# RE: Linear VS LTBS

From: Eleveld, DJ <d.j.eleveld>
Date: Fri, 21 Aug 2009 14:33:37 +0200

Hi Neil,

Well if you compare proportional+additive error model with a logarithmic error model then it shouldnt be suprising that they work differently and give you different residual variance. Logarithmic error model presumes that the accuracy of the observations, in absolute terms, becomes very good for low concentrations. With real-world (i.e. not simulated) measuments this might not be the case and this is probably the motivation for the proportional+additive type models. The best error model is the one that best matches the characteristics of the very(!) complex physical process behind the reporting of some number as "concentration of substance X in the sample".

If a proportional+additive error model works better than a logarithmic error model then I would check to see if the observations at small concentrations (usually the late observations) are possibly dominating the estimation for the logarithmic model. These samples influence the estimation less for propotional+additive error model because the additive term.

If you have many observations close to LOQ then there are a number of different suggestion in the literature how to handle these. I wouldnt make any conclusions about the best error model until you have decied how you are going to handle them.

There was some recent discussion on this list about the possibility of a logarithmic+additive model. It was complicated and I didnt really follow it.

Douglas Eleveld

________________________________

Van: owner-nmusers ndranil Bhattacharya
Verzonden: vr 21-8-2009 13:52
Aan: Grevel, Joachim
CC: nmusers
Onderwerp: Re: [NMusers] Linear VS LTBS

Hi Joachim, thanks for your suggestions/comments.

When using LTBS I had used a different error model and the error block is shown below
\$ERROR
IPRED = -5
IF (F.GT.0) IPRED = LOG(F) ;log transforming predicition
IRES=DV-IPRED
W=1
IWRES=IRES/W ;Uniform Weighting
Y = IPRED + ERR(1)

I also performed bootsrap on both LTBS and non-LTBS models and the non-LTBS CI were much more tighter and the precision was greater than non-LTBS.
I think the problem plausibly is with the fact that when fitting the non-transformed data I have used the proportional + additive model while using LTBS the exponential model (which converts to additional model due to LTBS) was used. The extra additive component also may be more important in the non-LTBS model as for some subjects the concentrations were right on LOQ.

I tried the dual error model for LTBS but does not provide a CV%. So I am currently running a bootstrap to get the CI when using the dual error model with LTBS.

Neil

On Fri, Aug 21, 2009 at 3:01 AM, Grevel, Joachim <Joachim.Grevel

Hi Neil,

1. When data are log-transformed the \$ERROR block has to change: additive error becomes true exponential error which cannot be achieved without log-transformation (Nick, correct me if I am wrong).

2. Error cannot "go away". You claim your structural model (THs) remained unchanged. Therefore the "amount" of error will remain the same as well. If you reduce BSV you may have to "pay" for it with increased residual variability.

3. Confidence intervals of ETAs based on standard errors produced during the covariance step are unreliable (many threads in NMusers). Do bootstrap to obtain more reliable C.I..

These are my five cents worth of thought in the early morning,

Good luck,

Joachim

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-----Original Message-----

From: owner-nmusers
Sent: 20 August 2009 17:07
To: nmusers
Subject: [NMusers] Linear VS LTBS

Hi, while data fitting using NONMEM on a regular PK data set and its log transformed version I made the following observations

- PK parameters (thetas) were generally similar between regular and when using LTBS.
-ETA on CL was similar
-ETA on Vc was different between the two runs.
- Sigma was higher in LTBS (51%) than linear (33%)

Now using LTBS, I would have expected to see the ETAs unchanged or actually decrease and accordingly I observed that the eta values decreased showing less BSV. However the %RSE for ETA on VC changed from 40% (linear) to 350% (LTBS) and further the lower 95% CI bound has a negative number for ETA on Vc (-0.087).

What would be the explanation behind the above observations regarding increased %RSE using LTBS and a negative lower bound for ETA on Vc? Can a negative lower bound in ETA be considered as zero?
Also why would the residual vriability increase when using LTBS?

Please note that the PK is multiexponential (may be this is responsible).

Thanks.

Neil

--
Indranil Bhattacharya

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Received on Fri Aug 21 2009 - 08:33:37 EDT

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