From:  "Eleveld, DJ" d.j.eleveld@anest.umcg.nl
Subject: [NMusers] Residuals and INTERACTION for simultaneous PK/PD, impossible? 
Date:  Fri, April 15, 2005 7:34 am 

Hi everyone, 

Thanks very much to the very knowledgeable users of the list I understand that INTERACTION 
should be used when residuals are expected to be heteroscastic and shouldnt be used when 
residuals are expected to be homoscastic. 

However I am confused as what to do in the simultaneous PK/PD case.  Here my PK residuals 
are expected to be heteroscastic (so INTEACTION should be used) but my PD residuals are 
expected to be homoscastic (so INTERACTION should not be used).  I cant do both at the same 
time, but my data does contain both kinds of residuals at the same time. 

There is much discussion in the archives about simultaneious PK/PD but they seem to 
discuss finding the 'right' parameters.  I could find no posts that brought up if 
INTERACTION should be used or not. 

I seem to get better fitting without INTERACTION, but I think this is simply just due to 
the fact that I have more PD data then PK data.  Anyone have any ideas about the correct 
way to approach this? 

Thanks very much, 

Doug Eleveld 
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From: "Piotrovskij, Vladimir [PRDBE]" VPIOTROV@PRDBE.jnj.com
Subject: RE: [NMusers] Residuals and INTERACTION for simultaneous PK/PD, impos sible? 
Date: Fri, April 15, 2005 3:18 pm 

Doug,
 
The only solution to your problem that I see is to make the residual error for the PK
model also homoscedastic. You can easily do this by converting concentrations into logarithms
and declaring log(C) as DV. Then you do the same for the model prediction F, e.g.
$ERROR CALLFL=0
 LOQ   = 1                               ; limit of quantification
 FLAG  = 0
 IF (F.LE.0) FLAG=1
 IPRE  = (1-FLAG)*LOG(F+FLAG) + FLAG*LOG(LOQ) ; returns log(LOQ) if F<=0
 Y = IPRE + EPS(1)
etc.
 
BTW, log transformation of concentrations is a preferable approach when you do just PK modeling. 
Best regards, 
Vladimir 

----------------------------------------------------------------- 

Vladimir Piotrovsky, Ph.D. 
Research Fellow, Advanced Modeling & Simulation 
Johnson & Johnson Pharmaceutical Research & Development 
Beerse 
Belgium 
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From: "Wang, Yaning" WangYA@cder.fda.gov
Subject: RE: [NMusers] Residuals and INTERACTION for simultaneous PK/PD,i mpos sible? 
Date: Fri, April 15, 2005 4:48 pm 

Eleveld:
In my opinion, you should be able to use INTERACTION even
though the residual error model is additive error model (or homoscastic). 
 
My understanding is that the impact of INTERACTION is in the process
of getting the posterior modes for those ETAs (Emperical Bayes, EB) if
the residual error model is heteroscastic. Then, this impact will be
carried into the estimation of the population parameters (THETAs) because
the marginal likelihood is approximated around those EBs. When you use FOCE
without INTERACTION for a heteroscastic residual error model, the posterior
function of ETAs is approximated by assigning zero to those unknown ETAs in
the residual error part of posterior function. When you use FOCE with INTERACTION,
those unknown ETAs in the residual error part of posterior function will be
replaced by the current EBs (ETAhat) instead of zero. But if your residual
error model is an additive error model,  the residual error part of posterior
function does not involve any ETA. It does not matter whether you use INTERACTION or not. 
 
Try FOCE with or without INTERACTION to fit a dataset with an additive residual
error model, you should get identical results. 
 
Yaning
 
 
Yaning Wang, Ph.D. 
Pharmacometrician 
Office of Clinical Pharmacology and Biopharmaceutics 
Center of Drug Research and Evaluation 
Food and Drug Administration 
Office: 301-827-9763 
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From: "Nick Holford" n.holford@auckland.ac.nz 
Subject: Re: [NMusers] Residuals and INTERACTION for simultaneous PK/PD,impossible? 
Date: Sat, April 16, 2005 1:35 am

Eleveld,

I agree with Yaning that it should make no difference if you use INTERACTION with a
homoscedastic residual error model. I like his elegant explanation of how NONMEM is
trying to solve the problem.

It seems to me that INTERACTION should be a default option for METHOD=CONDITIONAL. I
don't know how it can adversely effect the result except possibly for a bit of extra
computation time. The current default (no INTERACTION) is an unfortunate pitfall if
you are either unaware of this issue of simply overlook it in the excitement of
building a new model.

Nick

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