From: "Austin, Daren J" 
Subject: [NMusers] Approximate effect compartment
Date: Thu, 21 Mar 2002 22:05:10 -0000

Dear all,

not strictly a nonmem question but I would like to know whether this is
either valid or been done before.

I have some concentration-effect data which has some evidence of hysteresis.
I can therefore use an effect compartment and fit the PK profiles then the
PD. This has been done using a three-compartment model on IV data and a
post-hoc fit of a PD model.

I now have more data from inhaled, intranasal and IV and would like to fit
the PD response. Unfortunately the concentrations are pretty sparse, and I
don't really want all the hassle of fitting PK profiles to the three routes.

What I propose is the following (sorry for all the maths):

In a linear PK model with an effect compartment I can write the effect
concentration ode as

d(Ce)/dt = KEO(C(t) - Ce)

Since the central compartment is a sum of exponentials of the form C(t) =
Sum(i=1..n) A[i] Exp(-alpha[i].t) I can integrate to get (after rearranging)

Ce(t) = Sum(i=1..n) (KEO/(KEO-alpha[i])) Exp(-alpha[i].t)
(1-EXP(-(KEO-alpha[i]))t)

For a 1-cpt IV bolus this is just Ce(t) = C(t) (KEO/(KEO-ke))
(1-EXP(-(KEO-ke)t)

My question is can I use a similar tecnique in the various regions where
time ~ 1/alpha[i] or just take some value for alpha[i] characteristic of the
half life. Is this approximation likely to be any worse than trying to
acount for variability using inter-subject PK parameters, for example, with
sparse data?

I have tried this by fitting an Emax model to my data (850 pts) and assume
that the half life is known. Defining the approximate effect compartment and
introducing KEO and its ETA reduced the likelihood function by about 200
compared to using the observed concentration! The KEO comes out at about
4/hr which is lower but consistent with earlier two-stage predictions. I get
an excellent posthoc fit to the data with a largest weighted residual of
0.25 and no bias. All parameters are well defined with low CV's using
METHOD=0

Can anyone point me to any references where this might have been discussed
before?

Kind regards,

Daren

Dr. Daren J. Austin
Pharmacometrician
Clinical Pharmacology Discovery Medicine
GlaxoSmithKline
daren.austin@gsk.com
Tel: 7-711 2073 or +44 (0) 20 8966 2073
Fax: 7-711 2123 or +44 (0) 20 8966 2603


*******

From: "Bachman, William" 
Subject: RE: [NMusers] Approximate effect compartment
Date: Fri, 22 Mar 2002 07:39:27 -0500

Daren,

What you are proposing sounds like a lot of "hassle" to me.  Why not just
simultaneously fit all of your data from all routes of administration,
particularly because the newer data is sparse. Just fit it all using an
extravascular dosing model (e.g. ADVAN12).  The original IV data (dense?)
will stabilize the model and allow calculation of absolute F of the
intranasal formulation.  Am I missing something here?  (seems to be a
straight forward approach).

Bill

William J. Bachman, Ph.D.
GloboMax LLC
7250 Parkway Dr., Suite 430
Hanover, MD 21076
Voice (410) 782-2212
FAX (410) 712-0737
bachmanw@globomax.com


*******
From: "Kowalski, Ken" 
Subject: RE: [NMusers] Approximate effect compartment
Date: Fri, 22 Mar 2002 08:15:48 -0500

Daren,

You might want to take a look at my paper:

Kowalski, K.G. and Karim, A.  "A Semicompartmental Modeling Approach for
Pharmacodynamic Data Assessment," JPB 23:307-322 (1995).

In this paper I derive what I call a semicompartmental solution to the
effect-site concentration (Ce) where the only kinetic parameter that is
estimated is keo.  I assume a piecewise linear model for Cp (like doing the
trapezoidal AUC) and using the effect site link dCe/dt = keo(Cp - Ce), I
derive a recursive solution for Ce that only requires
"noncompartmental-like" calculations.  Using this solution for Ce requires
one to use the observed Cp as a covariate and then one can estimate, keo and
the PD parameters without having to specify a compartmental model for Cp.

Now the bad news.  This approach was developed for single subject data with
fairly dense sampling...enough for doing noncompartmental calculations.
Since you have sparse population data I don't think this approach will work
for you.  Moreover, even if you had dense sampling, some very special
programming using verbatim code would be needed if you wanted to implement
this method in NONMEM and plan to put an eta on keo.  It turns out that one
cannot "simply" specify recursive models using $PRED if those recursive
models involve etas because NONMEM won't calculate the derivatives properly.

Nevertheless, my paper might give you some additional insight.

Regards,

Ken

*******

From: Liping Zhang. [mailto:lpz@itsa.ucsf.edu]
Subject: Re: [NMusers] Approximate effect compartment
Date: Friday, March 22, 2002 3:51 PM

     The method will not work well when the PK data are sparse as expected. However if you
	 want to use NONMEM and put an eta on Keo, NONMEM can do it. For example, go to 
	 NONMEM Users Repository and then check PKPD-Lew Sheiner and then look for
     the 2nd file named "SEQPOP". 

     Best regards, 

     Liping Zhang 

     -- 
        _/  _/  _/_/ _/_/_/ _/_/_/  Liping Zhang  (liping@c255.ucsf.edu)
       _/  _/ _/    _/_    _/_/     4th year Graduate student 
      _/  _/ _/        _/ _/        Dr. Lewis Sheiner's group
      _/_/   _/_/ _/_/_/ _/         Biological and Medical Informatics Program
                                    Box 0626, UCSF, SF, CA, 94143-0626
                                    415-502-1989 (v), 415-476-2796 (fax)


*******

From: "Kowalski, Ken" 
Subject: RE: [NMusers] Approximate effect compartment
Date: Fri, 22 Mar 2002 16:30:04 -0500

Liping,
 
When I said that you can't easily put an eta on Keo (without verbatim code) I was referring
to my semicompartmental recursive solution for Ce.  If you use a fully compartmental solution
for Ce where you specify a compartmental model for Cp then there are no issues with putting
an eta on Keo even with sparse data.
 
Ken

*******

From:"Austin, Daren J" 
Subject: RE: [NMusers] Approximate effect compartment
Date: Fri, 22 Mar 2002 19:41:06 -0000

> Do you mean to use this equation?
> Ce(t) = C(t) (KEO/(KEO-alpha_i))*(1-EXP(-(KEO-alpha_i)t)
> and substitute alpha_i with ka or kel in the absorption or elimination
> phase
> of the pk profile?
> 
 
        [Austin, Daren J]  Yes
		
> The equation below seems to be missing the A(i) coefficients.
> Ce(t) = Sum(i=1..n) (KEO/(KEO-alpha[i])) Exp(-alpha[i].t)
> (1-EXP(-(KEO-alpha[i]))t)
> 
        [Austin, Daren J]  
        Yes, my solution was missing the A[i].

        Essentially my point is that although a multicompartment model fits
the dense PK data, I can generate very good PD fits by assuming the
one-compartment model solution and estimating an approximte Ce from the
observed plasma concentrations. It's really a question of how much the
effect compartment needs to follow the central compartment. My approximation
is that the dynamics of the effect compartment look one-compartment-like
irrespetive of the multi-compartments needed for the plasma PK. When
variability in KEO is added I wondered just how valid this approach would
be.

        Thanks for the reference Ken.

        Daren