From: "Vijay V. Upreti"  
Subject: [NMusers] sample size
Date: Thu, November 11, 2004 6:15 pm 

Hi all,
I have this very simpe question regarding the minimum sample size for 
population analysis. 
I have plasma concentration time data from 4 large mammals. There are 10 
sampling points and I was just wondering if I can use population analysis 
for this small sample size.
I am aware that NONMEM can be used for modeling single subject data but will 
n=4 suffice for population analysis, some thoughts please.
 
_______________ 
Vijay V Upreti
Gradaute Student
Pharmacokinetics-Biopharmaceutics Laboratory 
Department of Pharmaceutical Sciences
University of Maryland, School of Pharmacy 
20 Penn St., Baltimore, MD 21201 
Voice: 410-706-7388 
Fax: 410-706-5017
_______________________________________________________

From:"Serge Guzy" GUZY@xoma.com
Subject: RE: [NMusers] sample size
Date: Fri, November 12, 2004 3:37 pm

If the data are rich enough as you mention, 4 individuals would be
enough to estimate population means and population variances as well as
sigma. The results would certainly be very similar  to the one obtained
using individual fitting software(like Winnonlin).
Serge Guzy
President POP_PHARM

_______________________________________________________

From:"GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr
Subject: RE: [NMusers] sample size
Date: Sun, November 14, 2004 3:54 am 

Hi Vijay,
 
I would certainly not use populaton analysis with 4 individuals
even if NONMEM or any other algorithm gives you estimates. Basic
idea of parametric population analysis is to estimate parameter
statistical distributions, more precisely the first 2 moments
mean and variance, of a symetrically distributed random variable . 
 
I suggest that, without any fancy population software,  you
simply try to estimate the mean and  variance from 4 simulated
normally distributed values,  then compute their standard errors
of mean and variance.  In a second step, try to fit your population
model with NONMEM using the data of your 4 mammals and once again
have a look at the standard errors of all your parameters (THETA
and OMEGA). In both cases, you'll see how bad is the precision of
your estimates and realize that they have very little values,
except maybe for SIGMA since the estimates will be based on 40
values. The simple laws of statistics still apply in population
analysis, which is a powerful tool but certainly not a magic one.
 
Best regards,
 
Pascal
 
==========================================
Dr Pascal Girard
EA 3738 Ciblage Thérapeutique en Oncologie
Fac Médecine Lyon-Sud
BP12
69921 OULLINS Cedex
France
 
Tel 33 4 78 86 31 53
Fax 33 4 78 86 31 49
e-mail : Pascal.Girard@adm.univ-lyon1.fr
==========================================  
_______________________________________________________

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] sample size
Date: Sun, November 14, 2004 4:13 am

Hi,

 

I disagree with Pascal. If you look upon the options: Population
analysis, standard two-stage, naïve pooling or throw away the result
of your experiment, population analysis may well be the best option.
I don’t know anyone who has compared methods with as few as 4 subjects,
but we looked at 8 subjects with rich sampling and found that pop analysis
was better than STS for the situations we studied (AAPS PharmSci. 2000;2(3):E32).

Best regards,

Mats

--

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se

_______________________________________________________

From: "GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr
Subject: RE: [NMusers] sample size
Date: Sun, November 14, 2004 4:31 am 

Hi Mats,
 
I was certainly not recommanding STS neither. Having said
this, does better means good estimates? I don't know the work
you mention, but did you have a look at the confidence intervals?
Did you know the exact structural and PK-PD model (simulated or real
data set) ? How large were the random inter-individual variances? Did
you have outliers? All this may affect your results with few individuals.
That's why I was cautionning any population analysis (one or 2 stages)
with only 4 individuals, unless you have adressed all those questions
and accept to report your CI.
 
Have a good Sunday,
 
Pascal 
_______________________________________________________

From: "Mats Karlsson"  
Subject: RE: [NMusers] sample size
Date: Sun, November 14, 2004 4:38 am 

Hi again,

 

We looked at simulated data. Have a look at the paper
for the details. I certainly agree that less data is less
information, but you seemed to suggest that Vijay either
should throw away his data or analyse them by some other
means. I’m still not sure which of the two you recommend.
 

Best regards,

Mats

--

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se
_______________________________________________________

From: "Steve Duffull" sduffull@pharmacy.uq.edu.au
Subject: RE: [NMusers] sample size
Date: Sun, November 14, 2004 5:38 pm 

Hi Vijay (Pascal + Mats) 

In addition to the comments already - you could compute the amount of information in
your current design and then get a feeling for how well a population method would be
able to solve your problem.  This would allow you to assess whether the design is
sufficient to meet your needs vs the slightly different question does a particular
tool (e.g. NONMEM) perform well with the data that you have.  

To do this, you would need to have some feeling as to what the most likely model and
parameter values are, and it may well turn out that in some circumstances it is
possible to learn about some parameters from as little as 4 intensively sampled
subjects.

If you have the sampling design, and some feeling for the likely model(s) and
parameter values then I am happy to compute the information from the design for
you...

Steve

Stephen Duffull
School of Pharmacy
University of Queensland
Brisbane 4072
Australia
Tel +61 7 3365 8808
Fax +61 7 3365 1688
University Provider Number: 00025B
Email: sduffull@pharmacy.uq.edu.au
www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm
PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm
MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm
_______________________________________________________

From: "Mats Karlsson" 
Subject: RE: [NMusers] sample size
Date: Mon, November 15, 2004 4:16 am

Hi Steve,

Vijay wrote:

"I have plasma concentration time data from 4 large mammals."

Would it not be more straightforward and logical to actually analyse the
data rather than guess upon the model and then use an approximation to
investigate how well the design can characterize it?

Best regards,
Mats
--
Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se
_______________________________________________________

From: "Steve Duffull" sduffull@pharmacy.uq.edu.au
Subject: RE: [NMusers] sample size
Date: Mon, November 15, 2004 4:23 am

Mats
 
If you know nothing about the drug - then I agree.  However if the experiment was
supposed to be answering a question then it is possible that the investigators may
know something in which case the design could be assessed - this assessment could
also answer the yet to be asked question ... 'how many more animals are needed [to
answer the question of interest]?'
 
Steve

Stephen Duffull
School of Pharmacy
University of Queensland
Brisbane 4072
Australia
Tel +61 7 3365 8808
Fax +61 7 3365 1688
University Provider Number: 00025B
Email: sduffull@pharmacy.uq.edu.au
www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm
PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm
MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm
_______________________________________________________

From: "GIRARD PASCAL" PASCAL.GIRARD@adm.univ-lyon1.fr
Subject: RE: [NMusers] sample size
Date: Mon, November 15, 2004 4:44 am 

Hi Mats and All, 

The initial question of Vijay was: "I am aware that NONMEM can be used for modelling
single subject data but will n=4 suffice for population analysis?”. My answer
still is that I don't think anyone can pretend building a population model with n=4.


Now if the question is "May I take advantage of population framework for estimating
individual parameters, and get better results than modelling single subject?" I
agree that it may be worth trying. You simply have to keep in mind that the
objective of this initial analysis with n=4 is getting "individual parameters", not
population ones. Now I agree that it can also be considered as the very first step
of a population analysis. For this latter objective, Vijay could use Steve's
suggestion which is assessing how much mammals, points/mammals as well as value of
sample times that would be necessary to estimate, with a certain requested
precision, the population parameters.  

Best regards,

Pascal 
_______________________________________________________

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] sample size
Date: Mon, November 15, 2004 5:15 am

Hi Steve and Pascal,

Steve,

Even in the case you have some information about your system, I don't see
how the performing an assessment on the design before analyzing the data is
more informative than analyzing the data and then assess the appropriateness
of the design. Your guess at what the true model is must be better after
looking at the data. I can't imagine the situation where you would 1) guess
at the appropriate model, 2) assess the design and find that it is not
sufficient to characterize it, and therefore 3) throw away your data. You
are always going to analyse your data so why not take advantage of the
information you gain.


Pascal, 

I just reacted to your statement "I would certainly not use populaton
analysis with 4 individuals even if NONMEM or any other algorithm gives you
estimates." As it seems, we all agree that population, or non-linear mixed
effects, modeling actually may be the way to go here even if the amount of
information is limited with only 4 subjects.* Also, I do believe we are
interested in information about population parameters, not individual
parameters (unless we want to treat these specific 4 large mammals). These
individuals are of interest only because they can tell us something about
the population. The information will be very scarce, but it will be
information about the population.

*My guess is that nonlinear mixed effects modeling may be best, but wouldn't
be surprised is in some situations (balanced design, not very nonlinear
systems, ...) naïve pooling could give more precise and less biased
estimates for some population parameters.

Best regards,
Mats

--
Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se
_______________________________________________________

From: "Steve Duffull" 
Subject: RE: [NMusers] sample size
Date: Mon, November 15, 2004 6:36 am 

Hi Mats and Pascal
 
Firstly, Mats I agree that analysing the data is always the sensible option (never
throwing data away).  
 
Secondly, I am not in absolute agreement with Pascal --- it is possible that the
population characteristics of some drugs may be able to be determined with as little
as 4 patients/animals.
 
For argument, if in the example cited, the system were adequately described by a
1-cpt first order input-output model with exponential BSV on all parameters and
mixed residual error function and you had 10 samples per animal for each of the 4
animals and the sampling times extended for at least 3 half-lifes then it is
possible to estimate CL, V, Ka  and BSV(CL, V, Ka).  The standard errors of the BSV
parameters are not going to be great but not terrible (approx 70-80%).  Estimating
the proportional component of the residual variance will be for all intents and
purposes not possible.
 
Thirdly, analysing the data using NONMEM and then assessing the design helps to
learn about deterministic identifiability issues - i.e. are all parameters (fixed
effects and variance effects estimable).  I believe that in some cases it is
important to be informed from both what is theoretically possible to learn from the
design as well as to learn from the actual data gathered from the performing design
itself (they may be different things).
 
Steve

Stephen Duffull
School of Pharmacy
University of Queensland
Brisbane 4072
Australia
Tel +61 7 3365 8808
Fax +61 7 3365 1688
University Provider Number: 00025B
Email: sduffull@pharmacy.uq.edu.au
www: http://www.uq.edu.au/pharmacy/sduffull/duffull.htm
PFIM: http://www.uq.edu.au/pharmacy/sduffull/pfim.htm
MCMC PK example: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm
______________________________________________________