A POPULATION MODEL OF GENTAMICIN MADE WITH A NEW

APOPULATIONMODELOFGENTAMICINMADEWITHANEWNONPARAMETRICEMALGORITHMRogerW.Jelliffe,M.D.,PilarGomis,Pharm.D.,andAlanSchumitzky,Ph.D.TechnicalReport90-4LaboratoryofAppliedPharmacokineticsUniversityofSouthernCaliforniaSchoolofMedicineLosAngeles,CaliforniaAddressforreprints:RogerW.Jelliffe,M.D.,LaboratoryofAppliedPharmacokinetics,UniversityofSouthernCaliforniaSchoolofMedicine,2250AlcazarSt.,CSC134-B,LosAngeles,CA90033.(213)342-13002SupportedbyNIHGrantRR01629APOPULATIONMODELOFGENTAMICINMADEWITHANEWNONPARAMETRICEMALGORITHMABSTRACTAnonparametricEM(NPEM)algorithmforpopulationpharmacokineticmodelinghasbeenimplementedasacomputerprogramfortheIBMPCandcompatiblemachines.Itcomputesthejointprobabilitydensityfunction(PDF)fora1-compartmentpharmacokineticmodelwithintravenousdosing.Itcanoperateusingdataofonlyoneserumlevelperpatient.TheprogramutilizespatientdatafilesfromtheUSC*PACKPCclinicalprograms(1).Outputincludesa3DplotofthejointPDF,twomarginalPDFplots,means,variances,modes,quartiles,skewness,kurtosis,andcovarianceandcorrelationcoefficientbetweenparameters.ResultscanbeenteredintopopulationfilesforusewiththeUSC*PACKPCclinicalprograms.Thefirstclinicalstudywiththisalgorithm,ofpatientsreceivingintravenousgentamicin,isdescribed.Resultsarecomparedwiththestandard2-stagealgorithm.Variousparameterizationsandsparsedatasetsareanalyzed.TheNPEMPCcomputerprogrampermitspopulationpharmacokineticmodelingincommunityhospitals.INTRODUCTIONInterestinmodelingthepopulationpharmacokineticbehaviorofadruginagroupofpatientshasbeenstimulatedbytheuseofBayesianapproachestotheadaptivecontrolofdrugdosageregimens(2-7).Methodsofmakingpopulationmodelsofdrugshavebeenthoroughlyreviewed(8).Inthatreview,thestandard2-stagemethodisdescribed.BealandSheiner(9-11)madesignificantadvanceswhentheydevelopedthenonlinearmixed-effectsmodelwithfirstorderapproximation(NONMEM).Itisatruepopulationmodel-maker.Itconsiderssimultaneouslyalldatafromallpatientsinapopulation.Itcanoperatewithasfewserumleveldatapointsasoneperpatient.Itprovidesestimatesofthemeans,standarddeviations,andcovariancesofthepopulationdistribution.3AdifferentapproachwasdevelopedbyMallet(12,13)inwhichtheentirepopulationdistributionitselfisestimated.Fromthisestimateddistribution,themeans,standarddeviations,andcovariancescanbederivedalongwithanyotherstatisticsofthedistributionsuchaspercentiles.TheMalletapproachisnonparametricinthestatisticalsense,asthepopulationdistributiontobeestimatedisnotdefinedbyanyfinitesetofparameterssuchasmeans,standarddeviations,covariances,andthelike.TheapproachofMallethasrecentlybeenimplementedinadifferentmanner,usinganonparametricEM(NPEM)algorithmdevelopedbySchumitzky(14,seealso15,16).IthasnowbeenimplementedasacomputerprogramfortheIBMPCandcompatiblemachines(17).ThepresentreportdescribesthefirstclinicaluseoftheNPEMalgorithmandcomputerprogram,tomakea1-compartment(2-parameter)pharmacokineticmodelofgentamicin,basedondataof20patientspreviouslystudiedinourlaboratorybyIglesias(18-20).METHODSThePatientPopulationThepatientpopulationconsistedof12menand8women.Theirmeanagewas47±16(1SD)years,andtheirmeanweightwas63±15kg.Allpatientshadsignificantinfectionsrequiringgentamicin(18-20).Sixpatientshadsignificantliverdisease.Tenpatientshadhighlyunstablerenalfunctionduringtheirtherapy.Themeandurationoftherapywas7.3±4.7days,andrangedfrom1to17days.Atotalof177serumconcentrations(mean=8.85,SD=6.02,range=3to21perpatient)hadbeenobtained.Thedataoftheirdoses,the177serumconcentrations,theirweight,andtheiroftenchangingcreatinineclearance(CCr)werethebasisforthispopulationmodel.Lateron,tofurtherexaminetheabilityofthisnewalgorithmtomakeapopulationmodel,allserumleveldataweredeletedexceptthehighestandthelowestoneforeachpatient.Inarandommanner(coinflip),oneserumlevel,thehighestorthelowestone,wasthendiscardedtomakeapopulationdatabaseconsistingofonlyasingleserumlevel(ahighoralow)foreachpatient.Thisextremelysparsedatawasalsoanalysedbytheprogramandtheresultingpopulationmodelwasevaluated.Lastly,onlythesinglelowesttroughserumlevelwaspreservedfromeachpatient'sdata,andtheperformanceofthealgorithmunderthesetrulyabusiveconditionswasalsoexamined.TheModelParameterizationsExaminedFourdifferentparameterizationsofthepopulationmodelwereexamined.First,theeliminationrateconstant(K)andthetotalapparentvolumeofdistribution(V)wereexamined.Second,theslope(KS)oftherelationshipbetweenKandCCr,withthenonrenalintercept(KI)heldfixedatavalueof0.0069315hr-1(correspondingtoahalftimeof100hoursinananephricpatient),andVS,theslopeoftherelationshipbetweenVandbodyweight,wereexamined.Third,theparametersofclearance(C)4andVwereexamined.Fourth,theparametersoftheslope(CS)oftherelationshipbetweengentamicinclearanceandCCr,(withthenonrenalclearanceintercept(CI)beingfixedat0.00255044units,againequivalenttoahalf-timeof100hours),andtheVSwereexamined.Eachofthe4parameterizationswasevaluatedusingall177serumlevels.FinallytheCSandVSparameterizationwasexaminedinthetwosparsedatasets,eachusingonlyasinglelevelperpatient.Inallcases,thejointprobabilitydensitywasdescribedasa30by30point