From:Paul Hutson 
Subject:[NMusers] Cl/F and V/F
Date:Mon, 29 Jul 2002 16:01:24 -0500

Greetings all:
Using ADVAN2 TRANS2, I am fitting data from a parallel animal 
bioavailability study to determine the relative oral bioavailability of 5 
new formulations, with the bioavailability of the initial product set to 1. 
In fitting the clearance (CL) and volume (V)  to this 1 compartment model, 
I obtain a convergence and intra-subject variability in these parameters 
using the POSTHOC option.  My understanding was that the CL and V values 
reported out by NONMEM for the i-th animal are in fact CL(i)/F1(i) and 
V(i)/F1(i).  Therefore, by multiplying the output by F1, I anticipated that 
I would correct for the differences in relative bioavailability between 
formulations, eg:

TVF1=1
IF(FORM.EQ.1)TVF1=THETA(1)
IF(FORM.EQ.2)TVF1=THETA(2)
IF(FORM.EQ.3)TVF1=THETA(3)
IF(FORM.EQ.4)TVF1=THETA(4)
IF(FORM.EQ.5)TVF1=THETA(5)
F1=TVF1

KA=THETA(6); FIXED DUE TO LIMITED ABSORPTION PHASE DATA
CL=THETA(7)*EXP(ETA(1))
V=THETA(8)
CLT=CL*F1;  CLT is true clearance
SC=V/1000
VT=SC*F1;  VT is true dist volume.

Instead, the graph of the resulting CLT and VT show dichotomous values, 
varying by formulation.  In contrast, the values of CL and SC reported out 
by the NONMEM fit are uniform over the different animals and formulations, 
with the intersubject errors of course adding some fuzziness.

So, my question is, does NONMEM report out in ADVAN2 TRANS2 the "true" 
clearance and distribution volume, or are the values of CL and SC in fact 
CLtrue/F1 and Vtrue/F1?

If the latter, why would my results for the CL*F1 and SC*F1 have such 
formulation-dependent breaks or separation of the means?
Thanks,
Paul
  (Leonid and Nick: Thanks for your previous comments. I am back on the 
listserve because of the general nature of this question.)

Paul Hutson, Pharm.D.
Associate Professor (CHS)
UW School of Pharmacy
777 Highland Avenue
Madison, WI 53705-2222
Tel:    (608) 263-2496
FAX:    (608) 265-5421
Pager: (608) 265-7000, #7856


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From:"Gobburu, Jogarao V"  
Subject:RE: [NMusers] Cl/F and V/F
Date:Mon, 29 Jul 2002 17:14:41 -0400

Dear Paul,

1. You do not have to multiply the CL and V for F1. It is already taken care
of. Although, I am sure you realize that they are still apparent parameter
values. The adjustment you have for F1 is only relative, not absolute
(unless your formulation #1 is iv).

2. You do not need the first conditional: IF(FORM.EQ.1) TVF1=THETA(1). My
understanding from your email is that your reference is formulation#1, which
will be TVF1=1.

Regards,
Joga Gobburu,
Pharmacometrics,
CDER, FDA
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From:Nick Holford 
Subject:Re: [NMusers] Cl/F and V/F
DateTue, 30 Jul 2002 09:42:15 +1200

Paul,

I think you are making things more complicated than they really are. The post hoc estimates of
CL and V are NOT CL/F1 and V/F1. The CL, V and F1 parameters are separately estimated. However,
the values of CL and V are obtained under the assumption that F1 for formulation 0 is 1. This
assumption may be wrong but no harm comes to the modelling by assuming it.

I note that you do not allow any between subject variability in F1 in your code. I can see no
reason not to include this in the model. I would consider using:

F1=TVF1*EXP(ETA(F1))

This may be more important than including BSV on CL. Your rats may be essentially clones and
BSV on CL and V may be quite small but F1 depends on other factors (e.g. the formulation
variability). This could account for more rat to rat variation in the concs than disposition
parameters. Remember that the usual SHAM methods for bioequivalence make the assumption that CL
is identical and formulation differences in AUC are due only to differences in F1.

Nick