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From: Mats Karlsson <Mats.Karlsson_at_farmbio.uu.se>

Date: Thu, 2 Jun 2016 09:56:03 +0000

Dear Ahmad,

You don't havet o choose between normal or transformed concentrations in yo=

ur error model, you can let NONMEM estimate the most appropriate transforma=

tion for you. Combining this with a power transform error model I think is =

likely to solve your problem. See

A strategy for residual error modeling incorporating scedasticity of varian=

ce and distribution shape.

Dosne AG, Bergstrand M, Karlsson MO.

J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015=

-9460-y. Epub 2015 Dec 17.

It is automated in PsN as "execute -dtbs ..."

Besst regaards,

Mats

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

75124 Uppsala

Phone: +46 18 4714105

Fax + 46 18 4714003

www.farmbio.uu.se/research/researchgroups/pharmacometrics/<http://www.farmb=

io.uu.se/research/researchgroups/pharmacometrics/>

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On=

Behalf Of Jakob Ribbing

Sent: Thursday, June 02, 2016 6:32 AM

To: Abu Helwa, Ahmad Yousef Mohammad - abuay010

Cc: nmusers_at_globomaxnm.com

Subject: Re: [NMusers] Additive plus proportional error model for log-trans=

form data

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 a=

dditive+proportional on the log transformed scale, and I believe that has b=

een discussed on nmusers previously as well, many years ago.

You could possibly use a cut-off for when lower IPRE should not lead to hig=

her residual errors, but why not move to additive + proportional for the or=

iginal 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 p=

re-dose samples or before commence of absorption, then you set the concentr=

ation prediction to EXP(1)=3.14 concentration units.

Depending on what concentration scale you work on (i.e. if BLQ is much high=

er than this) it may be OK, but otherwise not.

Instead of applying a flag, just set IPRE to a negative value (low in relat=

ion 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<mailto:Jakob.Ribbing_at_Pharmetheus.com>

www.pharmetheus.com<http://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 th=

at is privileged and exempt from disclosure under applicable law. If you ar=

e not the intended recipient please notify us immediately. Please do not co=

py it or disclose its contents to any other person.

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

d.abuhelwa_at_mymail.unisa.edu.au<mailto: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 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:

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 - 05:56:03 EDT

Date: Thu, 2 Jun 2016 09:56:03 +0000

Dear Ahmad,

You don't havet o choose between normal or transformed concentrations in yo=

ur error model, you can let NONMEM estimate the most appropriate transforma=

tion for you. Combining this with a power transform error model I think is =

likely to solve your problem. See

A strategy for residual error modeling incorporating scedasticity of varian=

ce and distribution shape.

Dosne AG, Bergstrand M, Karlsson MO.

J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015=

-9460-y. Epub 2015 Dec 17.

It is automated in PsN as "execute -dtbs ..."

Besst regaards,

Mats

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

75124 Uppsala

Phone: +46 18 4714105

Fax + 46 18 4714003

www.farmbio.uu.se/research/researchgroups/pharmacometrics/<http://www.farmb=

io.uu.se/research/researchgroups/pharmacometrics/>

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On=

Behalf Of Jakob Ribbing

Sent: Thursday, June 02, 2016 6:32 AM

To: Abu Helwa, Ahmad Yousef Mohammad - abuay010

Cc: nmusers_at_globomaxnm.com

Subject: Re: [NMusers] Additive plus proportional error model for log-trans=

form data

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 a=

dditive+proportional on the log transformed scale, and I believe that has b=

een discussed on nmusers previously as well, many years ago.

You could possibly use a cut-off for when lower IPRE should not lead to hig=

her residual errors, but why not move to additive + proportional for the or=

iginal 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 p=

re-dose samples or before commence of absorption, then you set the concentr=

ation prediction to EXP(1)=3.14 concentration units.

Depending on what concentration scale you work on (i.e. if BLQ is much high=

er than this) it may be OK, but otherwise not.

Instead of applying a flag, just set IPRE to a negative value (low in relat=

ion 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<mailto:Jakob.Ribbing_at_Pharmetheus.com>

www.pharmetheus.com<http://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 th=

at is privileged and exempt from disclosure under applicable law. If you ar=

e not the intended recipient please notify us immediately. Please do not co=

py it or disclose its contents to any other person.

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

d.abuhelwa_at_mymail.unisa.edu.au<mailto: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 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:

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 - 05:56:03 EDT

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