From: "Eleveld, DJ" d.j.eleveld@anest.umcg.nl
Subject: [NMusers] POSTHOC and ETA values disagree 
Date: Wed, June 29, 2005 1:45 pm

Hi everyone, 

Thanks to the advice from this list, especially from Leonid and Katya, I have been
able to make NONMEM do estimations of my PD-potentiation model.   Many thanks.

Although I have no problem with individual fittings, I am having problems getting
population estimations to produce reasonable POSTHOC and ETA values for one of the
model parameters.  In some previous model-building advice, Leonid had suggested to 
simplify the model so I split the PK and PD estimations.  

What might cause all individual POSTHOC values to be exactly the same, while the 
corresponding ETA value might be some large value?  What might cause a gradient 
for an ETA to be zero? 

I am estimating PD parameters from 6 individuals and about 2500 total data points.
Individual fits work just fine, with an expected degree of variation in the 
parameters.  The model parameters I find from individual fits are:

THETA(1)  THETA(2)  THETA(3)  THETA(4)  THETA(5)  THETA(5) 
1.17E-01  1.22E+03  4.90E+00  1.26E-02  9.33E-02  9.62E+01 
1.47E-01  1.44E+03  4.64E+00  2.82E-03  3.56E-02  1.00E+02 
1.36E-01  1.74E+03  4.76E+00  4.38E-03  7.05E-02  9.71E+01 
1.02E-01  1.28E+03  3.41E+00  6.81E-03  7.99E-02  9.97E+01 
2.09E-01  1.60E+03  3.96E+00  1.22E-02  6.20E-01  9.82E+01 
1.69E-01  1.86E+03  5.80E+00  6.39E-03  1.07E-01  1.03E+02 

When I do a population fit (log-normal parameter distributions) I get reasonable THETA values: 
THETA(1)  THETA(2)  THETA(3)  THETA(4)  THETA(5)  THETA(5) 
1.47E-01  1.26E+03  4.45E+00  5.47E-03  6.26E-03  9.97E+01 

ETA and POSTHOC values for most of the parameters seem ok, however ETA(4) and the
POSTHOC values for THETA(4) are not reasonable:

ETA1      ETA2      ETA3      ETA4      ETA5      ETA6 
5.26E-02 
0.00E+00  4.62E-02 
0.00E+00  0.00E+00  9.62E-02 
0.00E+00  0.00E+00  0.00E+00  4.89E-01<-- This value is always similar to the initial value 
0.00E+00  0.00E+00  0.00E+00  0.00E+00  1.94E+01(*) 
0.00E+00  0.00E+00  0.00E+00  0.00E+00  0.00E+00  1.12E-03 

The POSTHOC values for the individuals: 
THETA(1)  THETA(2)  THETA(3)  THETA(4)  THETA(5)    THETA(5) 
1.13E-01  1.22E+03  5.23E+00  5.47E-03  3.92E-02    1.05E+02 
1.49E-01  1.40E+03  4.77E+00  5.47E-03  3.30E+02(*) 1.15E+02 
1.38E-01  1.74E+03  4.69E+00  5.47E-03  8.84E-02    9.59E+01 
1.01E-01  1.28E+03  3.45E+00  5.47E-03  6.65E-02    1.02E+02 
1.93E-01  1.29E+03  2.57E+00  5.47E-03  1.57E-04    9.56E+01 
1.68E-01  1.85E+03  5.82E+00  5.47E-03  9.17E-02    1.04E+02 
Values marked with (*) seem to be too high. 

The POSTHOC values for THETA(4) are the exactly the same for all individuals (equal to the 
typical value) while ETA(4) non-zero.  This seems illogical to me.  Can anyone suggest 
why this may be occurring?

During the estimation the gradient for ETA(4) remains zero or extremely small, and the 
value doesn’t seem to change much at all during estimation.  This seems to be true 
regardless of what initial value I use for ETA(4) for a wide range of values.  This 
could be the source of the ETA(4) and POSTHOC problems but I cannot imagine why this 
might be the case given that individual fits seemed to be just fine.

Thanks very much for all your help so far, 

Doug Eleveld 

----------------------------------------------------------------------------------------- 
$PROB  Potentiation fitting 
$DATA  potpd__.prn 
$INPUT ID TIME CPLA DV MDV AMT RATE 
$SUBROUTINES ADVAN9 TOL=4 
$ABBREVIATED COMRES=1 
$MODEL NCOMPARTMENTS=2 
       NPARAMETERS=6 
       COMP(POTENT NOOFF) 
       COMP(EFFECT NOOFF NODOSE) 
$PK 
    CALLFL=0 
    KEO=THETA(1)*EXP(ETA(1)) 
    EC50=THETA(2)*EXP(ETA(2)) 
    GAMM=THETA(3)*EXP(ETA(3)) 
    POTR=THETA(4)*EXP(ETA(4)) 
    POTK=THETA(5)*EXP(ETA(5)) 
    SCAL=THETA(6)*EXP(ETA(6)) 
    F1=COM(1)                   ; Also possible as AMT=COM(1) 
$DES 
    DADT(1)=-POTK*A(1)          ; Decay potentiation 
    DADT(2)=(CPLA-A(2))*KEO     ; Effect compartment conc 
$ERROR 
    FPOT=1+A(1)                 ; Potentiation factor 
    CEFF=A(2) 
    DPD1=CEFF**GAMM             ; Degree of NMB 
    DPD2=EC50**GAMM 
    MNMB=1-DPD1/(DPD1+DPD2) 
    Y=SCAL*FPOT*MNMB+ERR(1)     ; Twitch prediction 
    COM(1)=POTR*MNMB 
$THETA (0,0.137)(1000,1270,1500)(3,4.51,6) 
       (0,0.005)(0,0.129)(95,100,105) 
$OMEGA 0.5 0.5 0.5 0.5 0.5 0.1 
$SIGMA 1 
$ESTIMATION MAX=9999 SIG=3 
            METHOD=0 POSTHOC REPEAT 
            PRINT=1 
;$COVARIANCE 
$TABLE TIME KEO EC50 GAMM POTR POTK SCAL 
       NOAPPEND NOHEADER FILE=potent2.txt 
$TABLE TIME CEFF FPOT MNMB DV Y 
       NOAPPEND NOHEADER FILE=potent3.txt 
_______________________________________________________

From: "Leonid Gibiansky" leonidg@metrumrg.com
Subject:  Re: [NMusers] POSTHOC and ETA values disagree 
Date:  Wed, June 29, 2005 3:00 pm 

Doug,

You mix terminology and it makes the text hard to follow. THETAs are population
parameters. By 
definitions, they are the same for all individuals; POSTHOC does not change them.
You probably refer 
to population parameters that correspond to those THETAs. Initial values are given
to OMEGA matrix, 
not to ETAs.

If the individual fit is fine, you may not need random effect ETA(4). Try using only
fixed effect 
(POTR=THETA(4)) and see what happens. In general, it is not necessary to have random
effects on all 
parameters. Most likely, you may also remove ETA(5) without compromising the fit.
After you remove 
unnecessary random effects, you may try FOCE (starting from the final FO parameter
estimates)

Good luck,
Leonid
_______________________________________________________

From: "Eleveld, DJ" d.j.eleveld@anest.umcg.nl
Subject: RE: [NMusers] POSTHOC and ETA values disagree
Date:  Fri, July 1, 2005 6:00 am 

Hi Leonid, 

You are right that I am mixing terminology, I will try to be more careful. 

I agree with you that if one considers the POSTHOC values then one would come 
to the conclusion that random effect ETA(4) may not be needed.  I have done 
this in my further analysis.  I havent gotten FOCE analysis to work yet as 
it is producing floating-point errors or numerical difficulties during 
integration.  I still am trying to some more limited parameter ranges. 

However, if I had not chosen to perform POSTHOC analysis and only looked at 
the estimated ETA(4) value I would come to a very different conclusion, i.e. 
that random effect ETA(4) is necessary based on the ETA(4) estimation of 0.48. 
So in this case the conclusions based on inspection of the ETA values or on 
the POSTHOC values are very different.  

Ultimately, I agree with your conclusion but I am confused as to how that 
conclusion was reached.  If the POSTHOC values disagree with the estimated 
ETA values, which one is then "right"?  It seems that you (as I do) consider 
the POSTHOC results as more "important" than the estimated ETA results.  If 
this is in general a good idea then what are the estimated ETA values actually 
good for? 

From what I could gather from reading the NONMEM documentation I didnt see any 
strong advice to examine the POSTHOC values to determine the necessity of using 
specific random effects, only inspection of the estimated ETA values.  I got the 
impression that POSTHOC values are simply an interesting 'extra'.  So basing 
conclusions on the 'extra' POSTHOC information seems strange because I then have 
to ignore the 'essential' ETA information.  I think this is the basis of my 
confusion here. 

Unfortunately I cannot sensibly also remove random effect ETA(5) also as 
this would lead to all individuals exhbiting the same degree of potentiation. 
Visual inspection of the observations shows that this is not the case. 

Doug 
_______________________________________________________

From: "Leonid Gibiansky" leonidg@metrumrg.com
Subject: Re: [NMusers] POSTHOC and ETA values disagree 
Date:  Fri, July 1, 2005 8:03 am 

Doug,
POSTHOC is a separate computation useful to check assumptions used in the building
of the population 
model (e.g., normality of the random effect distributions). My point was that if the
fit is good 
enough with constant ETA(4) (and nearly constant ETA(5)) you may try to insert this
information into 
the population model by requesting OMEGA(4,4) = 0 (OMEGA(5,5)=0). If the fit of the
simplified model 
is good, I do not see any reasons in keeping extra effects in the model. 3-4%
variability of the 
parameter (as you have for ETA(5)) usually can be ignored.

You may also try HYBRID method for ETA(4).

Leonid
_______________________________________________________