Re: [NMusers] RE: IIV on res error

From: Nick Holford <>
Date: Sat, 17 Jan 2015 08:10:40 +1300

Hi Yuma and Bill,

I have a different perspective on the use of ETA on EPS.

The ETA on EPS describes (without explanation) random differences
between subjects in residual error. A key component of residual error is
model misspecification e.g. wrong structural model, wrong covariate
model, wrong model for between and within subject variability of fixed
effect parameters. If you improve the model by correcting the
misspecification then variance of the ETA on EPS should decrease and the
OFV should decrease. This is similar to what we expect when we add a
useful covariate to a parameter (e.g. CL) and see the variance of the
ETA on CL decrease along with decreased OFV.

The alternative assumption that all subjects have identical residual
error is a strong one. It is one I would have difficulty in justifying
on a priori grounds. I would therefore keep ETA on EPS in your model
while exploring some of the other aspects of the model that Bill suggests.

You can simplify your model by not taking the square root of THETA
squared when the error is just additive or proportional.

It is a poor practice to assign an arbitrary value to IPRED when the
actual prediction is zero. Stuart Beal (the statistician who developed
NONMEM) wrote (

"This code will usually not cause a problem, but on occasion there may be
observation event records where F=0, and this code is masking a problem
about which the user should become aware. Or use of this code may
encourage use of


reflecting the thinking that the addition of a small number in this way
will not significantly alter the results. However, this will very often
alter the results, especially when during the Estimation Step parameter
values are considered that lead to smaller values of F than might be ima-

He concluded "In general, when it can be avoided, any use of a fudge
factor (e.g. the .0001) is poor practice."

I would also recommend using a more biologically plausible model for
describing maturation with post menstrual age rather than GA (see
references below). A sigmoid hyperbolic maturation function using PMA
extrapolates correctly to 0 when PMA=0 and to 1 at adult ages (when
maturation is by definition complete). GA is a component of PMA but does
not account for maturation after birth so this model is obviously
misspecified unless you only study neonates on the day of birth when GA
is the same as PMA.

Best wishes,


Holford N. Dosing in children. Clin Pharmacol Ther. 2010;87(3):367-70.
Anderson BJ, Holford NHG. Tips and traps analyzing pediatric PK data.
Pediatric Anesthesia. 2011;21(3):222-37.
Holford N, Heo YA, Anderson B. A pharmacokinetic standard for babies and
adults. J Pharm Sci. 2013;102(9):2941-52.

On 17/01/2015 4:55 a.m., Denney, William S. wrote:
> Hi Yuma,
> IIV on residual error is effectively compound symmetry. What it is
> saying is that “some subjects are more variable than others” without
> suggesting a reason why. Your model below incorporates additive
> error, and you don’t have IIV on F1, so in your case, this ETA on EPS
> could be one of:
> ·Masking proportional error on PK
> ·Masking dose-related variability in PK if subjects received different
> doses
> ·Masking IIV on F1
> ·True compound symmetry where some subjects are more variable than others
> There are probably other options, but I would check some of those to
> see if they can improve your model before using ETA on EPS.
> Thanks,
> Bill
> *From:*
> [] *On Behalf Of *Y.A. Bijleveld
> *Sent:* Friday, January 16, 2015 9:09 AM
> *To:*
> *Subject:* [NMusers] IIV on res error
> Dear all,
> I am modeling multi-center log-transformed neonatal data and have
> constructed a 2-compartment model with ETA’s on Cl, V1 and V2.
> However, when introducing interindividual variability on the residual
> error the MOFV drops >150 points, while previously significant
> relationships between clearance and covariates disappear. I find it
> strange that the introduction of the IIV has such an impact and don't
> fully understand. I have already checked the data for (extreme) outliers.
> Can anyone shed some light?
> Thank you so much.
> Yuma Bijleveld.
> $PK
> F1=(BIO1**FDS12) * (BIO2**FDS34)
> TVV1=THETA(1)*(WT/70000)
> V1=TVV1*EXP(ETA(1))
> TVCL=THETA(2)*(WT/70000)**0.75*(GA/281)**THETA(6)
> TVQ=THETA(4)*(WT/70000)**0.75
> TVV2=THETA(5)*(WT/70000)
> V2=TVV2*EXP(ETA(3))
> S1=V1
> IPRED=LOG(0.0001)
> W=1
> IF(F.GT.0)W = SQRT(THETA(3)**2)
> Y = IPRED+W*EPS(1)*EXP(ETA(4))
> (0, 75.7) ;1 V1
> (0, 2.09) ;2 CL
> (0, 0.376) ;3 add
> (0, 3) ;4 Q
> (0, 31.8) ;5 V2
> (0, 3.3) ;6 GA
> 0.167 ;1 V1
> 0.0824 0.12 ;2 Cl
> 0.1 ;3 V2
> 0.1 ;4 RES
> 1 FIX
> ------------------------------------------------------------------------
> AMC Disclaimer :
> ------------------------------------------------------------------------

Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
office:+64(9)923-6730 mobile:NZ +64(21)46 23 53

Holford SD, Allegaert K, Anderson BJ, Kukanich B, Sousa AB, Steinman A, Pypendop, B., Mehvar, R., Giorgi, M., Holford,N.H.G. Parent-metabolite pharmacokinetic models - tests of assumptions and predictions. Journal of Pharmacology & Clinical Toxicology. 2014;2(2):1023-34.

Ribba B, Holford N, Magni P, Trocóniz I, Gueorguieva I, Girard P, Sarr,C., Elishmereni,M., Kloft,C., Friberg,L. A review of mixed-effects models of tumor growth and effects of anticancer drug treatment for population analysis. CPT: pharmacometrics & systems pharmacology. 2014;Accepted 15-Mar-2014.

Received on Fri Jan 16 2015 - 14:10:40 EST

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