Re: [NMusers] backward integration from t-a to t
Pavel,
It seems you prefer empirical curve fitting to science based modelling
because you do not seem to think that my suggestions were constructive.
I am glad I don't have your job.
Nick
On 18/01/2014 5:30 a.m., Pavel Belo wrote:
Thank you Nick.
We see the advantage and disadvantages this approach clear and
understand the difference between the modeling and the curve fitting
exercise. On the other hand, out motto is to keep an open mind and
to keep trying. There are scenarios where the approach may work and
where it will not work. In any case, it is useful to study it and
keep it in the library even if it is classified as a rare case.
It is easier to provide critique than to suggest something
constructive. Lets phrase Leonid for doing the constructive part and
being innovative. Lets thank Robert for providing the algorithm!
Take care,
Pavel
On Thu, Jan 16, 2014 at 07:48 PM, Nick Holford wrote:
Pavel,
Unless your drug is an alkylating agent the use of AUC will always
be mechanistically wrong.
I hope you also considered the possibility of disease progression
(i.e. changing baseline) and also the possibility of changing C50
due to potentiation or physiological changes.
Nick
On 17/01/2014 1:29 p.m., lgibian...@quantpharm.com wrote:
Hi Pavel,
You mentioned that the effect compartment did not help, and the model I
suggested is identical to the effect compartment. May be try something like
transit compartment model:
DADT(2)=C-K0*A(2)
DADT(3)=K0*A(2)-K0*A(3)
...
DADT(X)=K0*A(X-1)-K0*A(X)
AUCapprox=A(2)+...+A(X)
This will prolong the shape of AUCapprox(t). It could be a bit simpler and
smoother than tlag implementation
Leonid
Original email:
-
From: Pavel belonon...@optonline.net
Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST)
To:lgibian...@quantpharm.com,nmusers@globomaxnm.com
Subject: RE: [NMusers] backward integration from t-a to t
Hello Leonid,
Thank you bein helpful. You got the main point. AUC is a better
predictor than concentration, but it has to disppear very slowly but
surely.
A potential challenge is biological meaning of this approach. It will
be necessary to explain it to the biologists, who ask question like "Why
do you use 2 compartment in PK model while human body has so many
compartments?".
We will see!
Thanks,
Pavel
On Wed, Jan 15, 2014 at 01:19 AM,lgibian...@quantpharm.com wrote:
Pavel,
I think one can use equation
DADT(2)=C-K0*A(2)
where C is the drug concentration. When K0=0, A2 is cumulative AUC.
When
k0>0, A2 would represent something like AUC for the interval prior to
the current
time
The length of the interval would be proportional to 1/K0 (and equal to
infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination"
from the
system. PD then can be made dependent on A2, and the model would
select optimal
value of K0. One interesting case to understand the concept is when C
is constant.
Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So
roughly, A2 can
be interpreted as AUC over the interval of 1/K0. Leonid
Original email:
-
From: Pavel belonon...@optonline.net
Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
To:robert.ba...@iconplc.com,nmusers@globomaxnm.com
Subject: [NMusers] backward integration from t-a to t
Dear Robert,
Ã,
Efficacy isÃ, frequently considered aÃ, function of AUC.Ã, (AUC is just
an integral. It is obvious how to calculate AUC any software which can
solve ODE.)Ã, A disadvantage of this model of efficacyÃ, is that the
effect is irreversable becauseÃ, AUC of concentration can only
increase;Ã, it cannot decrease.Ã, In many cases, a more meaningful model
is a model where AUC is calculated form time tÃ, -a to t (kind of
"moving average"), where t is timeÃ, in the system of differential
equations (variable T in NONMEM).Ã, Ã, There are 2 obvious ways to
calculate AUC(t-a, t).Ã, The first is to do backward integration, which
looks like a hard and resource consuming way for NONMEM.Ã, The second
one is to keep in memory AUC for all time pointsÃ, usedÃ, during theÃ,
integrationÃ, and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there
AUC(t-a) can be interpolated using two closest time points below and
above t-a.Ã,
Ã,
Is there a way toÃ, access AUC forÃ, the past time points (> integration
routine?Ã, It seems like an easyÃ, thing to do.Ã, Ã, Ã,
Ã,
Kind regards,
PavelÃ, Ã,
mail2web - Check your email from the web at
http://link.mail2web.com/mail2web
--
RE: [NMusers] backward integration from t-a to t
Hello Leonid, I agree that the effect compartment model somewhat resembles the ALAG approach. Sometimes they can provide very similar outcome. We have the resolution and I'll update you when it is appropriate. Unfortunately, I cannot reveal some information right now. Thanks! Kind regards, Pavel On Thu, Jan 16, 2014 at 07:29 PM, lgibian...@quantpharm.com wrote: Hi Pavel, You mentioned that the effect compartment did not help, and the model I suggested is identical to the effect compartment. May be try something like transit compartment model: DADT(2)=C-K0*A(2) DADT(3)=K0*A(2)-K0*A(3) ... DADT(X)=K0*A(X-1)-K0*A(X) AUCapprox=A(2)+...+A(X) This will prolong the shape of AUCapprox(t). It could be a bit simpler and smoother than tlag implementation Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) To: lgibian...@quantpharm.com, nmusers@globomaxnm.com Subject: RE: [NMusers] backward integration from t-a to t Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, lgibian...@quantpharm.com wrote: Pavel, I think one can use equation DADT(2)=C-K0*A(2) where C is the drug concentration. When K0=0, A2 is cumulative AUC. When k0>0, A2 would represent something like AUC for the interval prior to the current time The length of the interval would be proportional to 1/K0 (and equal to infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" from the system. PD then can be made dependent on A2, and the model would select optimal value of K0. One interesting case to understand the concept is when C is constant. Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So roughly, A2 can be interpreted as AUC over the interval of 1/K0. Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) To: robert.ba...@iconplc.com, nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, à Efficacy isà frequently considered aà function of AUC.à (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.)à A disadvantage of this model of efficacyà is that the effect is irreversable becauseà AUC of concentration can only increase;à it cannot decrease.à In many cases, a more meaningful model is a model where AUC is calculated form time tà -a to t (kind of "moving average"), where t is timeà in the system of differential equations (variable T in NONMEM).à à There are 2 obvious ways to calculate AUC(t-a, t).à The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM.à The second one is to keep in memory AUC for all time pointsà usedà during theà integrationà and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a.à à Is there a way toà access AUC forà the past time points (> integration routine?à It seems like an easyà thing to do.à à à à Kind regards, Pavelà à mail2web - Check your email from the web at http://link.mail2web.com/mail2web myhosting.com - Premium Microsoft® Windows® and Linux web and application hosting - http://link.myhosting.com/myhosting
Re: [NMusers] backward integration from t-a to t
Thank you Nick. We see the advantage and disadvantages this approach clear and understand the difference between the modeling and the curve fitting exercise. On the other hand, out motto is to keep an open mind and to keep trying. There are scenarios where the approach may work and where it will not work. In any case, it is useful to study it and keep it in the library even if it is classified as a rare case. It is easier to provide critique than to suggest something constructive. Lets phrase Leonid for doing the constructive part and being innovative. Lets thank Robert for providing the algorithm! Take care, Pavel On Thu, Jan 16, 2014 at 07:48 PM, Nick Holford wrote: Pavel, Unless your drug is an alkylating agent the use of AUC will always be mechanistically wrong. I hope you also considered the possibility of disease progression (i.e. changing baseline) and also the possibility of changing C50 due to potentiation or physiological changes. Nick On 17/01/2014 1:29 p.m., lgibian...@quantpharm.com <mailto:lgibian...@quantpharm.com> wrote: Hi Pavel, You mentioned that the effect compartment did not help, and the model I suggested is identical to the effect compartment. May be try something like transit compartment model: DADT(2)=C-K0*A(2) DADT(3)=K0*A(2)-K0*A(3) ... DADT(X)=K0*A(X-1)-K0*A(X) AUCapprox=A(2)+...+A(X) This will prolong the shape of AUCapprox(t). It could be a bit simpler and smoother than tlag implementation Leonid Original email: - From: Pavel Belo non...@optonline.net <mailto:non...@optonline.net> Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) To: lgibian...@quantpharm.com <mailto:lgibian...@quantpharm.com> , nmusers@globomaxnm.com <mailto:nmusers@globomaxnm.com> Subject: RE: [NMusers] backward integration from t-a to t Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, lgibian...@quantpharm.com <mailto:lgibian...@quantpharm.com> wrote: Pavel, I think one can use equation DADT(2)=C-K0*A(2) where C is the drug concentration. When K0=0, A2 is cumulative AUC. When k0>0, A2 would represent something like AUC for the interval prior to the current time The length of the interval would be proportional to 1/K0 (and equal to infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" from the system. PD then can be made dependent on A2, and the model would select optimal value of K0. One interesting case to understand the concept is when C is constant. Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So roughly, A2 can be interpreted as AUC over the interval of 1/K0. Leonid Original email: - From: Pavel Belo non...@optonline.net <mailto:non...@optonline.net> Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) To: robert.ba...@iconplc.com <mailto:robert.ba...@iconplc.com> , nmusers@globomaxnm.com <mailto:nmusers@globomaxnm.com> Subject: [NMusers] backward integration from t-a to t Dear Robert, Ã, Efficacy isÃ, frequently considered aÃ, function of AUC.Ã, (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.)Ã, A disadvantage of this model of efficacyÃ, is that the effect is irreversable becauseÃ, AUC of concentration can only increase;Ã, it cannot decrease.Ã, In many cases, a more meaningful model is a model where AUC is calculated form time tÃ, -a to t (kind of "moving average"), where t is timeÃ, in the system of differential equations (variable T in NONMEM).Ã, Ã, There are 2 obvious ways to calculate AUC(t-a, t).Ã, The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM.Ã, The second one is to keep in memory AUC for all time pointsÃ, usedÃ, during theÃ, integrationÃ, and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a.Ã, Ã, Is there a way toÃ, access AUC forÃ, the past time points (> integration routine?Ã, It seems like an easyÃ, thing to do.Ã, Ã, Ã, Ã, Kind regards, PavelÃ, Ã, mail2web - Check your email from the web at http://link.mail2web.com/mail2web <http://link.mail2web.com/mail2web> myhosting.com - Premium Microsoft® Windows® and Linux web and application hosting - http://link.myhosting.com/myhosting <http://link.myhosting.com/myhosting> -- N
Re: [NMusers] backward integration from t-a to t
Pavel, Unless your drug is an alkylating agent the use of AUC will always be mechanistically wrong. I hope you also considered the possibility of disease progression (i.e. changing baseline) and also the possibility of changing C50 due to potentiation or physiological changes. Nick On 17/01/2014 1:29 p.m., lgibian...@quantpharm.com wrote: Hi Pavel, You mentioned that the effect compartment did not help, and the model I suggested is identical to the effect compartment. May be try something like transit compartment model: DADT(2)=C-K0*A(2) DADT(3)=K0*A(2)-K0*A(3) ... DADT(X)=K0*A(X-1)-K0*A(X) AUCapprox=A(2)+...+A(X) This will prolong the shape of AUCapprox(t). It could be a bit simpler and smoother than tlag implementation Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) To: lgibian...@quantpharm.com, nmusers@globomaxnm.com Subject: RE: [NMusers] backward integration from t-a to t Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, lgibian...@quantpharm.com wrote: Pavel, I think one can use equation DADT(2)=C-K0*A(2) where C is the drug concentration. When K0=0, A2 is cumulative AUC. When k0>0, A2 would represent something like AUC for the interval prior to the current time The length of the interval would be proportional to 1/K0 (and equal to infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" from the system. PD then can be made dependent on A2, and the model would select optimal value of K0. One interesting case to understand the concept is when C is constant. Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So roughly, A2 can be interpreted as AUC over the interval of 1/K0. Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) To: robert.ba...@iconplc.com, nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, Ã, Efficacy isÃ, frequently considered aÃ, function of AUC.Ã, (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.)Ã, A disadvantage of this model of efficacyÃ, is that the effect is irreversable becauseÃ, AUC of concentration can only increase;Ã, it cannot decrease.Ã, In many cases, a more meaningful model is a model where AUC is calculated form time tÃ, -a to t (kind of "moving average"), where t is timeÃ, in the system of differential equations (variable T in NONMEM).Ã, Ã, There are 2 obvious ways to calculate AUC(t-a, t).Ã, The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM.Ã, The second one is to keep in memory AUC for all time pointsÃ, usedÃ, during theÃ, integrationÃ, and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a.Ã, Ã, Is there a way toÃ, access AUC forÃ, the past time points (> integration routine?Ã, It seems like an easyÃ, thing to do.Ã, Ã, Ã, Ã, Kind regards, PavelÃ, Ã, mail2web - Check your email from the web at http://link.mail2web.com/mail2web myhosting.com - Premium Microsoft® Windows® and Linux web and application hosting - http://link.myhosting.com/myhosting -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand office:+64(9)923-6730 mobile:NZ +64(21)46 23 53 email: n.holf...@auckland.ac.nz http://holford.fmhs.auckland.ac.nz/ Holford NHG. Disease progression and neuroscience. Journal of Pharmacokinetics and Pharmacodynamics. 2013;40:369-76 http://link.springer.com/article/10.1007/s10928-013-9316-2 Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and adults. J Pharm Sci. 2013: http://onlinelibrary.wiley.com/doi/10.1002/jps.23574/abstract Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. 2013;2: http://www.nature.com/psp/journal/v2/n5/full/psp201318a.html Holford NHG. Clinical pharmacology = disease progression + drug action. British Journal of Clinical Pharmacology. 2013: http://onlinelibrary.wiley.com/doi/10./bcp.12170/abstract
RE: [NMusers] backward integration from t-a to t
Hi Pavel, You mentioned that the effect compartment did not help, and the model I suggested is identical to the effect compartment. May be try something like transit compartment model: DADT(2)=C-K0*A(2) DADT(3)=K0*A(2)-K0*A(3) ... DADT(X)=K0*A(X-1)-K0*A(X) AUCapprox=A(2)+...+A(X) This will prolong the shape of AUCapprox(t). It could be a bit simpler and smoother than tlag implementation Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) To: lgibian...@quantpharm.com, nmusers@globomaxnm.com Subject: RE: [NMusers] backward integration from t-a to t Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, lgibian...@quantpharm.com wrote: > Pavel, > I think one can use equation > DADT(2)=C-K0*A(2) > > where C is the drug concentration. When K0=0, A2 is cumulative AUC. > When > k0>0, A2 would represent something like AUC for the interval prior to > the current > time > The length of the interval would be proportional to 1/K0 (and equal to > infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" > from the > system. PD then can be made dependent on A2, and the model would > select optimal > value of K0. One interesting case to understand the concept is when C > is constant. > Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So > roughly, A2 can > be interpreted as AUC over the interval of 1/K0. Leonid > > > Original email: > - > From: Pavel Belo non...@optonline.net > Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) > To: robert.ba...@iconplc.com, nmusers@globomaxnm.com > Subject: [NMusers] backward integration from t-a to t > > > > > > Dear Robert, > > > > > à > > Efficacy isà frequently considered aà function of AUC.à (AUC is just > an integral. It is obvious how to calculate AUC any software which can > solve ODE.)à A disadvantage of this model of efficacyà is that the > effect is irreversable becauseà AUC of concentration can only > increase;à it cannot decrease.à In many cases, a more meaningful model > is a model where AUC is calculated form time tà -a to t (kind of > "moving average"), where t is timeà in the system of differential > equations (variable T in NONMEM).à à There are 2 obvious ways to > calculate AUC(t-a, t).à The first is to do backward integration, which > looks like a hard and resource consuming way for NONMEM.à The second > one is to keep in memory AUC for all time pointsà usedà during theà > integrationà and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there > AUC(t-a) can be interpolated using two closest time points below and > above t-a.à > > à > > Is there a way toà access AUC forà the past time points (> integration > routine?à It seems like an easyà thing to do.à à à > > à > > Kind regards, > > > Pavelà à > > > > mail2web - Check your email from the web at > http://link.mail2web.com/mail2web > > > myhosting.com - Premium Microsoft® Windows® and Linux web and application hosting - http://link.myhosting.com/myhosting
RE: [NMusers] backward integration from t-a to t
Hello Leonid, Thank you bein helpful. You got the main point. AUC is a better predictor than concentration, but it has to disppear very slowly but surely. A potential challenge is biological meaning of this approach. It will be necessary to explain it to the biologists, who ask question like "Why do you use 2 compartment in PK model while human body has so many compartments?". We will see! Thanks, Pavel On Wed, Jan 15, 2014 at 01:19 AM, lgibian...@quantpharm.com wrote: Pavel, I think one can use equation DADT(2)=C-K0*A(2) where C is the drug concentration. When K0=0, A2 is cumulative AUC. When k0>0, A2 would represent something like AUC for the interval prior to the current time The length of the interval would be proportional to 1/K0 (and equal to infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" from the system. PD then can be made dependent on A2, and the model would select optimal value of K0. One interesting case to understand the concept is when C is constant. Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So roughly, A2 can be interpreted as AUC over the interval of 1/K0. Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) To: robert.ba...@iconplc.com, nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert,  Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM).  There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a.  Is there a way to access AUC for the past time points (> integration routine? It seems like an easy thing to do.    Kind regards, Pavel  mail2web - Check your email from the web at http://link.mail2web.com/mail2web
RE: [NMusers] backward integration from t-a to t
Hello Jacob, It is the best to have fully-mechanistic model. Unfortunately, we rarely have the data to build such model. So, approximations are needed. In case we have the data, we know how to build the model; we understand the mechanisms. An effect compartment model does not work. It is a case when return back to baseline is very slow (or even not observed) and/or extremely variable. There are no both data and time to build a comprehensive, beautiful and fully-mechanistic model. A pragmatic and working model is needed. Such pragmatic model already exist, but it needs touch paint to account for additional data, which may arrive. The email from Robert provides an excellent introduction (accounts for scipped doses + very nonliner PK and eventual return to baseline). It is somewhat bulky because it almost doubles the number of differential equations, but it is much better than nothing. Eventually, a more elegant solution will be implemented. We are not perfect, but we are moving there! Science is moving to that exponential explosion of our knowledge, which is descrived by soome futurists. Stay tuned. Kind regards, Pavel Hello Jacob, Someone genious just helped me. Tlag can be used. How did I miss such simple solution? I was talking about multiple doses. There are cases AUC is better predictor than concentration (for example, long duration of treatment is needed; very slow but good drug effect), but when it comes to multiople doses, it does not work well because it is necessary to predict drug withdrawal. If "moving average"-like approach is used, the drug effect disappears slowly, which can be the case. Of course this approach has to tested for some unexpected results and adjusted if possible. Thanks, Pavel On Wed, Jan 15, 2014 at 07:49 AM, Ribbing, Jakob wrote: Hi Pavel, I agree with you it is not uncommon to have AUC drive efficacy or safety endpoints. However, you seem to have the impression this is commonly done using cumulative AUC and I can assure you that is rarely the case. I have only seen that for safety endpoints where it has been justified (treatment is limited to a few cycles due to accumulation of side effect which for practical purposes can be regarded as irreversible). Even for cases where treatment/disease is completely curative it is not a standard approach to use cumulative AUC to drive efficacy (e.g. antibiotics, where infection may be eradicated, but the bacterial-killing effect wears off after the drug has been eliminated; so even if disease does not come back the actual drug effect has worn off). At steady state multiple dosing, AUC over a dosing interval (or Cav,ss) can sometimes be used to drive steady-state efficacy or safety. However, it seems in your case you have fluctuations in drug response even at steady state? Otherwise, this AUC can be expressed as an analytical solution or added as an input variable in your dataset, in case you are concerned about run times. But with that approach you would not see a fluctuation in drug response at steady state, so in your case maybe better to use concentrations to drive efficacy? For a “moving average” it would sometimes be possible to calculate AUC analytically. However, a moving average AUC would rarely be a mechanistic description of effect delay. Leonid provide one possible solution (like an effect compartment). However, there are many alternatives and it is not possible to say which is the best in your specific case(s), without more information, e.g. · Are you thinking about single dose, multiple dosing, and in the latter case is it sufficient to describe your endpoint at stead state? · And is the effect appearing with great delay over many days/weeks or it rather fluctuates with fluctuating concentrations? (e.g. at multiple dosing for a low dose, do you have fluctuations over a dosing interval in your efficacy endpoint that are due fluctuations in PK, i.e. aside from any circadian variation?) · Does a higher dose reach its efficacy-steady state faster than a lower dose (time to efficacy-steady state; not the level of response which should be different)? · What is the mechanisms for effect delay (i.e. the delay in on and offset of effect that is not due to accumulation of PK at start of treatment) Are you aware of the standard models for effect delay that one would commonly consider and why did you dismiss these? Best regards Jakob From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Pavel Belo Sent: 14 January 2014 18:45 To: Bauer, Robert Cc: nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, Efficacy is frequently considered a function of AUC. (AUC
RE: [NMusers] backward integration from t-a to t
Pavel: I am glad someone informed you of the ALAG option for handling your problem. My colleague w...@buffalo.edu<mailto:w...@buffalo.edu> and his associates have published on the general aspects of time delay differential equations, of which yours is a particular example. Although Jacob Ribbing has already discussed as to whether or not using AUC for driving efficacy is appropriate from a mechanistic stand-point, and Leonid Gibiansky has offered another way of looking at the problem, it is nonetheless worthwhile to present to the nmusers audience an example of how to use the ALAG option for your particular case, from which they may generalize for use of other time delay problems. In the following simple absorption model example developed by me and Alison Boeckmann for illustration purposes, compartments 1, 2, and 3 are the "real time" depot, central, auc, and compartments 4,5,6 are the "delayed time" depot, central, auc. So, the base model (non-time delay) system (compartments 1,2,3) is replicated (compartments 4,5,6) for the time delay portion. In addition, the data set duplicates the dose information of compartment 1 into compartment 4, and setting ALAG4 to a non-zero value in the control stream file provides a lag time to any doses inputted into compartment 4 (so this would take care of multiple dose problems as well). This allows for assessment and availability of AUC(t) and AUCT(t-time-delay) at any time t. The comments explain the meaning of each compartment. $PROB TEST AUC DELAY $INPUT ID TIME AMT CMT DV $DATA DELAYDATA IGNORE=@ $SUBR ADVAN6 TOL=5 $MODEL COMP=(DEPOT) COMP=(CENTRAL) COMP=(AUC) COMP=(D_DEPOT) COMP=(D_CENTR) COMP=(D_AUC) COMP=(AUCDIFF) $PK TDY=THETA(1)*EXP(ETA(1)) ALAG4=TDY KA=THETA(2)*EXP(ETA(2)) KE=THETA(3)*EXP(ETA(3)) $DES DADT(1)=-KA*A(1) DADT(2)= KA*A(1)-KE*A(2) ; C(T) DADT(3)= A(2) ; AUC(T) DADT(4)=-KA*A(4) DADT(5)= KA*A(4)-KE*A(5) ; C(T-TDY) DADT(6)= A(5) ; AUC(T-TDY) DADT(7)= A(2)-A(5) ; AUC(T-TDY) $ERROR A1=A(1) A2=A(2) A3=A(3) A4=A(4) A5=A(5) A6=A(6) A7=A(7) DAUC=A(3)-A(6) ; AUC(T)-AUC(T-TDY) Y=F+EPS(1) $THETA 3 $THETA 1 2 $OMEGA 1 1 1 $SIGMA 1 $TABLE ID TIME A1 A2 A3 A4 A5 A6 A7 DAUC NOAPPEND NOPRINT FILE=aucdelay.tbl FORMAT=sF8.3 And the example data set: ID TIME AMT CMTDV 1 01001 . 1 01004 . 1 1 .2 . 1 2 .2 . 1 3 .2 . 1 4 .2 . 1 5 .2 . 1 6 .2 . 1 7 .2 . 1 8 .2 . 1 9 .2 . 1 10 .2 . 1 11 .2 . 1 12 .2 . 1 13 .2 . 1 14 .2 . 1 15 .2 . Robert J. Bauer, Ph.D. Vice President, Pharmacometrics, R&D ICON Development Solutions 7740 Milestone Parkway Suite 150 Hanover, MD 21076 Tel: (215) 616-6428 Mob: (925) 286-0769 Email: robert.ba...@iconplc.com<mailto:robert.ba...@iconplc.com> Web: www.iconplc.com<http://www.iconplc.com/> From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Pavel Belo Sent: Tuesday, January 14, 2014 1:45 PM To: Bauer, Robert Cc: nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM). There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a. Is there a way to access AUC for the past time points ( ICON plc made the following annotations. -- This e-mail transmission may contain confidential or legally privileged information that is intended only for the individual or entity named in the e-mail address. If you are not the intended recipient, you are hereby notified that any disclosure, copying, distribution, or reliance upon the contents of this e-mail is strictly prohibited. If you have received this e-mail transmission in error, please reply to the sender, so that ICON plc can arrange for proper delivery, and then please delete the message. Thank You, ICON plc South County Business Park Leopardstown Dublin 18 Ireland Registered number: 145835
RE: [NMusers] backward integration from t-a to t
Jello Jacob, Someone genious just helped me. Tlag can be used. How did I miss such simple solution? I was talking about multiple doses. There are cases AUC is better predictor than concentration (for example, long duration of treatment is needed; very slow but good drug effect), but when it comes to multiople doses, it does not work well because it is necessary to predict drug withdrawal. If "moving average"-like approach is used, the drug effect disappears slowly, which can be the case. Of course this approach has to tested for some unexpected results and adjusted if possible. Thanks, Pavel On Wed, Jan 15, 2014 at 07:49 AM, Ribbing, Jakob wrote: Hi Pavel, I agree with you it is not uncommon to have AUC drive efficacy or safety endpoints. However, you seem to have the impression this is commonly done using cumulative AUC and I can assure you that is rarely the case. I have only seen that for safety endpoints where it has been justified (treatment is limited to a few cycles due to accumulation of side effect which for practical purposes can be regarded as irreversible). Even for cases where treatment/disease is completely curative it is not a standard approach to use cumulative AUC to drive efficacy (e.g. antibiotics, where infection may be eradicated, but the bacterial-killing effect wears off after the drug has been eliminated; so even if disease does not come back the actual drug effect has worn off). At steady state multiple dosing, AUC over a dosing interval (or Cav,ss) can sometimes be used to drive steady-state efficacy or safety. However, it seems in your case you have fluctuations in drug response even at steady state? Otherwise, this AUC can be expressed as an analytical solution or added as an input variable in your dataset, in case you are concerned about run times. But with that approach you would not see a fluctuation in drug response at steady state, so in your case maybe better to use concentrations to drive efficacy? For a “moving average” it would sometimes be possible to calculate AUC analytically. However, a moving average AUC would rarely be a mechanistic description of effect delay. Leonid provide one possible solution (like an effect compartment). However, there are many alternatives and it is not possible to say which is the best in your specific case(s), without more information, e.g. · Are you thinking about single dose, multiple dosing, and in the latter case is it sufficient to describe your endpoint at stead state? · And is the effect appearing with great delay over many days/weeks or it rather fluctuates with fluctuating concentrations? (e.g. at multiple dosing for a low dose, do you have fluctuations over a dosing interval in your efficacy endpoint that are due fluctuations in PK, i.e. aside from any circadian variation?) · Does a higher dose reach its efficacy-steady state faster than a lower dose (time to efficacy-steady state; not the level of response which should be different)? · What is the mechanisms for effect delay (i.e. the delay in on and offset of effect that is not due to accumulation of PK at start of treatment) Are you aware of the standard models for effect delay that one would commonly consider and why did you dismiss these? Best regards Jakob From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Pavel Belo Sent: 14 January 2014 18:45 To: Bauer, Robert Cc: nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM). There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a. Is there a way to access AUC for the past time points (integration routine? It seems like an easy thing to do. Kind regards, Pavel
[NMusers] backward integration from t-a to t
Please never mind. Someone suggested tose tlag, which is a simple and efficient enough way to do it. Regards, Pavel Dear Robert, Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM). There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a. Is there a way to access AUC for the past time points (integration routine? It seems like an easy thing to do. Kind regards, Pavel
RE: [NMusers] backward integration from t-a to t
Hi Pavel, I agree with you it is not uncommon to have AUC drive efficacy or safety endpoints. However, you seem to have the impression this is commonly done using cumulative AUC and I can assure you that is rarely the case. I have only seen that for safety endpoints where it has been justified (treatment is limited to a few cycles due to accumulation of side effect which for practical purposes can be regarded as irreversible). Even for cases where treatment/disease is completely curative it is not a standard approach to use cumulative AUC to drive efficacy (e.g. antibiotics, where infection may be eradicated, but the bacterial-killing effect wears off after the drug has been eliminated; so even if disease does not come back the actual drug effect has worn off). At steady state multiple dosing, AUC over a dosing interval (or Cav,ss) can sometimes be used to drive steady-state efficacy or safety. However, it seems in your case you have fluctuations in drug response even at steady state? Otherwise, this AUC can be expressed as an analytical solution or added as an input variable in your dataset, in case you are concerned about run times. But with that approach you would not see a fluctuation in drug response at steady state, so in your case maybe better to use concentrations to drive efficacy? For a “moving average” it would sometimes be possible to calculate AUC analytically. However, a moving average AUC would rarely be a mechanistic description of effect delay. Leonid provide one possible solution (like an effect compartment). However, there are many alternatives and it is not possible to say which is the best in your specific case(s), without more information, e.g. · Are you thinking about single dose, multiple dosing, and in the latter case is it sufficient to describe your endpoint at stead state? · And is the effect appearing with great delay over many days/weeks or it rather fluctuates with fluctuating concentrations? (e.g. at multiple dosing for a low dose, do you have fluctuations over a dosing interval in your efficacy endpoint that are due fluctuations in PK, i.e. aside from any circadian variation?) · Does a higher dose reach its efficacy-steady state faster than a lower dose (time to efficacy-steady state; not the level of response which should be different)? · What is the mechanisms for effect delay (i.e. the delay in on and offset of effect that is not due to accumulation of PK at start of treatment) Are you aware of the standard models for effect delay that one would commonly consider and why did you dismiss these? Best regards Jakob From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Pavel Belo Sent: 14 January 2014 18:45 To: Bauer, Robert Cc: nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert, Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM). There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a. Is there a way to access AUC for the past time points (
RE: [NMusers] backward integration from t-a to t
Pavel, I think one can use equation DADT(2)=C-K0*A(2) where C is the drug concentration. When K0=0, A2 is cumulative AUC. When k0>0, A2 would represent something like AUC for the interval prior to the current time The length of the interval would be proportional to 1/K0 (and equal to infinity when k0=0). Conceptually, K0 is the rate of "AUC elimination" from the system. PD then can be made dependent on A2, and the model would select optimal value of K0. One interesting case to understand the concept is when C is constant. Then A2=C/K0 while AUC over some interval TAU is AUC=C*TAU. So roughly, A2 can be interpreted as AUC over the interval of 1/K0. Leonid Original email: - From: Pavel Belo non...@optonline.net Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) To: robert.ba...@iconplc.com, nmusers@globomaxnm.com Subject: [NMusers] backward integration from t-a to t Dear Robert,  Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM).  There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a.  Is there a way to access AUC for the past time points (http://link.mail2web.com/mail2web
[NMusers] backward integration from t-a to t
Dear Robert, Efficacy is frequently considered a function of AUC. (AUC is just an integral. It is obvious how to calculate AUC any software which can solve ODE.) A disadvantage of this model of efficacy is that the effect is irreversable because AUC of concentration can only increase; it cannot decrease. In many cases, a more meaningful model is a model where AUC is calculated form time t -a to t (kind of "moving average"), where t is time in the system of differential equations (variable T in NONMEM). There are 2 obvious ways to calculate AUC(t-a, t). The first is to do backward integration, which looks like a hard and resource consuming way for NONMEM. The second one is to keep in memory AUC for all time points used during the integration and calculate AUC(t-a,t) as AUC(t) - AUC(t-a), there AUC(t-a) can be interpolated using two closest time points below and above t-a. Is there a way to access AUC for the past time points (integration routine? It seems like an easy thing to do. Kind regards, Pavel
