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 (<t) from the integration routine? It seems like an easy thing to do.
Kind regards,
Pavel
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:
-----------------
Quoted reply history
From: Pavel Belo [email protected]
Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
To: [email protected], [email protected]
Subject: [NMusers] backward integration from t-a to t
Dear Robert,
Â
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.Â
Â
Is there a way to access AUC for the past time points (<t) from the
integration routine? It seems like an easy thing to do.  Â
Â
Kind regards,
Pavel Â
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http://link.mail2web.com/mail2web
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
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Pavel Belo
Sent: 14 January 2014 18:45
To: Bauer, Robert
Cc: [email protected]
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 (<t) from the integration
routine? It seems like an easy thing to do.
Kind regards,
Pavel
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 (<t) from the integration routine? It seems like an easy thing to do.
Kind regards,
Pavel
Pavel:
I am glad someone informed you of the ALAG option for handling your problem.
My colleague [email protected]<mailto:[email protected]> 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 CMT DV
1 0 100 1 .
1 0 100 4 .
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: [email protected]<mailto:[email protected]>
Web: http://www.iconplc.com/
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Pavel Belo
Sent: Tuesday, January 14, 2014 1:45 PM
To: Bauer, Robert
Cc: [email protected]
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 (<t) from the integration
routine? It seems like an easy thing to do.
Kind regards,
Pavel
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
Quoted reply history
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: [email protected] [ mailto: [email protected] ] On Behalf Of Pavel Belo
Sent: 14 January 2014 18:45
To: Bauer, Robert
Cc: [email protected]
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 (<t) from the integration routine? It seems like an easy thing to do.
Kind regards,
Pavel
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:
-----------------
Quoted reply history
From: Pavel Belo [email protected]
Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST)
To: [email protected], [email protected]
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, [email protected] 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 [email protected]
> Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
> To: [email protected], [email protected]
> Subject: [NMusers] backward integration from t-a to t
>
>
>
>
>
> Dear Robert,
>
>
>
>
> Ã
>
> 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;Ã it cannot decrease.Ã 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).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 pointsà usedà during theÃ
> 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.Ã
>
> Ã
>
> 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 Ã
>
> Ã
>
> Kind regards,
>
>
> Pavelà Ã
>
>
> --------------------------------------------------------------------
> mail2web - Check your email from the web at
> http://link.mail2web.com/mail2web
>
>
>
--------------------------------------------------------------------
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hosting - http://link.myhosting.com/myhosting
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
Quoted reply history
On 17/01/2014 1:29 p.m., [email protected] 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 [email protected]
> Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST)
> To: [email protected], [email protected]
> 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, [email protected] 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 [email protected]
> > Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
> > To: [email protected], [email protected]
> > 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: [email protected]
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/10.1111/bcp.12170/abstract
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
Quoted reply history
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., [email protected] < mailto: [email protected] > 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 [email protected] <mailto:[email protected]>
Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST)
To: [email protected] < mailto: [email protected] > , [email protected] < mailto: [email protected] >
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, [email protected] < mailto: [email protected] > 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 [email protected] <mailto:[email protected]>
Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
To: [email protected] < mailto: [email protected] > , [email protected] < mailto: [email protected] >
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,
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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: [email protected] <mailto:[email protected]>
http://holford.fmhs.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 < 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 < 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 < 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/10.1111/bcp.12170/abstract < http://onlinelibrary.wiley.com/doi/10.1111/bcp.12170/abstract >
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
Quoted reply history
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., [email protected] 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 [email protected]
> > Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST)
> > To:[email protected],[email protected]
> > 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,[email protected] 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 [email protected]
> > > Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST)
> > > To:[email protected],[email protected]
> > > 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:[email protected]
> 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/10.1111/bcp.12170/abstract
--
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: [email protected]
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/10.1111/bcp.12170/abstract