- On 20 Jul 2006 at 18:24:04, "vipul gupta" (vipul686.at.rediffmail.com) sent the message

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Hi All,

I have a general question for number of data points and parameters to

be estimated for a model. Are there some rules for having minimum

number of data points to estimate the number of parameters?

Thank you all.

Vipul

Vipul Kumar

Post Doc fellow

Pharmaceutics

University of Florida

Gainesville-FL (USA) - On 22 Jul 2006 at 16:34:12, "David S. Farrrier" (DFarrier.-at-.SummitPK.com) sent the message

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Dear Vipul,

"The more the merrier" (or better), is a good motto. Our PK Solutions

pharmacokinetics data analysis software [ see www.SummitPK.com ]

requires 5 sample points as a minimum, but this would put a strain on

any attempt to calculate parameters following an extravascular dose.

If the analyses are accurate and the individual subject variation is

minimal, 6+ samples can get you 75 PK parameters using PK Solutions.

But that should be considered only a pilot experiment to work out a

better and more complete sampling protocol.

David S. Farrier, Ph.D.

Summit Research Services

/\ /\

SummitPK.com /\ / \ /\ / \

/ / / /\ / \

==

David S. Farrier, Ph.D. Phone: 970-249-1389

Summit Research Services Fax: 970-249-1360

68911 Open Field Dr. Email: DFarrier.-a-.SummitPK.com

Montrose, CO 81401 Web: http://www.SummitPK.com - On 24 Jul 2006 at 09:46:44, Stephen Duffull (stephen.duffull.at.stonebow.otago.ac.nz) sent the message

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The following message was posted to: PharmPK

Vipul

> I have a general question for number of data points and parameters to

> be estimated for a model. Are there some rules for having minimum

> number of data points to estimate the number of parameters?

Yes and no :-)

Can you make your question more specific? If so then I may be able to

help more...

If this a single subject or a population design? If it is single

subject

then the minimum number of samples per subject = the number of fixed

effects parameters. If you are estimating residual variance then you

will

need another sample if the variance is additive.

If this is a population design - then it is more complex and I

suggest you

have a look at: Duffull et al. JPKPD 2005; 32:441-457.

Cheers

Steve

--

Professor Stephen Duffull

School of Pharmacy

University of Otago

PO Box 913

Dunedin

P 03 479 5044

F 03 479 7034 - On 24 Jul 2006 at 09:46:44, Stephen Duffull (stephen.duffull.at.stonebow.otago.ac.nz) sent the message

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The following message was posted to: PharmPK

Vipul

> I have a general question for number of data points and parameters to

> be estimated for a model. Are there some rules for having minimum

> number of data points to estimate the number of parameters?

Yes and no :-)

Can you make your question more specific? If so then I may be able to

help more...

If this a single subject or a population design? If it is single

subject

then the minimum number of samples per subject = the number of fixed

effects parameters. If you are estimating residual variance then you

will

need another sample if the variance is additive.

If this is a population design - then it is more complex and I

suggest you

have a look at: Duffull et al. JPKPD 2005; 32:441-457.

Cheers

Steve

--

Professor Stephen Duffull

School of Pharmacy

University of Otago

PO Box 913

Dunedin

P 03 479 5044

F 03 479 7034 - On 24 Jul 2006 at 19:06:26, "vipul gupta" (vipul686.at.rediffmail.com) sent the message

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Dear Prof Duffull and David S. Farrier,

Thank you for your response. To be more specific, my question

concerns estimating PK parameters for small number of subject (n=13)

and I am interested to calculate parameters for each individual

separately. This is because of the different PK profiles (single peak

vs Double peak) observed for different individuals.

I have around 9-11 data poionts per individual, however when I tried

to estimate model parameters using WinNonlin user define model for

two absorption sites, sometimes I got very high %CV for parameters

and at occassions WinNonlin crashed and I had to reinstall it again

to use it. So I was wondering was it because I do not have enough

data points given the number of parameters (6 in case of a two

absorption site model) or am I still missing something here!!!!

Thank you

Vipul

Vipul Kumar

Post Doc Associate

Dept of Pharmaceutics

University of Florida

Gainesville, FL-32601 - On 26 Jul 2006 at 14:48:33, "Ma Guangli" (guanglima.at.gmail.com) sent the message

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ear Vipul Kumar,

As my understanding, the more data points maybe could not solve

your problem. The more data points give the more exact description

about the model. But if the truth is that there is high CV% for the

parameters of the hypothetic model on this data set, the more data

points could do nothing.

The technique to estimate parameters is to minimize least square

(or some other function) as a target function. The limination of data

points comes not only from statistical part but also numerical part.

Yours

Ma Guangli - On 26 Jul 2006 at 09:57:12, "Dipesh Jayswal" (dipesh.jayswal.at.alembic.co.in) sent the message

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Dear groupmembers,

Is there any guideline or published paper which states the minimum

number of

concentration per subject required to obtain PK parameter like Cmax,

AUCt,

AUCi, t1/2,Kel,Tmax etc efficiently?

Please help me out in this....

thanks in advance.

Regards,

Dipesh Jayswal

Biostatistician,

BioArc Research Solution,

Vadodara - On 29 Jul 2006 at 20:40:29, =?ISO-8859-1?Q?Helmut_Sch=FCtz?= (helmut.schuetz.-at-.bebac.at) sent the message

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The following message was posted to: PharmPK

Dear David,

you wrote:

>If the analyses are accurate and the individual subject variation is

>minimal, 6+ samples can get you 75 PK parameters using PK Solutions.

>

Maybe I'm just old-fashioned, but I always thought that:

degrees of freedom = number of data points - number of parameters

Maybe you can force your software--I cannot do that with mine--

to calculate 75 parameters from 6 samples, but most likely only

with a confidence interval of -infinity to +infinity ;-)

best regards,

Helmut

--

Helmut Schuetz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

1070 Vienna/Austria

tel/fax +43 1 2311746

Web http://BEBAC.at

BE/BA Forum http://forum.bebac.at - On 31 Jul 2006 at 18:15:06, David Bourne (david.-at-.boomer.org) sent the message

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The following message was posted to: PharmPK

Hi Vipul

I am not aware of any particular designs that are so bad that would

require

you to have to reinstall your software ...

But without knowing more, it seems odd that you would need to have

more than

9-11 data points per individual in order to estimate the parameters

for a 6

parameter model, unless the sampling times were taken at very inoptimal

times.

Since you only have 13 individuals it might be difficult to get a

population

approach to run and get estimates of the variance of between subject

effects

for all parameters. However, it is probable that patients will share

some

common components of the PK profile, e.g. perhaps they have the same

structural aspects to their disposition model, and hence a population

approach might be helpful.

In the meantime, I suggest you quantify the informativeness of your

design

by either computing the asymptotic standard errors for your design

using say

ADAPT II or performing simulation-estimations to get empirical

estimates of

the standard errors. If you wanted to look at the informativeness of

your

design for a population setting then you could use POPT.

Regards

Steve

--

Professor Stephen Duffull

Chair of Clinical Pharmacy

School of Pharmacy

University of Otago

PO Box 913 Dunedin

New Zealand

E: stephen.duffull.-at-.otago.ac.nz

P: +64 3 479 5044

F: +64 3 479 7034 - On 31 Jul 2006 at 18:16:40, David Bourne (david.aaa.boomer.org) sent the message

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The following message was posted to: PharmPK

Dear David,

you wrote:

>If the analyses are accurate and the individual subject variation is

>minimal, 6+ samples can get you 75 PK parameters using PK Solutions.

>

Maybe I'm just old-fashioned, but I always thought that:

degrees of freedom = number of data points - number of parameters

Maybe you can force your software--I cannot do that with mine--

to calculate 75 parameters from 6 samples, but most likely only

with a confidence interval of -infinity to +infinity ;-)

best regards,

Helmut

--

Helmut Schuetz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

1070 Vienna/Austria

tel/fax +43 1 2311746

Web http://BEBAC.at

BE/BA Forum http://forum.bebac.at - On 31 Jul 2006 at 20:51:33, David Bourne (david.aaa.boomer.org) sent the message

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Dear Dipesh Jayswal,

I believe that there is no a minimum number for all of questions.

Compartment and noncompartment analysis are very different.

As my understanding, that 9 data points as a minimum value are

chosen in noncompartment analysis is because that there should be 3

data points in absorption, distribution, and elimation phase,

respectively to estimate the parameters,

To compartment analysis, the minimum number of data points is

according to your model.

Population PK analysis give a minimum number of data points anyway.

Yours

Ma Guangli - On 31 Jul 2006 at 21:21:28, David Bourne (david.aaa.boomer.org) sent the message

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The following message was posted to: PharmPK

Helmut

Theoretically parameters to be estimated cannot exceed data points.

It's right. But the condition is that each parameters should be

orthogonal

(independent to each other).

For PK parameters they are usually recalculated by others like ke =

CL/Vd as

you know.

Most of 75 PK parameters that PK sulutions put out are such ones, I

think.

Kyun-Seop Bae MD PhD

Assistant Professor

Department of Clinical Pharmacology & Therapeutics

Asan Medical Center, University of Ulsan

Tel: +82-2-3010-4611

Fax: +82-2-3010-4623

Mobile: +82-17-253-5048

Email: ksbae.at.amc.seoul.kr

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