From: "Lin Lin" llin@thresholdpharm.com
Subject: [NMusers] population size and confidence power  
Date: Mon, April 4, 2005 2:31 pm 

Could anyone explain a little bit on how big the population size (6 or 1000)
would be needed in a study in order to reach the enough confidence power at
the final PK/PD model? Could NONMEN provide this information or this
information has to be predetermined by a statistic program (SAS)?

Many thanks.

Lin Lin
Threshold Pharmaceuticals
1300 Seaport Blvd 
Redwood City, CA 
Email llin@thresholdpharm.com
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From:  "Leonid Gibiansky" leonidg@metrumrg.com
Subject: Re: [NMusers] population size and confidence power
Date:  Mon, April 4, 2005 3:27 pm 

Lin,
SAS will not help you. You will need either a good consultant who knows the drug and
can estimate 
the size based on his/her knowledge and intuition and/or a simulation study. The
population size 
will depend on:

Study design (dosing and sample times)
Complexity of the PK behavior (one-exponential vs two-exponential vs. three
exponential decay, 
linear or nonlinear, etc.)
Precision of the PK measurements (intra-patient PK variability)
Variability of the PK parameters (inter-patient PK variability)
Precision of the PD measurements (intra-patient PD variability)
Variability of the PK/PD parameters (inter-patient PK/PD variability)

When you know these parameters (or guess based on either earlier studies or similar
drugs), you 
simulate the study, fit the model and look on the results (parameter bias,
precision, confidence 
interval of the parameter estimates). You may need to do it more than once to
investigate how 
results depend on your assumptions. Simulations may include extra layer or
uncertainty (about 
population parameters: rather than select values for simulations you may assume
their distributions).

As a rough estimate, 6 is definitely too small, 1000 should be sufficient. I would
say 200-300 
should be sufficient unless you have a high variability of PK and/or PK/PD
parameters or strong 
non-linearity.
Leonid
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From:  "Nick Holford" n.holford@auckland.ac.nz
Subject: Re: [NMusers] population size and confidence power
Date: Mon, April 4, 2005 3:48 pm


NONMEM (note spelling) is not designed to directly compute power. However, it is
possible to use NONMEM (via simulation) to estimate the power of a design to test a
particular hypothesis.

IMHO any 'a priori' power prediction requires the user to specify:

1. The model parameters (CL, V, Emax, EC50, etc) and the effect size of interest
e.g. 30% difference in CL in a sub-population or Emax with some particular value.
2. The random effect size e.g. 50% apparent CV in CL, (and V etc) plus 10% residual
error.
3. The hypothesis testing procedure e.g. likelihood ratio test
4. A design e.g. 20 subjects with samples taken at 6 specified times
5. A model e.g. one compartment disposition with bolus input and immediate drug
effect described by an Emax model

Once you have thought about the problem and you can specify all these features you
are in a position to explore the power of the design by varying the number of
subjects in the design to see how power varies. You can use NONMEM to simulate a
large number of studies with a particular design and then test the hypothesis for
each simulated study. If 80 out of 100 such studies fail to reject the null
hypothesis then you could conclude that the power of the design is about 80%.

Your question is a bit ambiguous and perhaps you have something else in mind e.g.
you want to estimate a confidence interval for a parameter of the model. The most
robust method for doing this with NONMEM is to use a bootstrap approach (see
http://wfn.sourceforge.net/wfnbs.htm for some background on how this might be done).


Or perhaps you are interested in deciding which model is most suitable for making
predictions of response. The posterior predictive check and similar procedures that
use the model to simulate predicted values may be helpful (Yano et al 2001).

Nick

Yano Y, Beal SL, Sheiner LB. Evaluating pharmacokinetic/pharmacodynamic models using
the posterior predictive check. J Pharmacokinet Pharmacodyn 2001;28(2):171-92

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From:  "Nick Holford" n.holford@auckland.ac.nz
Subject: Re: [NMusers] population size and confidence power 
Date:  Mon, April 4, 2005 4:08 pm 

Oops...

Nick Holford wrote:

"If 80 out of 100 such studies fail to reject the null hypothesis then you could
conclude that the power of the design is about 80%."

This should have read:

"If 80 out of 100 such studies reject the null hypothesis then you could conclude
that the power of the design is about 80%.

Nick

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com
Subject: RE: [NMusers] population size and confidence power 
Date:  Mon, April 4, 2005 5:04 pm 

Lin Lin,

To add to Nick's comments regarding the various quantities that need to be
specified, for the hypothesis testing procedure (Nick's item 3 below) we
must also specify the type I error rate (alpha).  To this end, it is good
practice to perform simulations under the null hypothesis of no effect and
show that we only reject the null hypothesis alpha percent ( e.g., 5% if
alpha=0.05) of the time.  This is important as different estimation methods
may perform differently regarding maintaining the type I error rate (see
papers by Wahlby et al in JPP 2001;28:231-252 and JPP 2002;29:251-269).
Inflated type I errors are likely to result in inflated estimates of power
when using the test assuming that the type I error rate is maintained.

Ken
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