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

From: Jakob Ribbing <>
Date: Thu, 2 Jun 2016 06:31:32 +0200

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 additive+proportional on the log transformed scale, and I believe =
that has been discussed on nmusers previously as well, many years ago.
You could possibly use a cut-off for when lower IPRE should not lead to =
higher residual errors, but why not move to additive + proportional for =
the original 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 pre-dose samples or before commence of absorption, then you set the =
concentration prediction to EXP(1)=3.14 concentration units.

Depending on what concentration scale you work on (i.e. if BLQ is much =
higher than this) it may be OK, but otherwise not.
Instead of applying a flag, just set IPRE to a negative value (low in =
relation 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 =
<> wrote:

> 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 tested 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 slightly 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 concentrations are not =
representative of the model but a result of the residual error model =
> My questions:
> 1. Is there a way to solve this problem for the indicated =
> 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:
> W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2)
> 2. Formula 2: suggested by Leonid Gibiansky with fixing SIGMA to =
> 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
> W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2) ;FORMULA 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
> Australia

Received on Thu Jun 02 2016 - 00:31:32 EDT

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