From firstname.lastname@example.org Thu Oct 17 05:15:47 1996
Subject: Weights for AUC in a logistics regression
Dear NONMEM users,
In a recent population analysis, my data involved about 200 patients. Of which 50 had extensive sampling (16 samples) and the remaining 150 had about 4 samples each. I obtained a good fit for the data with NONMEM.
Upon examination of the eta's (subject deviations form the population estimates), the variability appears similar in the extensively sampled and in the sparsely sampled patient (which is a good thing).
My question is the following: Take clearance for example, defined as CL(i) = CL * exp[eta(i)], where i refers to the ith subject. Should CL(i) be more precisely estimated if the ith subject is extensively sampled compared to when sparsely sampled (a consequence of the weighted LS method implemented in NONMEM) ? If so, how more precise ? Is there an obvious measure out of NONMEM to use.
I am interested in using AUC(i)=dose/CL(i) as a covariate in a logistic regression whereby my response variable is success/failure to treatment. Do you advise to use a weight for AUC such that it reflects the precision with which AUC was calculated ?
I look forward to hearing you reply.
From email@example.com Thu Oct 17 08:18:11 1996
Subject: Re: Weights for AUC in a logistics regression
We are at the moment looking at the problem you're asking about. In your specific case, I don't think you need weighting, the difference in the precision of CL estimates from a model-based analysis of 4 and 16 is minor, provided the sampling strategy is decent for the sparse sampling. This is also indicated in the results you describe.
An alternative may be to do a simultaneous analysis of the PK and the PD data. NONMEM supports logistic regression, but I don't know if you can simultaneously fit continuous PK data. If this doesn't work there is a possibility for you to obtain SE's of your individual CL estimates. How this is done is explained in NONMEM manual II. You may, however, want to think about how you would use these in your regression (we don't have enough experience to say that a certain treatment is superior to others)..
Mats Karlsson & Niclas Jonsson
From alison Thu Oct 17 13:54:15 1996
Subject: Users Guide II
In reply to Farkad's question, Mats says:
"there is a possibility for you to obtain SE's of your individual CL estimates. How this is done is explained in NONMEM manual II."
Here is an NM-TRAN control stream and a data file for the Bayesian regression example of Guide II Section C.
Please refer to that manual for a discussion.
Two things to note (from Stuart Beal):
(1) Use MAT=R when wanting SE's with single subject Bayesian regression.
(2) With single subject Bayesian regression, the SE is called the "standard deviation of the posterior variance", and not really an SE.
$PROBLEM BAYESIAN NONLIN REG OF CP VS TIME DATA FROM ONE SUBJECT - PREDPP
$INPUT DOSE=AMT TIME DV TYPE ID=L1
$SUBROUTINES ADVAN2 TRANS1
$THETAS (.4 1.7 7) (.025 .102 .4) (.3 3 30)
$OMEGA BLOCK(3) 5.55 .00524 .00024 -.128 .00911 .515 FIXED
$OMEGA BLOCK(1) .388 FIXED
IF (TYPE.EQ.0) M0=1
IF (TYPE.EQ.1) M1=1
IF (TYPE.EQ.2) M2=1
IF (TYPE.EQ.3) M3=1
Y0=F+ERR(4) ; WHEN TYPE=0, TRUE VALUE OF CP
Y1=THETA(1)+ERR(1) ; WHEN TYPE=1, TRUE VALUE OF THETA(1)
Y2=THETA(2)+ERR(2) ; WHEN TYPE=2, TRUE VALUE OF THETA(2)
Y3=THETA(3)+ERR(3) ; WHEN TYPE=3, TRUE VALUE OF THETA(3)
$TABLE TYPE TIME
$SCAT (DV PRED RES) * TIME BY TYPE
$SCAT PRED VS DV BY TYPE UNIT
320 0 0 0 0
0 0 2.77 1 0
0 0 .0781 2 0
0 0 2.63 3 0
0 .27 1.71 0 1
0 .52 7.91 0 2
0 1.0 8.31 0 3
0 1.92 8.33 0 4
0 3.5 6.85 0 5
0 5.02 6.08 0 6
0 7.03 5.4 0 7
0 9.0 4.55 0 8
0 12.0 3.01 0 9
0 24.3 .903 0 10
Results from the run:
THETA - VECTOR OF FIXED EFFECTS
2.12E+00 8.97E-02 3.02E+00
STANDARD ERROR OF ESTIMATE
THETA - VECTOR OF FIXED EFFECTS
2.81E-01 8.81E-03 2.34E-01
From firstname.lastname@example.org Fri Oct 18 06:35:45 1996
Subject: Weights for AUC in a logistics regre
Hi Farkad and Mats,
Just to answer the following specific point raised by Mats after Farkad Email:
> An alternative may be to do a simultaneous analysis of the PK and the
> PD data. NONMEM supports logistic regression, but I don't know if you
> can simultaneously fit continuous PK data. If this doesn't work there is
To my knowledge, without any additional FORTRAN coding you cannot right now do a simultaneous analysis of continuous PK and categorical PD data. The reason for this is that either your PRED routine computes a prediction for your continuous DV based on the model and parameter values, or it computes a probability (e.g. P(Y=1 | THETA, OMEGA) with Y= 1 for yes, Y=0 for no).
In the first case the prediction is passed to NONMEM which computes the default contribution of the current observation to the (conditional) objective function. In the second case (as written in NONMEM help for CCONTR):
"A user-supplied CCONTR subroutine is used to compute the (non-default) contribution to the conditional objective function from a level 2 record. It is used to override the NONMEM default. CCONTR may be used only when a user-supplied CONTR routine is used.
CCONTR is required when there are no epsilons or etas and in other situations, e.g., with categorical population data."
The reason for this is that in the case of a logistic regression, the probability that you compute is directly a piece of your likelihood, and as you know, NONMEM objective function is nothing else than -twice the log likelihood.
With NONMEM version IV you have to write your own CONTR.f and CCONTR.f in the case of logistic regression. This will be automatically implemented within next version V using option F=LIKE in $ESTIM, as presented by Stuart at the last PAGE.
However, to go back to the initial question, I don't see any theoretical reason for not being able to compute simultaneously the likelihood for continuous and categorical data. The question is how to implement it in NONMEM? I'm pretty sure that we can imagine, based on an indicator variable, some coding to tell NONMEM wether the F is a prediction computed by some ADVAN (for PK data) or a probability computed in ERROR subroutine, with alternative call to the correct CONTR annd CCONTR functions. Stuart would surely be of great help for doing so.
A suivre, ...
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