POSTHOC and ETA values disagree

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 _______________________________________________________