RE: [NMusers] Additive plus proportional error model for log-transform data

From: Mats Karlsson <>
Date: Thu, 2 Jun 2016 09:56:03 +0000

Dear Ahmad,

You don't havet o choose between normal or transformed concentrations in yo=
ur error model, you can let NONMEM estimate the most appropriate transforma=
tion for you. Combining this with a power transform error model I think is =
likely to solve your problem. See
A strategy for residual error modeling incorporating scedasticity of varian=
ce and distribution shape.
Dosne AG, Bergstrand M, Karlsson MO.
J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015=
-9460-y. Epub 2015 Dec 17.

It is automated in PsN as "execute -dtbs ..."

Besst regaards,
Mats Karlsson, PhD
Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala

Phone: +46 18 4714105
Fax + 46 18 4714003<http://www.farmb=>

From: [] On=
 Behalf Of Jakob Ribbing
Sent: Thursday, June 02, 2016 6:32 AM
To: Abu Helwa, Ahmad Yousef Mohammad - abuay010
Subject: Re: [NMusers] Additive plus proportional error model for log-trans=
form data

Hi Ahmad,

The two error models are equivalent (only that with Leonids suggested code,=
 the additive-on-log-transformed error term (TH16) is estimated on variance=
 scale, instead of standard deviation scale (approximate CV).
This inflated error rates for very low concentrations is what you get for a=
dditive+proportional on the log transformed scale, and I believe that has b=
een discussed on nmusers previously as well, many years ago.
You could possibly use a cut-off for when lower IPRE should not lead to hig=
her residual errors, but why not move to additive + proportional for the or=
iginal concentration scale?

Also, this implementation may be unfortunate:
Y=(1-FLAG)*IPRE + W*EPS(1)

Effectively, when concentration predictions are zero (FLAG=1), e.g. for p=
re-dose samples or before commence of absorption, then you set the concentr=
ation prediction to EXP(1)=3.14 concentration units.
Depending on what concentration scale you work on (i.e. if BLQ is much high=
er than this) it may be OK, but otherwise not.
Instead of applying a flag, just set IPRE to a negative value (low in relat=
ion to LOG(BLQ)), if you want to stay on the log-transformed scale.

I hope this helps to solve your problem.

Best regards


Jakob Ribbing, Ph.D.

Senior Consultant, Pharmetheus AB

Cell/Mobile: +46 (0)70 514 33 77<><>

Phone, Office: +46 (0)18 513 328

Uppsala Science Park, Dag Hammarskjölds väg 52B

SE-752 37 Uppsala, Sweden

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On 02 Jun 2016, at 04:27, Abu Helwa, Ahmad Yousef Mohammad - abuay010 <ahma=<>> =

Dear NMusers,

I am developing a PK model using log-transformed single-dose oral data. My =
question relates to using combined error model for log-transform data.

I have read few previous discussions on NMusers regarding this, which were =
really helpful, and I came across two suggested formulas (below) that I tes=
ted in my PK models. Both formulas had similar model fits in terms of OFV =
(OFV using Formula 2 was one unit less than OFV using Formula1) with slight=
ly changed PK parameter estimates. My issue with these formulas is that the=
 model simulates very extreme concentrations (e.g. upon generating VPCs) at=
 the early time points (when drug concentrations are low) and at later time=
 points when the concentrations are troughs. These simulated extreme concen=
trations are not representative of the model but a result of the residual e=
rror model structure.

My questions:
1. Is there a way to solve this problem for the indicated formulas?
2. Are the two formulas below equally valid?
3. Is there an alternative formula that I can use which does not have=
 this numerical problem?
4. Any reference paper that discusses this subject?

Here are the two formulas:
1. Formula 1: suggested by Mats Karlsson with fixing SIGMA to 1:

2. Formula 2: suggested by Leonid Gibiansky with fixing SIGMA to 1:
W = SQRT(THETA(16)+ (THETA(17)/EXP(IPRE))**2 )

The way I apply it in my model is this:

IF (F.EQ.0) FLAG=1


Y=(1-FLAG)*IPRE + W*EPS(1)

1. FIX

Best regards,

Ahmad Abuhelwa
School of Pharmacy and Medical Sciences
University of South Australia- City East Campus
Adelaide, South Australia

Received on Thu Jun 02 2016 - 05:56:03 EDT

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