The npde library for R to compute normalised prediction distribution errors

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Submitted on 13 Jul 2012

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The npde library for R to compute normalised

prediction distribution errors

Emmanuelle Comets, Thi Huyen Tram Nguyen, France Mentré

To cite this version:

Emmanuelle Comets, Thi Huyen Tram Nguyen, France Mentré. The npde library for R to compute

normalised prediction distribution errors. 1ères Rencontres R, Jul 2012, Bordeaux, France.

�hal-00717550�

Emmanuelle Comets

a,b

,Thi Huyen Tram Nguyen

a,b

and Fran e Mentré

a,b

a

INSERM, UMR 738 Paris, Fran e emmanuelle. ometsinserm.fr

b

Univ ParisDiderot

Sorbonne ParisCité

Paris, Fran e

Mots lefs : Non-linear mixed ee t models; model evaluation; normalised predi tion

distri-bution errors

Obje tives: Overthelastfewyears, severalnewapproa hesin ludingVPC(VisualPredi tive

Che k)[1℄,predi tiondis repan ies(pd)[2℄andnormalisedpredi tiondistributionerrors(npde)

[3℄ have been proposed to evaluate nonlinear mixed ee t models. npde are now in luded in

the output of NONMEM [4℄ and Monolix [5℄, and we reated a R library to fa ilitate the

omputationof pdand npde using simulationsunderthe model[6℄. Wepropose anew version

of this library with methods to handle data below the limit of quanti ation (BQL) [7℄ and

new diagnosti graphs [8℄.

Methods: BQL data o urr in many PK/PD appli ations, parti ularly in HIV/HCV trials

where multi-therapies are now so e ient that viral loads be ome undete table after a short

treatmentperiod. Thesedata aregenerallyomittedfromdiagnosti graphs,introdu ingbiases.

Here,weproposetoimputethepdforaBQLobservationbysamplinginU(0,p

BQL

)wherep

BQL

is the model-predi tedprobability of being BQL. To ompute the npde, ensored observations

are rst imputed fromthe imputed pd, using the predi tive distribution fun tion obtained by

simulations,then npde are omputed for the ompleted dataset[3℄.

New graphi aldiagnosti s in ludea graph ofthe empiri al umulative distributionfun tion of

pd and npde. Predi tion intervals, obtained using simulations under the model, an be added

to ea h graph to assess how the distribution of observed data and metri s ompare to the

expe ted distributionunder the model. Tests an beperformed to ompare the distribution of

the npde relative to the expe ted standard normal distribution. In addition,graphs and tests

to help sele ting ovariate models have been added [9℄.

These extensions were implemented inanew version of the npde library. The new library uses

S4 lasses fromR toprovide aneasieruser-interfa e tothe many new graphs,while remaining

mostly ompatiblewiththe previousversion. Ex eptionsarethat omputingthepdinaddition

tothe npdeisnowadefaultoption. Several newoptionsarealsoavailableinthe omputations.

Results: We illustratethe new library on data simulatedusing the designof the

COPHAR3-ANRS 134 trial. In the trial, viral loads were measured for 6 months in34naiveHIV-infe ted

patients afterinitiationof atri-therapy,and up to 50% of datawere BQL.Ignoring BQL data

well asnew graphs, in ludingVPCand predi tion intervalsfor distributions.

Referen es

[1℄HolfordN(2005). TheVisualPredi tiveChe k: superioritytostandarddiagnosti (Rors ha h)

plots. 14th meeting of the Population Approa h Group in Europe, Pamplona, Spain, (Abstr

738).

[2℄Mentré Fand S Es olanoS (2006). Predi tion dis repan iesfor the evaluationof nonlinear

mixed-ee tsmodels. J Pharma okinet Biopharm, 33, 345-67.

[3℄ Brendel K, Comets E, Laont C, Laveille C, Mentré F (2006). Metri s for external model

evaluation with an appli ation to the population pharma okineti s of gli lazide. Pharm Res,

23, 2036-49.

[4℄BealS,SheinerLB,Boe kmannA,BauerRJ(2009). NONMEMUser'sGuides. (1989-2009),

I onDevelopment Solutions, Elli ott City, MD, USA.

[5℄ Lavielle M (2010). MONOLIX (MOdèles NOn LInéaires à eets miXtes) User Guide.

MONOLIX group, Orsay, Fran e. URL: http://software.monolix.org/

[6℄ Comets E, Brendel K, Mentré F (2008). Computing normalised predi tion distribution

errors to evaluate nonlinear mixed-ee t models: The npde add-on pa kage for R. Comput

Meth Prog Biomed;90, 154-66.

[7℄ Nguyen THT, Comets E, Mentré F (2011). Predi tion dis repan ies (pd) for evaluation of

modelswithdataunderlimitofquanti ation. 20thmeetingof thePopulationApproa hGroup

in Europe, Athens, Gree e, (Abstr 2182).

[8℄CometsE,BrendelK,Mentré F(2010). Modelevaluationinnonlinearmixed ee t models,

with appli ations topharma okineti s. J-SFdS:1, 106-28.

[9℄ Brendel K, Comets E, Laont C, Mentré F (2010). Evaluation of dierent tests based on