From: "Tsai, Max" max.tsai@spcorp.com
Subject: [NMusers] Indirect response PD model
Date: Fri, January 28, 2005 4:38 pm 

Hello. I am rather new at modeling with NONMEM.  As a learning
opportunity, I'm trying to verify the results of a model that I
ran successfully using WinNonMix.  I have a set of PD data (shown
below). The PK data has already been modeled and the PK parameters
are fixed in the control stream (shown below). The PD model is an
indirect response model with inhibition of production.  When I
run the model, it goes through many, many iterations before it
fails.  I have tried many different things such as changing
initial estimates and altering error structures, but I come
across the same errors: either there are rounding errors or
r matrix is algorithmically singular and non-positive definite. 
I'm sure that the model can fit the data unless the algorithms
for the two programs are that different (has anyone ever seen
one program converge, but not the other?) If anyone could shed
some light on this issue, it would be much appreciated.

-Max

$PROB  PK-PD DATA

$INPUT  ID AMT TIME DV CMT

$DATA CXCRPD.csv

$SUBROUTINE ADVAN6 TOL=3

$MODEL NCOMP = 4

  COMP = (GUT)

  COMP = (CENTRAL)

  COMP = (PERIPH)

  COMP = (EFFECT)

$PK

;PK MODEL

   V = 216

   KA = 2.35

   K20 = 0.55

   K23 = 0.17

   K32 = 0.074

   S2 = V/1000

;PD MODEL

   TVKIN = THETA(1)

   TVKOUT = THETA(2)

   TVIC50 = THETA(3)

   KIN = TVKIN * EXP(ETA(1))

   KOUT = TVKOUT * EXP(ETA(2))

   IC50 = TVIC50 * EXP(ETA(3))

$DES

DADT(1) = -KA * A(1)

DADT(2) = (KA * A(1)) - ((K20 + K23) * A(2)) + (K32 * A(3))

DADT(3) = K23 * A(2) - K32 * A(3)

CP = A(2)/S2

COEF = 1 - (CP / (IC50 + CP))

DADT(4) = KIN * COEF - KOUT * A(4)

$THETA   (0, 15);  KIN

                 (0, 0.15);  KOUT                    

                  (0, 5);  IC50                 

$OMEGA   0.1;  KIN

                 0.1;  KOUT

                 0.1;  IC50

                                                

$ERROR

   Y = F  + EPS(1)

$SIGMA  0.1

$EST     MAXEVAL=5000  PRINT=1  

$COV

$SCAT           (RES WRES) VS TIME

Partial data set

ID      AMT     TIME    DV       CMT

101     10      0       .       1      
101     .       0       6.4     4      
101     .       2       5.7     4      
101     .       4       4.9     4      
101     .       6       3.8     4      
101     .       8       3.5     4      
101     .       12      2.2     4      
101     .       24      2.4     4      
102     10      0       .       1      
102     .       0       3.566667        4      
102     .       2       3       4      
102     .       4       2.4     4      
102     .       6       1.6     4      
102     .       8       1.8     4      
102     .       12      2.4     4      
102     .       24      2.9     4      
104     10      0       .       1      
104     .       0       2.666667        4      
104     .       2       2.2     4      
104     .       4       1.6     4      
104     .       6       1.4     4      
104     .       8       1.4     4      
104     .       12      2       4      
104     .       24      2.3     4      


Max Tsai, Ph.D.
Senior Scientist (DM/PK)
Schering-Plough Corporation
2015 Galloping Hill Road
K-15-2-2650
Kenilworth, NJ 07033-0530
(:  (908) 740-3911
:  (908) 740-2916
*:  max.tsai@spcorp.com  
_______________________________________________________

From: "Sam Liao" sliao@pharmaxresearch.com
Subject: Re: [NMusers] Indirect response PD model 
Date: Fri, January 28, 2005 6:30 pm

Hi Max:

You need to set up the initial condition for CMT 4.  WinNonMix set it up 
for you.  But in nmv, you need to do it in the data and control file.  
Please see the nmv usernet archiev for detailed discussion.
http://www.cognigencorp.com/nonmem/nm/99oct052000.html
*Subject: * PD initialization
*Posting: * October 5, 2000

Best regards,
Sam Liao
Pharmax Research
_______________________________________________________

From: "mathangi" mathangi@msn.com
Subject: Re: [NMusers] Indirect response PD model 
Date: Fri, January 28, 2005 7:11 pm

Hello Max,
 
The indirect model you have used requires initialization
of baseline response.  It could be done the following way
in the data set and control file.
 
CONTROL FILE
;PD MODEL

   TVKIN = THETA(1)

   TVKOUT = THETA(2)

   TVIC50 = THETA(3)

   KIN = TVKIN * EXP(ETA(1))

   KOUT = TVKOUT * EXP(ETA(2))

   IC50 = TVIC50 * EXP(ETA(3))

   F4 = KIN/KOUT            ;Initializing to baseline; R0 = kin/kout

 DATA SET

101     10      0       .       1

101       1      0       0        4      
101     .       0       6.4     4      
101     .       2       5.7     4      
101     .       4       4.9     4      
101     .       6       3.8     4      
101     .       8       3.5     4      
101     .       12      2.2     4      
101     .       24      2.4     4     

The modified model runs successfully. Hope this is helpful.

Just a suggestion.

Parametrizing in terms of CL and V would lead to meaningful interpretation of the model.

Thanks

Mathangi
_______________________________________________________

From: "Tsai, Max" max.tsai@spcorp.com
Subject: RE: [NMusers] Indirect response PD model 
Date: Mon, January 31, 2005 8:34 am 

Thanks to Sam and Mathangi for the helpful advice.  It appears that was all
that was needed.  Is this initialization required only when working with
differential equations for PK-PD modeling?

-Max
_______________________________________________________

From: "Sam Liao" sliao@pharmaxresearch.com
Subject: Re: [NMusers] Indirect response PD model 
Date: Mon, January 31, 2005 10:26 am 

Hi  Max:

It is needed only when the initial condition is not zero.  In this case, 
the initial condition is set to be the steady-state value.

Also, you may want to use an integral function for the drug 
concentrations in stead of solving it in three DE to cut down your run time.

Best regards,
Sam Liao
Pharmax Research
_______________________________________________________

From: "MANOJ KHURANA" manoj2570@yahoo.com
Subject: Re: [NMusers] Indirect response PD model
Date: Mon, January 31, 2005 11:36 am

Hi Sam,
This is pretty new to me but could you please elaborate on
your suggestion "Also, you may want to use an integral function
for the drug concentrations in stead of solving it in three DE
to cut down your run time." in terms of how it is done in NONMEM
and would be nice if you can show some examples how those equations
are written and also explain how would they cut down the run time.

Thanks
Manoj
_______________________________________________________

From: "Sam Liao" sliao@pharmaxresearch.com
Subject: Re: [NMusers] Indirect response PD model
Date: Mon, January 31, 2005 12:14 pm

Hi MANOJ:

Please see the nmv usernet archieve below for an example,
http://www.cognigencorp.com/nonmem/nm/99jan311996.html
*Subject: *PK/PD analysis
*Posting: * January 31, 1996

Max may be able to tell you later how much nmv run time can be saved 
using the integral equation for Cp.

Best regards,
Sam Liao
Pharmax Research
_______________________________________________________

From: "Tendolkar, Amol" amol.tendolkar@spcorp.com
Subject: RE: [NMusers] Indirect response PD model
Date: Tue, February 1, 2005 5:29 am

Hi Max,

Before you apply a programmatic solution to this problem,  I would like to
point out that the Indirect Pharmacologic Response model could be set up as
a Direct or Indirect link model.  It appears from your model setup, that you
have an effect compartment, however, you have not linked it to either
peripheral or central compartment with 'keo'. 

I also noticed that you are not simultaneously fitting pk and pd models.
Therefore, you do not need a 4 compartment setup.  A 1 compartment model
(just for the response variable) should be adequate.

Amol
_______________________________________________________

From: "Tsai, Max" max.tsai@spcorp.com
Subject:  RE: [NMusers] Indirect response PD model 
Date: Tue, February 1, 2005 12:59 pm

I agree that the 4 compartment setup is not necessary if the plasma
concentrations from the PK model are entered into the dataset and the
control stream is coded properly.  However, I thought that since there is no
mass actually being transferred to the effect compartment in the indirect
response model, there is no need for a rate constant such as k1e to link the
effect compartment and the central compartment, in my case.  If anyone else
in the users group would like to comment on this issue, please feel free.

-Max
_______________________________________________________

From: "Sam Liao" sliao@pharmaxresearch.com
Subject: Re: [NMusers] Indirect response PD model
Date: Tue, February 1, 2005 2:45 pm

Hi Max:
If you used the plasma conc (Cp) in the data set to run this model, you 
need to do some sort of interpolation of the Cp within the $DES block.  
Otherwise, the solution of the PD effect compartment will not be correct 
because the ODE solver will use a step function instead of a continuous 
curve of Cp.

Best regards,
Sam Liao
Pharmax Research
_______________________________________________________