From:Toufigh Gordi 
Subject:[NMusers] Michaelis-Menten model i nonmem
Date:Mon, 17 Feb 2003 11:25:39 -0500

Hi!

I am trying to implement a "simple" binding action of a drug in nonmem. The 
PK of the drug is characterized (3-comp). The binding is given as %bound 
receptors (between 0-100). I have the following coding:

$ERROR
IPRED=F
W=1
IRES=DV-IPRED
IWRES=IRES/W
Y1=IPRED+(IPRED*EPS(1)+EPS(2))*W
Y2=(BMAX*IPRED/(BC50+IPRED))+EPS(3)
Q=1
IF (PKPD.EQ.2) Q=0
Y=Q*Y1+(1-Q)*Y2

All PK parameters (including eps (1) and (2)) are fixed. Altough the model 
gives expected estimates of BMAX and BC50, EPS(3) is large (over 300%), 
which results in poor individual fits.

Any suggestions?

Toufigh Gordi
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From:  Nick Holford 
Subject: Re: [NMusers] Michaelis-Menten model i nonmem
Date:Tue, 18 Feb 2003 08:08:23 +1300

Toufigh,

First suggestion is to make your model account for reality more closely and put in a term for
non-specific binding. 

I also wonder how you know the % bound (in order to compute the DV for bound conc) if you don't
already know the binding parameters? It's often a good idea to fit the raw binding observation
rather than transforming it into a % of something that is usually not really known very well.

Also remember that the binding model assumes CONC is unbound. Is this really the case for the conc
that your PK model is predicting? Or is this total (bound+unbound) conc?

You might also consider a proportional residual error for the binding prediction.

Finally, there is no need for the variables Q and W in your code. It can be expressed more clearly
(IMHO) as follows:

$ERROR
CONC=F
IF (PKPD.EQ.2) THEN
   Y=BMAX*CONC/(BC50+CONC) + CONC*NS + EPS(3) ; NS is non-specific binding parameter
ELSE
   Y=CONC*(1+EPS(1)) + EPS(2)
ENDIF
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