From: tgordi@buffalo.edu
Subject:[NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 2:48 PM

Dear all,

I have been asked by a friend to estimate the parameters of a simple
binding study. Different infusion concentrations were administered to
rats and 1 single sample was collected at 30 seconds after the start
of he infusion (rats were sacrificed at this time point). There are
several "dose" levels in the study. The data was first analysed using
Winnonlin and Km, Bmax (maximum binding), and base line were estimated.
The estimates look reasonable and in line with previous studies. I tried
the same model (simple Hill equation) in NONMEM, running the model first
in FOCE and then FO mode. The parameter estimates are very off from the
expected range, not even close to the more reasonable Winnonlin estimates.
I started with different initial values and the model has problems in
getting to the same final estimates. Could the nature of the data, 
i.e. single sample per subject, explain the poor performance of the run?
Is there any remedy for this?

regards,

Toufigh Gordi  
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From: GUZY@xoma.com
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 4:27 PM

I am surprised that you could evaluate 2 parameters with one single data
point using Winnonlin (does not do a population fit). 
Using Population modeling, I think that the same time point for each rat
(30 minutes)  can easily make the problem non identifiable. If it is
identifiable, you need anyway to fix the intraindividual variance to
some value.

Serge Guzy
President POP-PHARM
Head of Preclinical Statistics and Pharmacometrics, Xoma

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From: tgordi@buffalo.edu
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 4:37 PM

Dear Serge,

I am not trying to fit a kinetic model. This is data from a cell binding
study. If one plots the incoming infusion (different concentrations) vs.
the cell binding data from each rat, a saturable system is observed, where
a Hill function can be applied. I don't see the problem of estimating Vmax
and Km from such data. There is no time involved in this model. This
observation vs. effect.

I didn't do the Winnonlin analysis myself.

Toufigh 

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From: lgibiansky@emmes.com
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 5:03 PM
 
Toufigh,
I think you will need to provide more info concerning your model (e.g., NONMEM
control stream and data sample). Otherwise, it is difficult to discuss the
problem without knowing what exactly you are trying to do. In general, NONMEM
can fit nonlinear model without difficulties. If you have one sample per animal,
you cannot fit population model, you will need to approach this as an "average"
pooled data fit. In this case you should not face problems if your data support
the model (i.e., describe the full profile).

Leonid 
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From: GUZY@xoma.com
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 5:37 PM

Dear Toufigh
If I understand, you plot effect versus concentration and fit the data
using Winnonlin which gave you reasonable values for Vm and Km. When you
used NONMEM, my understanding is that you took into account that each
observation came from a different rat and you are trying to retrieve
both the fixed effect (Mean values) as well as random effects
(variability across the population of rats). Since you have only one
data point per rat (am I right?) you must fix the intra-individual
variance parameters to a specific value. Did you do that?
Serge 

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From: GUZY@xoma.com
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 5:55 PM

If you have a good idea about the assay errors, you can assume fixed
intra-individual variance parameters (let say for example 15% CV) and
then perform a population fit. I did it many times with our MCPEM
(Monte-Carlo Parametric Expectation Maximization) algorithm which
optimize the same objective function as NONMEM (FOCE with interaction).
If you are interested I could get the data and try our software to
retrieve both fixed and random effects.
Serge

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From: tgordi@buffalo.edu
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/19/2003 6:55 PM

I apologize for not having provided the control stream. It is now given
at the end of this mail. As you might guess, the V1 and CL values are
arbitrary. Beside this model, I also tried one where DADT(1) was set
equal to -A(1)*CL/V1. That model gives almost identical result as the
one presented here.

Thank you!

Toufigh 

$PROB CELL
$INPUT ID AMT TIME DV REG CMT
$DATA ind.csv IGNORE=#
$SUBROUTINE ADVAN6 TRANS1 TOL=5
$MODEL NCOMP=1
COMP=CENT
$PK

        V1=1
        CL=0.00001

        S1=V1

        IMAX=THETA(1)*EXP(ETA(1))
        KM=THETA(2)
        KNS =THETA(3)

$DES
DADT(1)=0

$ERROR
        CONC=F
        LAM=(IMAX*CONC/(KM+CONC))+KNS*CONC
        Y=LAM*(1+EPS(1))
  
$THETA (0, 500)    ;1 IMAX
$THETA (0, 10000)  ;2 KM
$THETA (0, 0.001)  ;3 KNS

$OMEGA 0.1         ;1 IIV IMAX

$SIGMA 0.1         ;1 PROP ERROR

$ESTIMATION NOABORT POSTHOC MAXEVAL=9999 PRINT=3 METHOD=1 MSFO=MSF1
$COVARIANCE
$TABLE ID TIME Y                     NOPRINT ONEHEADER FILE=SDTAB1
$TABLE ID TIME IMAX KM KNS ETA1      NOPRINT ONEHEADER FILE=PATAB1
$TABLE ID REG                        NOPRINT ONEHEADER FILE=CATAB1




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From: GibianskyE@guilfordpharm.com
Subject: RE: [NMusers] Model estimates based on 1 sample per subject
Date: 8/20/2003 9:26 AM

Toufigh,
 
as Leonid and Serge pointed out, with one point per rat you can't fit a
population model (i.e have both ETA and EPS in the control stream). Also, to
fit an algebraic function you do not need to have a differential equation
and a ficticious compartment. You can use $PRED instead (then you do not
need $SUBROUTINE, $MODEL, $PK and $ERROR).
 
Katya

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