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

From: Leonid Gibiansky <lgibiansky_at_quantpharm.com>
Date: Thu, 2 Jun 2016 03:46:40 -0400

I also like this version:

W = SDL-(SDL-SDH)*TY/(SD50+TY)
Y=LTY+W*EPS(1)

Here SDL is the standard deviation (in logs) at low concentrations, SDH is
the standard deviation at high concentrations, TY is the individual
prediction, LTY is LOG(TY). SIGMA should be fixed at 1

Leonid

On Wed, Jun 1, 2016 at 10:27 PM, Abu Helwa, Ahmad Yousef Mohammad -

> 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 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:
>
> W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2)
>
>
>
> 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:
>
>
>
> FLAG=0 ;TO AVOID ANY CALCULATIONS OF LOG (0)
>
> IF (F.EQ.0) FLAG=1
>
> IPRE=LOG(F+FLAG)
>
>
>
> W=SQRT(THETA(16)**2+THETA(17)**2/EXP(IPRE)**2) ;FORMULA 1
>
>
>
> IRES=DV-IPRE
>
> IWRES=IRES/W
>
> Y=(1-FLAG)*IPRE + W*EPS(1)
>
>
>
> \$SIGMA
>
> 1. FIX
>
>
>
> Best regards,
>
>
>
>
> School of Pharmacy and Medical Sciences
>
> University of South Australia- City East Campus
>
> Adelaide, South Australia
>
> Australia
>
>
>

--
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566

Received on Thu Jun 02 2016 - 03:46:40 EDT

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