Has anyone every tried to use a mixture model with logistic regression? I have
data on a AE in several hundred patients, measured multiple times (10-20 times
per patient). Examining the data it is clear that, independent of drug
concentration, there is very wide distribution of this AE, 68% of the patients
never have the AE, 25% have it about 20% of the time and the rest have it
pretty much continuously, regardless of drug concentration. (in ordinary
logistic regression, just glm in R, there is also a nice concentration effect
on the AE in addition). Running the usual logistic model, not surprisingly, I
get a really big ETA on the intercept, with 68% of the people having ETA small
negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
predictive of the post hoc ETA. I thought I could use a mixture model, with 3
modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd
distribution, still with the really large OMEGA for the intercept. Even when I
FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd
and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd
distribution (and OMEGA), and it still gave me a very small difference in the
intercept for the 2nd and 3rd populations.
Is there an issue with using mixture models with logistic regression? I'm just
using FOCE, Laplacian, without interaction, and LIKE.
Any ideas?
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. (tm)
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<[email protected]>
http://www.nuventra.com
Mixture model with logistic regression
Use of mixture model may not be suitable here, if the underlying distribution
of eta's for the different subgroups is not normally distributed. Based on the
description, it looks like you have 3 degenerate eta distributions(ETA ~0 for
no AE; ETA ~1 for 25% AE and ETA ~10 for 7% with all AE), which violates the
normality assumption.
Upon quick search, I came across this article, where they have described almost
a similar situation as yours. They have used a two part mixture distribution
to take care of the large proportions of the subjects with no AE. Hope it is
helpful.
http://www.ncbi.nlm.nih.gov/pubmed/14977163
Kowalski, Kenneth G., Lynn McFadyen, Matthew M. Hutmacher, Bill
Frame, and Raymond Miller. "A Two-Part Mixture Model for Longitudinal Adverse
Event Severity Data." Journal of Pharmacokinetics and Pharmacodynamics 30, no.
5 (October 2003): 315-36.
Thanks.
Mathangi Gopalakrishnan, MS, PhD
Research Assistant Professor
Center for Translational Medicine (CTM)
School of Pharmacy, UMB
Ph: 410-706-7842
http://www.ctm.umaryland.edu/
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Mark Sale
Sent: Friday, February 19, 2016 5:30 PM
To: [email protected]
Subject: [NMusers] Mixture model with logistic regression
Has anyone every tried to use a mixture model with logistic regression? I have
data on a AE in several hundred patients, measured multiple times (10-20 times
per patient). Examining the data it is clear that, independent of drug
concentration, there is very wide distribution of this AE, 68% of the patients
never have the AE, 25% have it about 20% of the time and the rest have it
pretty much continuously, regardless of drug concentration. (in ordinary
logistic regression, just glm in R, there is also a nice concentration effect
on the AE in addition). Running the usual logistic model, not surprisingly, I
get a really big ETA on the intercept, with 68% of the people having ETA small
negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
predictive of the post hoc ETA. I thought I could use a mixture model, with 3
modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd
distribution, still with the really large OMEGA for the intercept. Even when I
FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd
and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd
distribution (and OMEGA), and it still gave me a very small difference in the
intercept for the 2nd and 3rd populations.
Is there an issue with using mixture models with logistic regression? I'm just
using FOCE, Laplacian, without interaction, and LIKE.
Any ideas?
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. (tm)
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<[email protected]>
http://www.nuventra.com
This sounds like a good case for a nonparametric method - if you use the one
in NONMEM, you might try
expanding Omega to counter shrinkage. The versions in USC*PACK and PHOENIX
NLME optimize over
both support point positions and probabilities, so this is not necessary with
those methods.
Quoted reply history
________________________________
From: [email protected] [[email protected]] on behalf of
Mark Sale [[email protected]]
Sent: Friday, February 19, 2016 4:30 PM
To: [email protected]
Subject: [NMusers] Mixture model with logistic regression
Has anyone every tried to use a mixture model with logistic regression? I have
data on a AE in several hundred patients, measured multiple times (10-20 times
per patient). Examining the data it is clear that, independent of drug
concentration, there is very wide distribution of this AE, 68% of the patients
never have the AE, 25% have it about 20% of the time and the rest have it
pretty much continuously, regardless of drug concentration. (in ordinary
logistic regression, just glm in R, there is also a nice concentration effect
on the AE in addition). Running the usual logistic model, not surprisingly, I
get a really big ETA on the intercept, with 68% of the people having ETA small
negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
predictive of the post hoc ETA. I thought I could use a mixture model, with 3
modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd
distribution, still with the really large OMEGA for the intercept. Even when I
FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd
and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd
distribution (and OMEGA), and it still gave me a very small difference in the
intercept for the 2nd and 3rd populations.
Is there an issue with using mixture models with logistic regression? I'm just
using FOCE, Laplacian, without interaction, and LIKE.
Any ideas?
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<UrlBlockedError.aspx>
http://www.nuventra.com
Bob,
That certainly makes sense, but that options seems to not be available in
NONMEM, using LIKE seems to require using FOCE LAPLACE
LIKELIHOOD
This is designed mainly, but not exclusively, for use with non-
continuous observed responses ("odd-type data"). Indicates that
Y (with NM-TRAN abbreviated code) or F (with a user-supplied PRED
or ERROR code) will be set to a (conditional) likelihood. Upon
simulation it will be ignored, and the DV data item will be set
directly to the simulated value in abbreviated or user code.
Also etas, if any, are understood to be population etas. Epsilon
variables and the $SIGMA record may not be used. The L2 data
item may not be used. The CONTR and CCONTR options of the $SUB-
ROUTINES record may not be used. NONMEM cannot obtain the ini-
tial estimate for omega. If the data are population, and MAXE-
VALS=0 is not coded, then METHOD=1 LAPLACE is required. Compare
with PREDICTION option.
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<[email protected]>
http://www.nuventra.com
Empower your Pipeline
CONFIDENTIALITY NOTICE The information in this transmittal (including
attachments, if any) may be privileged and confidential and is intended only
for the recipient(s) listed above. Any review, use, disclosure, distribution or
copying of this transmittal, in any form, is prohibited except by or on behalf
of the intended recipient(s). If you have received this transmittal in error,
please notify me immediately by reply email and destroy all copies of the
transmittal.
Quoted reply history
________________________________
From: Bob Leary <[email protected]>
Sent: Saturday, February 20, 2016 8:45 AM
To: Mark Sale; [email protected]
Subject: RE: Mixture model with logistic regression
This sounds like a good case for a nonparametric method - if you use the one
in NONMEM, you might try
expanding Omega to counter shrinkage. The versions in USC*PACK and PHOENIX
NLME optimize over
both support point positions and probabilities, so this is not necessary with
those methods.
________________________________
From: [email protected] [[email protected]] on behalf of
Mark Sale [[email protected]]
Sent: Friday, February 19, 2016 4:30 PM
To: [email protected]
Subject: [NMusers] Mixture model with logistic regression
Has anyone every tried to use a mixture model with logistic regression? I have
data on a AE in several hundred patients, measured multiple times (10-20 times
per patient). Examining the data it is clear that, independent of drug
concentration, there is very wide distribution of this AE, 68% of the patients
never have the AE, 25% have it about 20% of the time and the rest have it
pretty much continuously, regardless of drug concentration. (in ordinary
logistic regression, just glm in R, there is also a nice concentration effect
on the AE in addition). Running the usual logistic model, not surprisingly, I
get a really big ETA on the intercept, with 68% of the people having ETA small
negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
predictive of the post hoc ETA. I thought I could use a mixture model, with 3
modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd
distribution, still with the really large OMEGA for the intercept. Even when I
FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd
and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd
distribution (and OMEGA), and it still gave me a very small difference in the
intercept for the 2nd and 3rd populations.
Is there an issue with using mixture models with logistic regression? I'm just
using FOCE, Laplacian, without interaction, and LIKE.
Any ideas?
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<UrlBlockedError.aspx>
http://www.nuventra.com
Hi Mark,
The pattern you see in the posthocs could possibly be a shrinkage
phenomenon. I.e. patients with AE most of the time will have the same ETA,
while patients with no AE will have the same ETA and there will be a third
group in between. If shrinkage is causing this, you should not expect any
improvement with a mixture model. Before you reject your original model I
would therefore also evaluate it by simulation and re-estimation. I think
it is quite possible that you will retreive a similar pattern in the
posthocs even when you simulate based on a normal distribution.
Best,
Matts Kågedal
Pharmacometrics, Genentech.
Quoted reply history
On Fri, Feb 19, 2016 at 2:30 PM, Mark Sale <[email protected]> wrote:
> Has anyone every tried to use a mixture model with logistic regression? I
> have data on a AE in several hundred patients, measured multiple times
> (10-20 times per patient). Examining the data it is clear that,
> independent of drug concentration, there is very wide distribution of this
> AE, 68% of the patients never have the AE, 25% have it about 20% of the
> time and the rest have it pretty much continuously, regardless of
> drug concentration. (in ordinary logistic regression, just glm in R, there
> is also a nice concentration effect on the AE in addition). Running the
> usual logistic model, not surprisingly, I get a really big ETA on the
> intercept, with 68% of the people having ETA small negative, 25% ETA ~ 1
> and 7% ETA ~ 10. No covariates seem particularly predictive of the post hoc
> ETA. I thought I could use a mixture model, with 3 modes, but it refused
> to do that, giving me essentially 0% in the 2nd and 3rd distribution, still
> with the really large OMEGA for the intercept. Even when I FIX the OMEGA
> to a reasonable number, I still get essentially no one in the 2nd and 3rd
> distribution. I tried fixing the fraction in the 2nd and 3rd distribution
> (and OMEGA), and it still gave me a very small difference in the intercept
> for the 2nd and 3rd populations.
>
> Is there an issue with using mixture models with logistic regression? I'm
> just using FOCE, Laplacian, without interaction, and LIKE.
>
>
>
>
> Any ideas?
>
>
> Mark
>
>
>
> Mark Sale M.D.
>
> Vice President, Modeling and Simulation
>
> Nuventra, Inc. ™
>
> 2525 Meridian Parkway, Suite 280
>
> Research Triangle Park, NC 27713
>
> Office (919)-973-0383
>
> [email protected] http://[email protected]
>
> www.nuventra.com
>
>
>
>
Hi Mark,
Is it indeed a logistical model or is it an ordered categorical? I assume you refer to the latter. Not sure how you get your second category otherwise.
Anyway, to me it reads like you are trying to have the mixture model describe exactly what the omega is trying to describe. Perhaps you could drop the omega all together? (or fix to a small value)
I also like Bob's suggestion, I would go for it ($NPAR!).
Hope this helps,
Jeroen
http://pd-value.com
[email protected]
@PD_value
+31 6 23118438
-- More value out of your data!
Op 20-02-16 om 21:01 schreef Mark Sale:
> Matts,
>
> Thanks for your insights. But, the issue isn't the post hoc values. With the mixture model the OMEGA on the intercept is huge (680), and the entire population is in the low intercept value group (Intercept = -11). Then to accommodate the patients with frequent AEs, it assigns a (post hoc) ETA of +15, giving an individual value for intercept of 6 (and a probability of the AE of ~1, as it should. My question is whey does it refuse to simply put those 8% of the patients in a sub population with intercept = 6, ETA=0. rather than saying the expected value is -11, with ETA = +15. Even when I fix the fractions in the subpopulations for the observed values, and fix OMEGA to a small, reasonable value, and fix the intercept values for the 3 populations to reasonable values it will still do this. The only thing that has worked is to assign each subject to the apparent population in the data set.
>
> Mark
>
> Mark Sale M.D.
>
> Vice President, Modeling and Simulation
>
> Nuventra, Inc. ™
>
> 2525 Meridian Parkway, Suite 280
>
> Research Triangle Park, NC 27713
>
> Office (919)-973-0383
>
> [email protected] <[email protected]>
>
> www.nuventra.com http://www.nuventra.com
>
> */
> /*
>
> */Empower your Pipeline/*
>
> CONFIDENTIALITY NOTICE The information in this transmittal (including attachments, if any) may be privileged and confidential and is intended only for the recipient(s) listed above. Any review, use, disclosure, distribution or copying of this transmittal, in any form, is prohibited except by or on behalf of the intended recipient(s). If you have received this transmittal in error, please notify me immediately by reply email and destroy all copies of the transmittal.
>
> ------------------------------------------------------------------------
> *From:* Matts Kågedal <[email protected]>
> *Sent:* Saturday, February 20, 2016 2:44 PM
> *To:* Mark Sale
> *Cc:* [email protected]
> *Subject:* Re: [NMusers] Mixture model with logistic regression
> Hi Mark,
>
> The pattern you see in the posthocs could possibly be a shrinkage phenomenon. I.e. patients with AE most of the time will have the same ETA, while patients with no AE will have the same ETA and there will be a third group in between. If shrinkage is causing this, you should not expect any improvement with a mixture model. Before you reject your original model I would therefore also evaluate it by simulation and re-estimation. I think it is quite possible that you will retreive a similar pattern in the posthocs even when you simulate based on a normal distribution.
>
> Best,
> Matts Kågedal
> Pharmacometrics, Genentech.
>
Quoted reply history
> On Fri, Feb 19, 2016 at 2:30 PM, Mark Sale < [email protected] < mailto: [email protected] >> wrote:
>
> Has anyone every tried to use a mixture model with logistic
> regression? I have data on a AE in several hundred patients,
> measured multiple times (10-20 times per patient). Examining the
> data it is clear that, independent of drug concentration, there is
> very wide distribution of this AE, 68% of the patients never have
> the AE, 25% have it about 20% of the time and the rest have it
> pretty much continuously, regardless of drug concentration. (in
> ordinary logistic regression, just glm in R, there is also a nice
> concentration effect on the AE in addition). Running the usual
> logistic model, not surprisingly, I get a really big ETA on the
> intercept, with 68% of the people having ETA small negative, 25%
> ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
> predictive of the post hoc ETA. I thought I could use a mixture
> model, with 3 modes, but it refused to do that, giving me
> essentially 0% in the 2nd and 3rd distribution, still with the
> really large OMEGA for the intercept. Even when I FIX the OMEGA
> to a reasonable number, I still get essentially no one in the 2nd
> and 3rd distribution. I tried fixing the fraction in the 2nd and
> 3rd distribution (and OMEGA), and it still gave me a very small
> difference in the intercept for the 2nd and 3rd populations.
>
> Is there an issue with using mixture models with logistic
> regression? I'm just using FOCE, Laplacian, without interaction,
> and LIKE.
>
> Any ideas?
>
> Mark
>
> Mark Sale M.D.
>
> Vice President, Modeling and Simulation
>
> Nuventra, Inc. ™
>
> 2525 Meridian Parkway, Suite 280
>
> Research Triangle Park, NC 27713
>
> Office (919)-973-0383 <tel:%28919%29-973-0383>
>
> [email protected] http://[email protected]
>
> www.nuventra.com http://www.nuventra.com
Hi Mark,
My first suggestion is you can start from simpler mixture model (e.g. 2
distributions) and only focus on those have AEs. 68% patients without AE is
a big disturbance to intercept. Only negative infinity of intercept in
logistic model can give a probability=0. Secondly, you can try to use SAEM
method with mu reference. Based on my own experience, FOCE method is not as
powerful as SAEM in likelihood estimations. Good luck.
BW,
Yucheng Sheng
UCL School of Pharmacy
29-39 Brunswick Square
London WC1N 1AX
Email. [email protected]
Quoted reply history
On 19 February 2016 at 22:30, Mark Sale <[email protected]> wrote:
> Has anyone every tried to use a mixture model with logistic regression? I
> have data on a AE in several hundred patients, measured multiple times
> (10-20 times per patient). Examining the data it is clear that,
> independent of drug concentration, there is very wide distribution of this
> AE, 68% of the patients never have the AE, 25% have it about 20% of the
> time and the rest have it pretty much continuously, regardless of
> drug concentration. (in ordinary logistic regression, just glm in R, there
> is also a nice concentration effect on the AE in addition). Running the
> usual logistic model, not surprisingly, I get a really big ETA on the
> intercept, with 68% of the people having ETA small negative, 25% ETA ~ 1
> and 7% ETA ~ 10. No covariates seem particularly predictive of the post hoc
> ETA. I thought I could use a mixture model, with 3 modes, but it refused
> to do that, giving me essentially 0% in the 2nd and 3rd distribution, still
> with the really large OMEGA for the intercept. Even when I FIX the OMEGA
> to a reasonable number, I still get essentially no one in the 2nd and 3rd
> distribution. I tried fixing the fraction in the 2nd and 3rd distribution
> (and OMEGA), and it still gave me a very small difference in the intercept
> for the 2nd and 3rd populations.
>
> Is there an issue with using mixture models with logistic regression? I'm
> just using FOCE, Laplacian, without interaction, and LIKE.
>
>
>
>
> Any ideas?
>
>
> Mark
>
>
>
> Mark Sale M.D.
>
> Vice President, Modeling and Simulation
>
> Nuventra, Inc. ™
>
> 2525 Meridian Parkway, Suite 280
>
> Research Triangle Park, NC 27713
>
> Office (919)-973-0383
>
> [email protected] http://[email protected]
>
> www.nuventra.com
>
>
>
>
Kudos to Jeroen, who solved this for me, needed the NOINTER option on $EST,
then you can use SAEM, which gave a reasonable answer, unlike FOCE.
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<[email protected]>
http://www.nuventra.com
Empower your Pipeline
CONFIDENTIALITY NOTICE The information in this transmittal (including
attachments, if any) may be privileged and confidential and is intended only
for the recipient(s) listed above. Any review, use, disclosure, distribution or
copying of this transmittal, in any form, is prohibited except by or on behalf
of the intended recipient(s). If you have received this transmittal in error,
please notify me immediately by reply email and destroy all copies of the
transmittal.
Quoted reply history
________________________________
From: Jeroen Elassaiss-Schaap (PD-value B.V.) <[email protected]>
Sent: Saturday, February 20, 2016 4:35 PM
To: Mark Sale
Cc: [email protected]
Subject: Re: [NMusers] Mixture model with logistic regression
Hi Mark,
Is it indeed a logistical model or is it an ordered categorical? I assume you
refer to the latter. Not sure how you get your second category otherwise.
Anyway, to me it reads like you are trying to have the mixture model describe
exactly what the omega is trying to describe. Perhaps you could drop the omega
all together? (or fix to a small value)
I also like Bob's suggestion, I would go for it ($NPAR!).
Hope this helps,
Jeroen
http://pd-value.com
[email protected]<mailto:[email protected]>
@PD_value
+31 6 23118438
-- More value out of your data!
Op 20-02-16 om 21:01 schreef Mark Sale:
Matts,
Thanks for your insights. But, the issue isn't the post hoc values. With
the mixture model the OMEGA on the intercept is huge (680), and the entire
population is in the low intercept value group (Intercept = -11). Then to
accommodate the patients with frequent AEs, it assigns a (post hoc) ETA of +15,
giving an individual value for intercept of 6 (and a probability of the AE of
~1, as it should. My question is whey does it refuse to simply put those 8% of
the patients in a sub population with intercept = 6, ETA=0. rather than saying
the expected value is -11, with ETA = +15. Even when I fix the fractions in the
subpopulations for the observed values, and fix OMEGA to a small, reasonable
value, and fix the intercept values for the 3 populations to reasonable values
it will still do this. The only thing that has worked is to assign each
subject to the apparent population in the data set.
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383
[email protected]<[email protected]>
http://www.nuventra.com
Empower your Pipeline
CONFIDENTIALITY NOTICE The information in this transmittal (including
attachments, if any) may be privileged and confidential and is intended only
for the recipient(s) listed above. Any review, use, disclosure, distribution or
copying of this transmittal, in any form, is prohibited except by or on behalf
of the intended recipient(s). If you have received this transmittal in error,
please notify me immediately by reply email and destroy all copies of the
transmittal.
________________________________
From: Matts Kågedal <[email protected]><mailto:[email protected]>
Sent: Saturday, February 20, 2016 2:44 PM
To: Mark Sale
Cc: [email protected]<mailto:[email protected]>
Subject: Re: [NMusers] Mixture model with logistic regression
Hi Mark,
The pattern you see in the posthocs could possibly be a shrinkage phenomenon.
I.e. patients with AE most of the time will have the same ETA, while patients
with no AE will have the same ETA and there will be a third group in between.
If shrinkage is causing this, you should not expect any improvement with a
mixture model. Before you reject your original model I would therefore also
evaluate it by simulation and re-estimation. I think it is quite possible that
you will retreive a similar pattern in the posthocs even when you simulate
based on a normal distribution.
Best,
Matts Kågedal
Pharmacometrics, Genentech.
On Fri, Feb 19, 2016 at 2:30 PM, Mark Sale
<[email protected]<mailto:[email protected]>> wrote:
Has anyone every tried to use a mixture model with logistic regression? I have
data on a AE in several hundred patients, measured multiple times (10-20 times
per patient). Examining the data it is clear that, independent of drug
concentration, there is very wide distribution of this AE, 68% of the patients
never have the AE, 25% have it about 20% of the time and the rest have it
pretty much continuously, regardless of drug concentration. (in ordinary
logistic regression, just glm in R, there is also a nice concentration effect
on the AE in addition). Running the usual logistic model, not surprisingly, I
get a really big ETA on the intercept, with 68% of the people having ETA small
negative, 25% ETA ~ 1 and 7% ETA ~ 10. No covariates seem particularly
predictive of the post hoc ETA. I thought I could use a mixture model, with 3
modes, but it refused to do that, giving me essentially 0% in the 2nd and 3rd
distribution, still with the really large OMEGA for the intercept. Even when I
FIX the OMEGA to a reasonable number, I still get essentially no one in the 2nd
and 3rd distribution. I tried fixing the fraction in the 2nd and 3rd
distribution (and OMEGA), and it still gave me a very small difference in the
intercept for the 2nd and 3rd populations.
Is there an issue with using mixture models with logistic regression? I'm just
using FOCE, Laplacian, without interaction, and LIKE.
Any ideas?
Mark
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra, Inc. ™
2525 Meridian Parkway, Suite 280
Research Triangle Park, NC 27713
Office (919)-973-0383<tel:%28919%29-973-0383>
[email http://[email protected]
http://www.nuventra.com