??????
2
σ
i
2

23. Dr. RameshBhandari
The Bayes Estimator
Whenthepharmacokineticparameter,P,isestimatedfroma
setofplasmadrugconcentrationdata(Ci)havingseveral
potentialsourcesoferrorwithdifferentvariance,theOLS
methodforparameterestimationisnolongeradequate(it
yieldstrivialestimates).
Theintersubjectvariation,intrasubjectvariance,and
randomerrormustbeminimizedproperlytoallowefficient
parameterestimation.
Theweightedleast-squaresfunctionwassuggestedby
SheinerandBeal.
Theequationrepresentstheleast-squaresestimationofthe
concentrationbyminimizingdeviationsquares,anddeviation
ofpopulationparametersquares.

24. Dr. RameshBhandari
The Bayes Estimator
Following equation is called the Bayes estimator.
This approach is frequently referred to as extended
least-squares (ELS).
IntrasubjectC
i= f(P,X
i) + ℇ
i
IntersubjectP
k= Pˆ
k+ n
k
OBJ
BAYES= σ
??????=1
????????????
??????
−??????ˆ
??????
2
σ
i
2
+ σ
??????=1
??????
??????
??????
−??????ˆ
??????
2
ω
??????
2

25. ANALYSIS OF POPULATION
PHARMACOKINETIC DATA

26. Dr. RameshBhandari
Traditional Pharmacokinetic
Studies
Involvetakingmultiplebloodsamplesperiodicallyovertime
inafewindividualpatients,and
characterizingbasicpharmacokineticparameterssuchask,
VD,andCl.
Becausethestudiesaregenerallywelldesigned,thereare
fewerparametersthandatapoints.
Traditionalpharmacokineticparameterestimationisvery
accurate,providedthatenoughsamplescanbetakenforthe
individualpatient.
Thedisadvantageisthatonlyafewrelativelyhomogeneous
healthysubjectsareincludedinpharmacokineticstudies,from
whichdosingindifferentpatientsmustbeprojected.

27. Dr. RameshBhandari
Traditional Pharmacokinetic
Studies
Intheclinicalsetting,patientsareusuallyless
homogeneous;patientsvaryinsex,age,andbodyweight.
Theymayhaveconcomitantdiseaseandmaybereceiving
multipledrugtreatments.
Eventhediet,lifestyle,ethnicity,andgeographiclocation
candifferfromaselectedgroupof“normal”subjects.
Further,itisoftennotpossibletotakemultiplesamplesfrom
thesamesubject,and,therefore,nodataareavailableto
reflectintra-subjectdifference,
Sothatiterativeproceduresforfindingthemaximum
likelihoodestimatecanbecomplexandunpredictabledue
toincompleteormissingdata.

28. Dr. RameshBhandari
Traditional Pharmacokinetic
Studies
However,thevitalinformationneededaboutthe
pharmacokineticsofdrugsinpatientsatdifferentstagesof
theirdiseasewithvarioustherapiescanonlybeobtainedfrom
thesamepopulation,orfromacollectionofpooledblood
samples.
Theadvantagesofpopulationpharmacokineticanalysisusing
pooleddatawerereviewedbySheinerandLudden(1992)
andincludedasummaryofpopulationpharmacokineticsfor
dozensofdrugs.
Pharmacokineticanalysisofpooleddataofplasmadrug
concentrationfromalargegroupofsubjectsmayrevealmuch
informationaboutthedispositionofadruginapopulation.

29. Dr. RameshBhandari
Traditional Pharmacokinetic
Studies
Unlikedatafromanindividualsubjectcollectedover
time,inter-andintra-subjectvariationsmustbe
considered.
Bothpharmacokineticandnon-pharmacokinetic
factors,suchasage,weight,sex,andcreatinine
concentration,shouldbeexaminedinthemodelto
determinetherelevancetotheestimationof
pharmacokineticparameters.

30. Dr. RameshBhandari
Population Pharmacokinetic
Data Analysis
1)NONMEM Method
2)Standard two stage (STS) method
3)First Order Method

31. Dr. RameshBhandari
Non-Linear Mixed Effect Model
(NONMEM)
The nonlinearmixed-effectmodel
(NONMEM)issocalledbecausethemodeluses
bothfixedandrandomfactorstodescribethe
data.
TheKnown,observablepropertiesof
individualsthatcausethePKparameterstovary
acrossthepopulationarecalledfixedeffects.
Fixedfactorssuchaspatientweight,age,
gender,andcreatinineclearanceareassumedto
havenoerror.

32. Dr. RameshBhandari
Non-Linear Mixed Effect Model
(NONMEM)
Whereas,randomfactorsincludeinter-and
intra-individualdifferences.
Randomeffectscan’tbepredictedin
advance.

33. Dr. RameshBhandari
Non-Linear Mixed Effect Model
(NONMEM)
NONMEM isastatisticalprogramwrittenin
FortranthatallowsBayesianpharmacokinetic
parameterstobeestimatedusinganefficient
algorithmcalledthefirst-order(FO)method.
Theparametersmaynowbeestimatedalsowitha
firstorderconditionalestimate(FOCE)algorithm.
Inaddition,topharmacokineticparameters,many
examplesofpopulationplasmadatahavebeen
analyzedtodeterminepopulationfactors.

34. Dr. RameshBhandari
Non-Linear Mixed Effect Model
(NONMEM)
NONMEM fitsplasmadrugconcentration
dataforallsubjectsinthegroups
simultaneouslyandestimatesthepopulation
parameteranditsvariance.
Theparametermaybeclearanceand/orVD.
Themodelmayalsotestforotherfixed
effectsonthedrugduetofactorssuchas
age,weight,andcreatinineclearance.

35. Dr. RameshBhandari
Non-Linear Mixed Effect Model
(NONMEM)
Themodeldescribestheobservedplasmadrug
concentration(Ci)intermsofamodelwith:
1.P
k=fixedeffectparameters,whichinclude
pharmacokineticparametersorpatientfactorparameters.
Forexample,P
1isC
l,P
2isthemultiplicativecoefficient
includingcreatininefactor,andP
3isthemultiplicative
coefficientforweight.
2.Randomeffectparameters,including(a)thevarianceof
thestructural(kinetic)parameter,P
k,orinter-subject
variabilitywithinthepopulation,ω
2
;and(b)theresidual
intra-subjectvarianceorvarianceduetomeasurement
errors,fluctuationsinindividualparametervalues,andall
othererrorsnotaccountedforbytheotherparameters.

36. Dr. RameshBhandari
Population Pharmacokinetic
Data Analysis
1)Standard two stage (STS) method
2)First Order Method

37. Dr. RameshBhandari
1)Standard two stage (STS)
method
Estimatesparametersfromtheplasmadrug
concentrationdataforanindividualsubjectduring
thefirststage.
Theestimatesfromallsubjectsarethencombinedto
obtainanestimateoftheparametersforthe
population.
Themethodisusefulbecauseunknownfactorsthat
affecttheresponseinonepatientwillnotcarry
overandbiasparameterestimatesoftheothers.
Themethodworkswellwhensufficientdrug
concentration–timedataareavailable.

38. Dr. RameshBhandari
2)First Order Method
lesswellunderstood
Theestimationprocedureisbasedonminimizationofan
extendedleast-squarescriterion,whichwasdefinedthroughan
FOTaylorseriesexpansionoftheresponsevectoraboutthe
fixedeffectsandwhichutilizedaNewton–Raphson-like
algorithm.
Thismethodattemptstofitthedataandpartitionthe
unpredictabledifferencesbetweentheoreticalandobserved
valuesintorandomerrorterms.
Whenthismodelincludesconcomitanteffects,itiscalleda
mixed-effectstatisticalmodel.
TheadvantageoftheFOmodelisthatitisapplicableeven
whentheamountoftime–concentrationdataobtainedfrom
eachindividualissmall,providedthatthetotalnumberof
individualsissufficientlylarge.

39. Thank you