From: "Wang, Yaning" WangYA@cder.fda.gov
Subject: [NMusers] How does NONMEM $DES work?
Date: Tue, December 21, 2004 7:46 pm 

Dear all:

I am using an indirect model to describe the profile of an endogenous
compound (A). And the elimination of this compound is affected by the
exposure of a drug (B). Since it is almost impossilbe to find a model to
describe the time course of drug B and there are enough pairs of drug B
concentration and compound A level, I want to use the observed drug B
concentration in the indirect model as follows:

$DES
DADT(1)=K0-KE{1+EMAX*C/(EC50+C)}*A(1)
where C is the observed drug B concentration and A(1) is the endogenous
compound level. 

I am concerned about how NONMEM handles this differential equations during
the time interval where there are no inputs for C. For example, if we have
data rows at day 1 and day 2 (for both A and B), how can NONMEM fit compound
A level at day 2 without the drug B level information (C) during the
interval between day 1 and day2? Is NONMEM assuming some interpolated values
for C based on C1 and C2?

If this approach is wrong, then consider another case. Suppose clearance
(CL) follows a covariate model, e.g. CL=THETA(1)*(WT/70)**THETA(2). 

CL=THETA(1)*(WT/70)**THETA(2)*EXP(ETA())
$DES
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)-CL*A(2)

Even though we have the same body weight at each row for one subject, how
can NONMEM know WT is not a time dependent covariate? What if WT IS a time
dependent covariate? Has anyone used the covariate model this way(or in a
closed-form equation pattern)?

Thanks a lot for any comment.

Yaning Wang, PhD
Pharmacometrician
OCPB, FDA
_______________________________________________________

From: "Nick Holford" n.holford@auckland.ac.nz
Subject: Re: [NMusers] How does NONMEM $DES work?
Date:  Tue, December 21, 2004 8:58 pm

Yaning,

NONMEM uses the value of the data item, e.g. C, specified in the record for which a
solution is sought e.g.

ID TIME C  DV
1   1   0  10
1   2   1  8

When NONMEM solves the DE system for the second record (TIME=2) it will assume that
C is 1 throughout the interval from TIME=1 to TIME=2.

If you are unable to find a model for C then you can interpolate a value using the T
variable in $DES. There are several ways to do this but the most efficient might be
to pre-compute the slope connecting each two values of C and use this to predict C
at T. Add this slope to the data set and use it in $DES.

e.g.
ID TIME C  DV SLOP
1   1   0  10  0
1   2   1  8   1

$DES
  CNOW=C-SLOP*T

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: "Wang, Yaning" WangYA@cder.fda.gov
Subject: [NMusers] How does NONMEM $DES work?
Date: Tue, December 21, 2004

Nick:

I just want to make sure I correctly understand your response. By default,
NONMEM uses the value of C2(=1 in your example) at TIME2 as the value for C
throughout the interval from TIME1 (=1) to TIME2 (=2) in order to solve the
DE system for DV at TIME2 (=2). Is this right?

By following this, I derived the interpolated value for C between TIME1 and
TIME2.
Suppose at TIME=1.3, we assume C should be 0.3 based on a linear
interpolation.

In eqation CNOW=C-SLOPE*T, I think C=1 and SLOPE=1 at TIME=1.3(C2 and SLOPE2
in data set are used throughout the interval by default). In order to get
CNOW=0.3, T has to be 0.7 at TIME=1.3. How is T in $DES related to the TIME
variable in the data set?

Again, thanks a lot for the help.

Yaning

_______________________________________________________

From:  "Nick Holford" n.holford@auckland.ac.nz
Subject: Re: [NMusers] How does NONMEM $DES work? 
Date: Wed, December 22, 2004 2:37 pm 


Yaning,

Sorry for the confusion. I wrote the reply in some haste because of pre-Christmas
pressures and got the predictive formula for C(T) wrong.

One solution is to add C from the previous record as a data item (CPRE) and TIME as
TPRE:

 ID TIME TPRE C  CPRE SLOP DV
 1   1   1    0  0    0    10 ; first record for this subject
 1   2   1    1  0    1     8 
 1   3   2    3  1    2     4 

then compute C(T) in $DES:

$DES
   CNOW=CPRE+SLOP*(T-TPRE)

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________