RE: [NMusers] Using sparse data to develop Population PK model for pediatrics

[Jacob Brogren]

Dear Daping,

In order to provide more than just general comments it would be useful to get 
some more information.


-  What is the purpose of developing the PopPK model?

-  What is the medical condition/disease?

-  What is the relation between plasma concentration and clinical 
effect/safety?

-  What age groups are included in your data set?

You have a limited number of patients in your data set, which is often the case 
with pediatric studies. There are different opinions about this, but I think 
you are doing the right thing to compare your estimates with literature values 
as a sanity check. Maybe you should consider including previous data or use 
parameters found in the literature as priors.

As you probably know, the dependence of PK parameters on body size and organ 
maturation is frequently incorporated in pediatric PopPK models. You can find 
more information in the scientific literature (Anderson and Holford, 2013) 
about how to implement this.

You assumed that all concentrations in one individual was resulting from the 
same dose. Further, you assumed no drug accumulation (three times daily dosing 
seem to be in line with that). These assumptions can in theory be tested by 
using alternative models and comparing how well the different models fit your 
data. But again, your data is limited and some models may not run.

Please feel free to tell us more about your problem.

Best Regards

Jacob Brogren

Ref.
Anderson, Brian J., and Nick HG Holford. "Understanding dosing: children are 
small adults, neonates are immature children." Archives of disease in childhood 
98.9 (2013): 737-744.


Jacob Brogren, MSc
Senior Consultant
[Description: QPharmetra_noTag_FA little.png]
+46 72-350 88 69 (M)
jacob.brog...@qpharmetra.com | 
http://qPharmetra.com

This e-mail communication is confidential and is intended only for the 
individual(s) or entity named above and others who have been specifically 
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From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of DAPING ZHANG
Sent: den 3 juni 2015 03:29
To: nmusers@globomaxnm.com
Subject: [NMusers] Using sparse data to develop Population PK model for 
pediatrics

Dear all,

I would like to develop a population PK model for a drug used in pediatrics. We 
got drug concentrations from 15 patients. The drug was given 3 times a day. 
Only one plasma sample were drawn every week for 4 weeks. They record the exact 
sampling time after drug was given. So for each patient, we had 4 
concentrations from 4 weeks.

I assumed all the 4 samples were from one dose and developed a Pop PK model. 
This assumption did not consider disease progress and drug accumulation. The 
result was still comparable with literature. I will be very appreciated your 
comments and suggestions for this model.

Regards

--
Daping Zhang
Ph.D. Candidate
University of Houston

[NMusers] Fwd: Should we generate VPCs with or without uncertainty?

[Matts Kågedal]

Hi all,

Creation of VPCs is a way to assess if simulated data generated by the
model is compatible with observed data.
VPCs are usually based on parameter point estimates of the model. Sometimes
parameter uncertainty is also accounted for in the generation of VPCs
(PPCs) where each simulated replicate of the data set is based on a new set
of parameter values representing the uncertainty of the estimates (e.g.
based on a bootstrap).

I wonder if inclusion of uncertainty in this way is really appropriate or
if it just makes the confidence intervals wider and hence easier to qualify
the model. Is it possible based on such an approach, that a model might
look good, when in fact no likely combination of parameter values (based on
parameter uncertainty) would generate data that are compatible with the
observations?

To illustrate my question:
I could generate 100 sets of parameters reflecting parameter uncertainty
(e.g. from a bootstrap). Based on each set of parameters I could then
generate a separate VPC (e.g. showing median, 5 and 95% percentile) to see
if any of the parameter sets are compatible with data. I would then have
100 VPCs, each based on a separate set of parameter values reflecting the
parameter correlations and uncertainty.

If the VPC based on point estimates looks bad, I would (generally) expect
that the other VPCs would be worse (they all have lower likelihood), so
that we have 101 VPCs that does not look good. Some might over predict and
some underpredict, some might describe parts of the relation better than
the VPC based on the point estimates.

By putting the VPCs together from all parameter vectors, the CI becomes
wider, and perhaps now includes the observed data. So based on a set of 100
parameter vectors which individually are not compatible with the observed
data I have now generated a VPC (PPC) where the confidence interval
actually includes the observed metric (e.g median). It seems to me that
based on such an approach it is possible that a model might look good, when
in fact no likely individual set of parameter values would generate data
that are compatible with the observations.

Simulation based on parameter uncertainty is useful when we want to make
inference, but I am unsure of its use for model qualification. In any case
it is confusing that we some times simulate based on point estimates and
sometimes based on parameter uncertainty without any particular rationale
as far as I understand.

Would be interested if someone could shed some light on the inclusion of
uncertainty in simulations for model qualification (VPCs).

Best regards,
Matts Kagedal

Pharmacometrician, Genentech

Re: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

[Devin Pastoor]

Matts,

The way I see the CI's around the point estimates provided in the VPC can
help provide a useful indication of model robustness, especially in regards
to the impact of random effects components, in that portion of your model.
Especially for heterogeneous data (or even all rich data for that matter)
there are a number of binning strategies that can be used, which can impact
the aforementioned intervals.

At the end of the day, we must use our judgement for how the model is being
used to support decisions, and whether information regarding uncertainty
can provide additional support towards the overall evaluation of the key
questions you are trying to address. Eg, if you are dealing with a narrow
therapeutic index drug the value of having a 'feel' for the robustness of
the ability of your model to describe the tails may be valuable
information, even as a qualitative indication of model robustness. On the
other hand, if you are trying to make a decision regarding dose adjustment
between different populations and are looking to normalize large
differences, as well as are constrained to certain oral dosage options,
uncertainty in the point estimates will likely provide very little support
to an argument one way or the other.

Finally, in my opinion, inclusion/exclusion also relies on what the plot is
trying to communicate. Are you trying to personally evaluate model
adequacy, sure, but if using to convey to non- modelers/quantitative people
that your model describes the data - include a visualization of uncertainty
at your own peril :-)

So, for better or worse, I would say - it depends, though I would be highly
concerned if major decisions rode on inclusion/exclusion of parameter
uncertainty, in most cases.


Devin Pastoor
Center for Translational Medicine
University of Maryland, Baltimore



On Mon, Jun 8, 2015 at 11:57 AM Matts Kågedal 
wrote:

> Hi all,
>
> Creation of VPCs is a way to assess if simulated data generated by the
> model is compatible with observed data.
> VPCs are usually based on parameter point estimates of the model.
> Sometimes parameter uncertainty is also accounted for in the generation of
> VPCs (PPCs) where each simulated replicate of the data set is based on a
> new set of parameter values representing the uncertainty of the estimates
> (e.g. based on a bootstrap).
>
> I wonder if inclusion of uncertainty in this way is really appropriate or
> if it just makes the confidence intervals wider and hence easier to qualify
> the model. Is it possible based on such an approach, that a model might
> look good, when in fact no likely combination of parameter values (based on
> parameter uncertainty) would generate data that are compatible with the
> observations?
>
> To illustrate my question:
> I could generate 100 sets of parameters reflecting parameter uncertainty
> (e.g. from a bootstrap). Based on each set of parameters I could then
> generate a separate VPC (e.g. showing median, 5 and 95% percentile) to see
> if any of the parameter sets are compatible with data. I would then have
> 100 VPCs, each based on a separate set of parameter values reflecting the
> parameter correlations and uncertainty.
>
> If the VPC based on point estimates looks bad, I would (generally) expect
> that the other VPCs would be worse (they all have lower likelihood), so
> that we have 101 VPCs that does not look good. Some might over predict and
> some underpredict, some might describe parts of the relation better than
> the VPC based on the point estimates.
>
> By putting the VPCs together from all parameter vectors, the CI becomes
> wider, and perhaps now includes the observed data. So based on a set of 100
> parameter vectors which individually are not compatible with the observed
> data I have now generated a VPC (PPC) where the confidence interval
> actually includes the observed metric (e.g median). It seems to me that
> based on such an approach it is possible that a model might look good, when
> in fact no likely individual set of parameter values would generate data
> that are compatible with the observations.
>
> Simulation based on parameter uncertainty is useful when we want to make
> inference, but I am unsure of its use for model qualification. In any case
> it is confusing that we some times simulate based on point estimates and
> sometimes based on parameter uncertainty without any particular rationale
> as far as I understand.
>
> Would be interested if someone could shed some light on the inclusion of
> uncertainty in simulations for model qualification (VPCs).
>
> Best regards,
> Matts Kagedal
>
> Pharmacometrician, Genentech
>
>
>

RE: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

[Stefano Zamuner]

Hi Devin and Matts,

Of interest, we had similar internal discussion within our department about 
this topic quite recently.

I would agree with Devin that it is preferable to include parameters 
uncertainty in a VPC, especially if they are used for relevant decision making. 
It may result on large CI around your 5th, median and 95th percentiles, however 
it means that you likely have limited information to estimate some of the 
variability terms. Don’t forget that any “standard VPC” still provides some 
uncertainty around your percentiles based on random effects and sample size.

There are several ways to embed params uncertainty, I found quite useful to use 
the covariance-matrix (from NM) to embed it in a simulation script – it is 
quite straightforward to do that in R with some coding effort (I think Pirana 
has R code for that as well), but I’m sure it can  be easily replicated with 
different tools available.

I guess it would be interesting to see how pharmacometricians would derive the 
parameters uncertainty: i.e, covariance matrix vs bootstrap or other means. I 
recently saw an elegant and efficient solution of bootstrap VPC done from a 
colleague of mine.

Cheers
Stefano

Stefano Zamuner PhD
Senior Director Clinical Pharmacology

GSK

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Devin Pastoor
Sent: 08 June 2015 17:30
To: Matts Kågedal; nmusers@globomaxnm.com
Subject: Re: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

Matts,

The way I see the CI's around the point estimates provided in the VPC can help 
provide a useful indication of model robustness, especially in regards to the 
impact of random effects components, in that portion of your model. Especially 
for heterogeneous data (or even all rich data for that matter) there are a 
number of binning strategies that can be used, which can impact the 
aforementioned intervals.

At the end of the day, we must use our judgement for how the model is being 
used to support decisions, and whether information regarding uncertainty can 
provide additional support towards the overall evaluation of the key questions 
you are trying to address. Eg, if you are dealing with a narrow therapeutic 
index drug the value of having a 'feel' for the robustness of the ability of 
your model to describe the tails may be valuable information, even as a 
qualitative indication of model robustness. On the other hand, if you are 
trying to make a decision regarding dose adjustment between different 
populations and are looking to normalize large differences, as well as are 
constrained to certain oral dosage options, uncertainty in the point estimates 
will likely provide very little support to an argument one way or the other.

Finally, in my opinion, inclusion/exclusion also relies on what the plot is 
trying to communicate. Are you trying to personally evaluate model adequacy, 
sure, but if using to convey to non- modelers/quantitative people that your 
model describes the data - include a visualization of uncertainty at your own 
peril :-)

So, for better or worse, I would say - it depends, though I would be highly 
concerned if major decisions rode on inclusion/exclusion of parameter 
uncertainty, in most cases.


Devin Pastoor
Center for Translational Medicine
University of Maryland, Baltimore



On Mon, Jun 8, 2015 at 11:57 AM Matts Kågedal 
mailto:mattskage...@gmail.com>> wrote:
Hi all,

Creation of VPCs is a way to assess if simulated data generated by the model is 
compatible with observed data.
VPCs are usually based on parameter point estimates of the model. Sometimes 
parameter uncertainty is also accounted for in the generation of VPCs (PPCs) 
where each simulated replicate of the data set is based on a new set of 
parameter values representing the uncertainty of the estimates (e.g. based on a 
bootstrap).

I wonder if inclusion of uncertainty in this way is really appropriate or if it 
just makes the confidence intervals wider and hence easier to qualify the 
model. Is it possible based on such an approach, that a model might look good, 
when in fact no likely combination of parameter values (based on parameter 
uncertainty) would generate data that are compatible with the observations?

To illustrate my question:
I could generate 100 sets of parameters reflecting parameter uncertainty (e.g. 
from a bootstrap). Based on each set of parameters I could then generate a 
separate VPC (e.g. showing median, 5 and 95% percentile) to see if any of the 
parameter sets are compatible with data. I would then have 100 VPCs, each based 
on a separate set of parameter values reflecting the parameter correlations and 
uncertainty.

If the VPC based on point estimates looks bad, I would (generally) expect that 
the other VPCs would be worse (they all have lower likelihood), so that we have 
101 VPCs that does not look good. Some might over predict and some 
underpredict, some might describe parts of the rela

RE: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

[Mats Karlsson]

Dear Matts,

For assessing model adequacy, I would use the point estimates. If your best 
model is contradicted by the data by showing a poor VPC, there seems little 
meaning in trying to include uncertainty. There could be a role for VPCs with 
uncertainty though. If you plan to perform simulations with parameter 
uncertainty for deciding on trial design etc, I may perform a VPC with 
uncertainty and assure myself that the parameter uncertainty does not lead to 
unrealistic predictions (indicated by too wide confidence intervals of outer 
percentiles). [An alternative is to perform a VPC with every population 
parameter vector used in the clinical trial simulation and look for 
outrageously poor description of the original data, but that is a bit too much 
for most, including me. Better to rely on good methods for parameter 
uncertainty).

Best regards,
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/

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Devin Pastoor
Sent: Monday, June 08, 2015 6:30 PM
To: Matts Kågedal; nmusers@globomaxnm.com
Subject: Re: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

Matts,

The way I see the CI's around the point estimates provided in the VPC can help 
provide a useful indication of model robustness, especially in regards to the 
impact of random effects components, in that portion of your model. Especially 
for heterogeneous data (or even all rich data for that matter) there are a 
number of binning strategies that can be used, which can impact the 
aforementioned intervals.

At the end of the day, we must use our judgement for how the model is being 
used to support decisions, and whether information regarding uncertainty can 
provide additional support towards the overall evaluation of the key questions 
you are trying to address. Eg, if you are dealing with a narrow therapeutic 
index drug the value of having a 'feel' for the robustness of the ability of 
your model to describe the tails may be valuable information, even as a 
qualitative indication of model robustness. On the other hand, if you are 
trying to make a decision regarding dose adjustment between different 
populations and are looking to normalize large differences, as well as are 
constrained to certain oral dosage options, uncertainty in the point estimates 
will likely provide very little support to an argument one way or the other.

Finally, in my opinion, inclusion/exclusion also relies on what the plot is 
trying to communicate. Are you trying to personally evaluate model adequacy, 
sure, but if using to convey to non- modelers/quantitative people that your 
model describes the data - include a visualization of uncertainty at your own 
peril :-)

So, for better or worse, I would say - it depends, though I would be highly 
concerned if major decisions rode on inclusion/exclusion of parameter 
uncertainty, in most cases.


Devin Pastoor
Center for Translational Medicine
University of Maryland, Baltimore



On Mon, Jun 8, 2015 at 11:57 AM Matts Kågedal 
mailto:mattskage...@gmail.com>> wrote:
Hi all,

Creation of VPCs is a way to assess if simulated data generated by the model is 
compatible with observed data.
VPCs are usually based on parameter point estimates of the model. Sometimes 
parameter uncertainty is also accounted for in the generation of VPCs (PPCs) 
where each simulated replicate of the data set is based on a new set of 
parameter values representing the uncertainty of the estimates (e.g. based on a 
bootstrap).

I wonder if inclusion of uncertainty in this way is really appropriate or if it 
just makes the confidence intervals wider and hence easier to qualify the 
model. Is it possible based on such an approach, that a model might look good, 
when in fact no likely combination of parameter values (based on parameter 
uncertainty) would generate data that are compatible with the observations?

To illustrate my question:
I could generate 100 sets of parameters reflecting parameter uncertainty (e.g. 
from a bootstrap). Based on each set of parameters I could then generate a 
separate VPC (e.g. showing median, 5 and 95% percentile) to see if any of the 
parameter sets are compatible with data. I would then have 100 VPCs, each based 
on a separate set of parameter values reflecting the parameter correlations and 
uncertainty.

If the VPC based on point estimates looks bad, I would (generally) expect that 
the other VPCs would be worse (they all have lower likelihood), so that we have 
101 VPCs that does not look good. Some might over predict and some 
underpredict, some might describe parts of the relation better than the VPC 
based on the point estimates.

By puttin

RE: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

[Ken Kowalski]

Hi All,

 

I have done it both ways (with and without including parameter uncertainty).  

 

It is important to note that the resulting VPC intervals are degenerate when 
you don’t take into account parameter uncertainty.  That is, with infinite 
sample size these intervals will collapse to the predictions based on the point 
estimates (since you’ll essentially be averaging out the sampling variation 
(etas and epsilons) when you make a mean/median prediction across a very large 
number of subjects).  Thus, in situations where you have a very large sample 
size for the bins, the VPC intervals can be too narrow and it can be almost 
hopeless to demonstrate that the observed values will be contained within these 
narrow VPC intervals.  This is because one would still expect some 
discrepancies between the observed and predicted due to parameter uncertainty.

 

On the other hand, suppose that you have a relatively small dataset such that 
VPC intervals are considerably wider when taking into account parameter 
uncertainty. If the observed data (e.g., means, median, etc) are not contained 
within the degenerate VPC intervals, but are contained within the VPC intervals 
that take into account the parameter uncertainty, this may or may not mean you 
have a good predictive model.  It may simply mean you just don’t have enough 
data to “validate” your model via a VPC given the small sample size and that 
you need to collect more data before you can truly evaluate the predictive 
performance of your model.

 

Best,

 

Ken

 

Kenneth G. Kowalski

President & CEO

A2PG - Ann Arbor Pharmacometrics Group, Inc.

301 N. Main St., Suite 102

Ann Arbor, MI 48104

Work:  734-274-8255

Cell:  248-207-5082

Fax: 734-913-0230

ken.kowal...@a2pg.com

www.a2pg.com  

 

 

 

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Mats Karlsson
Sent: Monday, June 08, 2015 1:27 PM
To: Devin Pastoor; Matts Kågedal; nmusers@globomaxnm.com
Subject: RE: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

 

Dear Matts,

 

For assessing model adequacy, I would use the point estimates. If your best 
model is contradicted by the data by showing a poor VPC, there seems little 
meaning in trying to include uncertainty. There could be a role for VPCs with 
uncertainty though. If you plan to perform simulations with parameter 
uncertainty for deciding on trial design etc, I may perform a VPC with 
uncertainty and assure myself that the parameter uncertainty does not lead to 
unrealistic predictions (indicated by too wide confidence intervals of outer 
percentiles). [An alternative is to perform a VPC with every population 
parameter vector used in the clinical trial simulation and look for 
outrageously poor description of the original data, but that is a bit too much 
for most, including me. Better to rely on good methods for parameter 
uncertainty).

 

Best regards,

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/

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Devin Pastoor
Sent: Monday, June 08, 2015 6:30 PM
To: Matts Kågedal; nmusers@globomaxnm.com
Subject: Re: [NMusers] Fwd: Should we generate VPCs with or without uncertainty?

 

Matts,

The way I see the CI's around the point estimates provided in the VPC can help 
provide a useful indication of model robustness, especially in regards to the 
impact of random effects components, in that portion of your model. Especially 
for heterogeneous data (or even all rich data for that matter) there are a 
number of binning strategies that can be used, which can impact the 
aforementioned intervals.

 

At the end of the day, we must use our judgement for how the model is being 
used to support decisions, and whether information regarding uncertainty can 
provide additional support towards the overall evaluation of the key questions 
you are trying to address. Eg, if you are dealing with a narrow therapeutic 
index drug the value of having a 'feel' for the robustness of the ability of 
your model to describe the tails may be valuable information, even as a 
qualitative indication of model robustness. On the other hand, if you are 
trying to make a decision regarding dose adjustment between different 
populations and are looking to normalize large differences, as well as are 
constrained to certain oral dosage options, uncertainty in the point estimates 
will likely provide very little support to an argument one way or the other.

 

Finally, in my opinion, inclusion/exclusion also relies on what the plot is 
trying to communicate. Are you trying to personally evaluate model adequacy

Re: [NMusers] Using sparse data to develop Population PK model for pediatrics

[DAPING ZHANG]

Dear Jacob,

Thanks a lot for your comments. I am also very appreciated the reference
you sent to me.

Regarding to your questions, the purpose of this study was to explain the
PK variability of an immunosuppresant drug in pediatric population post
hematopoietic stem cell transplantation. The age ranges from 8 months to 12
years old.

The CL and V are comparable to literature adult values if the effect of
body size was accounted for a priori by allometric scaling of CL and V
in the construction of base model. But the RSE of the intra-individual
variability is large.

To test my assumptions, what models do you suggest to use?

Regards,
Daping


On Mon, Jun 8, 2015 at 3:25 AM, Jacob Brogren 
wrote:

>  Dear Daping,
>
>
>
> In order to provide more than just general comments it would be useful to
> get some more information.
>
>
>
> -  What is the purpose of developing the PopPK model?
>
> -  What is the medical condition/disease?
>
> -  What is the relation between plasma concentration and clinical
> effect/safety?
>
> -  What age groups are included in your data set?
>
>
>
> You have a limited number of patients in your data set, which is often the
> case with pediatric studies. There are different opinions about this, but I
> think you are doing the right thing to compare your estimates with
> literature values as a sanity check. Maybe you should consider including
> previous data or use parameters found in the literature as priors.
>
>
>
> As you probably know, the dependence of PK parameters on body size and
> organ maturation is frequently incorporated in pediatric PopPK models. You
> can find more information in the scientific literature (Anderson and
> Holford, 2013) about how to implement this.
>
>
>
> You assumed that all concentrations in one individual was resulting from
> the same dose. Further, you assumed no drug accumulation (three times daily
> dosing seem to be in line with that). These assumptions can in theory be
> tested by using alternative models and comparing how well the different
> models fit your data. But again, your data is limited and some models may
> not run.
>
>
>
> Please feel free to tell us more about your problem.
>
>
>
> Best Regards
>
>
>
> Jacob Brogren
>
>
>
> Ref.
>
> Anderson, Brian J., and Nick HG Holford. "Understanding dosing: children
> are small adults, neonates are immature children." Archives of disease in
> childhood 98.9 (2013): 737-744.
>
>
>
>
>
> *Jacob Brogren, MSc*
>
> Senior Consultant
>
> [image: Description: QPharmetra_noTag_FA little.png]
>
> +46 72-350 88 69 (M)
>
> jacob.brog...@qpharmetra.com | http://qPharmetra.com
> 
>
>
>
> This e-mail communication is confidential and is intended only for the
> individual(s) or entity named above and others who have been specifically
> authorized to receive it. If you are not the intended recipient, please do
> not read, copy, use or disclose the contents of this communication to
> others. Please notify the sender that you have received this e-mail in
> error by replying to the e-mail or by telephoning +46723508869. Please
> then delete the e-mail and any copies of it. Thank you.
>
>
>
>
>
>
>
> *From:* owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com]
> *On Behalf Of *DAPING ZHANG
> *Sent:* den 3 juni 2015 03:29
> *To:* nmusers@globomaxnm.com
> *Subject:* [NMusers] Using sparse data to develop Population PK model for
> pediatrics
>
>
>
> Dear all,
>
>
>
> I would like to develop a population PK model for a drug used in
> pediatrics. We got drug concentrations from 15 patients. The drug was given
> 3 times a day. Only one plasma sample were drawn every week for 4 weeks.
> They record the exact sampling time after drug was given. So for each
> patient, we had 4 concentrations from 4 weeks.
>
>
>
> I assumed all the 4 samples were from one dose and developed a Pop PK
> model. This assumption did not consider disease progress and drug
> accumulation. The result was still comparable with literature. I will be
> very appreciated your comments and suggestions for this model.
>
>
>
> Regards
>
>
>
> --
>
> Daping Zhang
>
> Ph.D. Candidate
>
> University of Houston
>
>
>



-- 
Daping Zhang
Ph.D. Candidate
Department of Pharmacological & Pharmaceutical Sciences (PPS)
University of Houston
Cell: 713-855-9668
E-mail Address: dzhan...@uh.edu