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From: Jakob Ribbing <jakob.ribbing_at_pharmetheus.com>

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

Jakob Ribbing, Ph.D.

Senior Consultant, Pharmetheus AB

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

Jakob.Ribbing_at_Pharmetheus.com

www.pharmetheus.com

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

Uppsala Science Park, Dag Hammarskjölds väg 52B

SE-752 37 Uppsala, Sweden

This communication is confidential and is only intended for the use of =

the individual or entity to which it is directed. It may contain =

information that is privileged and exempt from disclosure under =

applicable law. If you are not the intended recipient please notify us =

immediately. Please do not copy it or disclose its contents to any other =

person.

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

<ahmad.abuhelwa_at_mymail.unisa.edu.au> 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 =

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,
*

*>
*

*> 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

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:

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

Jakob Ribbing, Ph.D.

Senior Consultant, Pharmetheus AB

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

Jakob.Ribbing_at_Pharmetheus.com

www.pharmetheus.com

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

Uppsala Science Park, Dag Hammarskjölds väg 52B

SE-752 37 Uppsala, Sweden

This communication is confidential and is only intended for the use of =

the individual or entity to which it is directed. It may contain =

information that is privileged and exempt from disclosure under =

applicable law. If you are not the intended recipient please notify us =

immediately. Please do not copy it or disclose its contents to any other =

person.

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

<ahmad.abuhelwa_at_mymail.unisa.edu.au> wrote:

data. My question relates to using combined error model for =

log-transform data.

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.

formulas?

have this numerical problem?

1:

(0)

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

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