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

From: Abu Helwa, Ahmad Yousef Mohammad - abuay010 <>
Date: Thu, 2 Jun 2016 02:27:29 +0000

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 Wed Jun 01 2016 - 22:27:29 EDT

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