Recently in an interaction with the FDA they asked us to power a
pharmacokinetic study to a given precision in a parameter estimate based
on a pop pk model in a population we have no experience with. In other
words, they wanted us to power a study to ensure that the standard error
of the population mean clearance was less than 30% CV. Does anyone know
how to do this a priori? Does this seem to be something new?
Thanks,
pete bonate
Peter L. Bonate, PhD, FCP
Genzyme Corporation
Senior Director, Pharmacokinetics
4545 Horizon Hill Blvd
San Antonio, TX 78229 USA
[EMAIL PROTECTED]
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
sample size issue
Hi Pete -
You can do this through trial simulation/estimation or through information theoretic approaches (e.g. POPT, PFIM, PopED, etc.). Both methods will give you an estimate of expected parameter estimation precision under a given design. Simulation/estimation approaches will also provide an estimate of parameter estimation bias.
The challenge is to accurately select the parameters (and model) a priori. If you choose a model with fixed point estimates of THETA, OMEGA and SIGMA, then your conclusions are only valid if the model and parameters are an accurate representation of the truth. Since you are extrapolating to a new population you could run into trouble in this regard; there may considerable uncertainty in the extrapolation of your current parameters to the new population.
A more useful approach would be to conduct the simulations or information theory analyses over a joint probability distribution representing uncertainty in the model parameters (and maybe the model itself). For information theoretic methods, PopED allows you to do something like this (I don't mean to leave out other approaches that may also accommodate this). For simulation-estimation methods, you can implement this level of parameter uncertainty at the inter-trial level using simulation tools like Trial Simulator, or the R functions we've developed for simulation from uncertainty distributions in NONMEM (NMSUDS: http://metruminstitute.org/downloads/index.shtml ). The joint uncertainty distributions can be derived from Bayesian posterior distributions, bootstrap results or just an educated guess about plausible distributions encompassing the uncertainty in parameters due to the extrapolation to the new population.
For each trial replicate, you'll get an estimate of parameter precision (and bias), resulting in a probability distribution of trial outcomes. You can then examine the sensitivity of the outcome (e.g. %precision of typical CL) to the uncertainty in your simulation parameters (and even model) by plotting trial outcome vs. the trial- specific draws of a given parameter from its uncertainty distribution. Do this for all parameters in your model. If there are regions of these sensitivity curves that do not achieve the desired target response, you could 1) modify the trial design to make it robust enough to achieve the target across the distribution of parameter uncertainty or 2) gain more information about the model parameters (e.g. a pilot study in the new population), reducing the range of uncertainty, and re-run the simulation exercise to determine if the proposed design is sufficient given the improved estimates of model parameters. You'll have to balance practical considerations in either case.
In my experience, this sort of request is not new, especially in populations such as pediatrics. Some recent poster presentations on this topic are listed here and are available for download at http:// metrumrg.com/publications.htm:
1. Gastonguay MR, Gibiansky L. Acknowledging and Incorporating Uncertainty in Model-Based Inferences. ECPAG Conference (2006) Workshop Poster Session, Abstract. 2. Gibiansky L and MR Gastonguay. R/NONMEM Toolbox for Simulation from Posterior Parameter (Uncertainty) Distributions. L. Gibiansky and M.R. Gastonguay. PAGE ( 2006) Abstract 958. 3. Mondick JT, Gibiansky L, Gastonguay MR, Veal GJ, Barrett JS. Acknowledging parameter uncertainty in the simulation-based design of an actinomycin-D pharmacokinetic study in pediatric patients with Wilms’ Tumor or rhabdomyosarcoma. PAGE 15 (2006) Abstract 938. 4. Gastonguay MR, Gibiansky L. Acknowledging Parameter Uncertainty by Simulating from Posterior Distributions with NONMEM and R. MUFPADA Annual Meeting (2006) Abstract.
2005
5. Gastonguay MR, El-Tahtawy A. Modeling and Simulation Guided Design of a Pediatric Population Pharmacokinetic Trial for Hydromorphone. The AAPS Journal. Vol. 7, No. S2, Abstract W5318, 2005.
Hope this helps.
Marc
Marc R. Gastonguay, Ph.D.
President & CEO, Metrum Research Group LLC [www.metrumrg.com]
Scientific Director, Metrum Institute [www.metruminstitute.org]
Email: [EMAIL PROTECTED] Direct: +1.860.670.0744 Main: +1.860.735.7043
Quoted reply history
On Aug 29, 2007, at 11:28 AM, Bonate, Peter wrote:
> Recently in an interaction with the FDA they asked us to power a pharmacokinetic study to a given precision in a parameter estimate based on a pop pk model in a population we have no experience with. In other words, they wanted us to power a study to ensure that the standard error of the population mean clearance was less than 30% CV. Does anyone know how to do this a priori? Does this seem to be something new?
>
> Thanks,
>
> pete bonate
>
> Peter L. Bonate, PhD, FCP
> Genzyme Corporation
> Senior Director, Pharmacokinetics
> 4545 Horizon Hill Blvd
> San Antonio, TX 78229 USA
> [EMAIL PROTECTED]
> phone: 210-949-8662
> fax: 210-949-8219
> crackberry: 210-315-2713
Dr. Bonate,
Now that you have one of the renouned experts respond in some details< I am
nots ure how beneficial my reponse would be. Here are my "two-cents" though.
There is some published work that maybe helpful in answering your question.
Kowalski *et al.* did some work to assess power and sample size
requirements for a population pharmacokinetic (PK) substudy of a phase III
clinical trial. The simulations were based on a population PK model
developed from phase I healthy volunteer data. Also, there is the chapter 12
in the Pharmacometrics book by Ette that actually addresses some of the
issue pertaining to the power and design of the population PK studies based
on anyeven remotely related information. I am not advocating any specific
method or software since I haven't had vast experience with many of them.
I am including citation to both references below. The references listed by
Dr. Gastonguay are excellent!
*1-* Design evaluation for a population pharmacokinetic study using
clinical trial simulations: a case study, Kenneth G. Kowalski *, Matthew M.
Hutmacher. Vol 20, issue 1 page 75-91. ( *I have a PDF if you need it*)
*2- *Designing Population Pharmacokinetic Studies for Efficient Parameter
Estimation Chapter Authors: Ene I. Ette, Amit Roy.
Let me know if this helps answer your question. If not, maybe you can give
me some less confidential information and I will be happy to give it more
thought.
*P.S.* Your book has been a great aid for modelers and students learning how
to do things right.
Regards,
*
**Murad melhem, PhD
Cognigen Corporation
Buffalo, NY
*
Quoted reply history
On 8/29/07, Gastonguay, Marc <[EMAIL PROTECTED]> wrote:
>
> Hi Pete - You can do this through trial simulation/estimation or through
> information theoretic approaches (e.g. POPT, PFIM, PopED, etc.). Both
> methods will give you an estimate of expected parameter estimation precision
> under a given design. Simulation/estimation approaches will also provide an
> estimate of parameter estimation bias.
>
> The challenge is to accurately select the parameters (and model) a priori.
> If you choose a model with fixed point estimates of THETA, OMEGA and SIGMA,
> then your conclusions are only valid if the model and parameters are an
> accurate representation of the truth. Since you are extrapolating to a new
> population you could run into trouble in this regard; there may considerable
> uncertainty in the extrapolation of your current parameters to the new
> population.
>
> A more useful approach would be to conduct the simulations or information
> theory analyses over a joint probability distribution representing
> uncertainty in the model parameters (and maybe the model itself).
> For information theoretic methods, PopED allows you to do something like
> this (I don't mean to leave out other approaches that may also accommodate
> this). For simulation-estimation methods, you can implement this level of
> parameter uncertainty at the inter-trial level using simulation tools like
> Trial Simulator, or the R functions we've developed for simulation from
> uncertainty distributions in NONMEM (NMSUDS:
> http://metruminstitute.org/downloads/index.shtml). The joint uncertainty
> distributions can be derived from Bayesian posterior distributions,
> bootstrap results or just an educated guess about plausible distributions
> encompassing the uncertainty in parameters due to the extrapolation to the
> new population.
>
> For each trial replicate, you'll get an estimate of parameter precision
> (and bias), resulting in a probability distribution of trial outcomes. You
> can then examine the sensitivity of the outcome (e.g. %precision of
> typical CL) to the uncertainty in your simulation parameters (and even
> model) by plotting trial outcome vs. the trial-specific draws of a given
> parameter from its uncertainty distribution. Do this for all parameters in
> your model. If there are regions of these sensitivity curves that do not
> achieve the desired target response, you could 1) modify the trial design to
> make it robust enough to achieve the target across the distribution of
> parameter uncertainty or 2) gain more information about the model parameters
> (e.g. a pilot study in the new population), reducing the range of
> uncertainty, and re-run the simulation exercise to determine if the proposed
> design is sufficient given the improved estimates of model parameters.
> You'll have to balance practical considerations in either case.
>
> In my experience, this sort of request is not new, especially in
> populations such as pediatrics. Some recent poster presentations on this
> topic are listed here and are available for download at
> http://metrumrg.com/publications.htm:
>
> 1. Gastonguay MR, Gibiansky L. Acknowledging and Incorporating Uncertainty
> in Model-Based Inferences. ECPAG Conference (2006) Workshop Poster Session,
> Abstract.
> 2. Gibiansky L and MR Gastonguay. R/NONMEM Toolbox for Simulation from
> Posterior Parameter (Uncertainty) Distributions. L. Gibiansky and M.R.
> Gastonguay. PAGE ( 2006) Abstract 958.
> 3. Mondick JT, Gibiansky L, Gastonguay MR, Veal GJ, Barrett JS.
> Acknowledging parameter uncertainty in the simulation-based design of an
> actinomycin-D pharmacokinetic study in pediatric patients with Wilms' Tumor
> or rhabdomyosarcoma. PAGE 15 (2006) Abstract 938.
> 4. Gastonguay MR, Gibiansky L. Acknowledging Parameter Uncertainty by
> Simulating from Posterior Distributions with NONMEM and R. MUFPADA Annual
> Meeting (2006) Abstract.
> 2005
> 5. Gastonguay MR, El-Tahtawy A. Modeling and Simulation Guided Design of a
> Pediatric Population Pharmacokinetic Trial for Hydromorphone. The AAPS
> Journal. Vol. 7, No. S2, Abstract W5318, 2005.
>
> Hope this helps.
> Marc
>
>
>
> Marc R. Gastonguay, Ph.D.
> President & CEO, Metrum Research Group LLC [www.metrumrg.com]
> Scientific Director, Metrum Institute [www.metruminstitute.org]
> Email: [EMAIL PROTECTED] Direct: +1.860.670.0744 Main: +1.860.735.7043
>
>
> On Aug 29, 2007, at 11:28 AM, Bonate, Peter wrote:
>
> Recently in an interaction with the FDA they asked us to power a
> pharmacokinetic
> study to a given precision in a parameter estimate based on a pop pk model
> in a population we have no experience with. In other words, they wanted us
> to power a study to ensure that the standard error of the population mean
> clearance
> was less than 30% CV. Does anyone know how to do this a priori? Does
> this seem to be something new?
>
> Thanks,
>
> pete bonate
>
> Peter L. Bonate, PhD, FCP
> Genzyme Corporation
> Senior Director, Pharmacokinetics
> 4545 Horizon Hill Blvd
> San Antonio, TX 78229 USA
> [EMAIL PROTECTED]
> phone: 210-949-8662
> fax: 210-949-8219
> crackberry: 210-315-2713
>
>
>
>
Pete: CV (when not large) for a PK variable on the actual scale is
approximately the s.d. of the Log (PK), where Log (PK) can be assumed to
be normal. So one way to think it may be power the study in terms of
the sample standard deviation on the log-scale, referring a chi-square
test. Theoretically it might be doable. However, it is rare to see a
research hypothesis is framed in terms of s.d. and I have not seen a
study powered in terms of s.d..
- Bo
_____________________________________
BO JIN, Ph.D.
Clinical Pharmacology Statistics
Merck Research Labs
UG1D-44
PO Box 1000
351 North Sumneytown Pike
North Wales, PA 19454
Phone: 267-305-7876
Quoted reply history
________________________________
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Bonate, Peter
Sent: Wednesday, August 29, 2007 11:29 AM
To: [email protected]
Subject: [NMusers] sample size issue
Recently in an interaction with the FDA they asked us to power a
pharmacokinetic study to a given precision in a parameter estimate based
on a pop pk model in a population we have no experience with. In other
words, they wanted us to power a study to ensure that the standard error
of the population mean clearance was less than 30% CV. Does anyone know
how to do this a priori? Does this seem to be something new?
-
Thanks,
pete bonate
Peter L. Bonate, PhD, FCP
Genzyme Corporation
Senior Director, Pharmacokinetics
4545 Horizon Hill Blvd
San Antonio, TX 78229 USA
[EMAIL PROTECTED]
phone: 210-949-8662
fax: 210-949-8219
crackberry: 210-315-2713
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