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RE: backward integration from t-a to t

From: Pavel Belo <nonmem>
Date: Thu, 16 Jan 2014 11:40:40 -0500 (EST)

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 =
build a comprehensive, beautiful and fully-mechanistic model.  A
pragmatic and working model is needed.  Such pragmatic model alre=
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 tha=
exponential explosion of our knowledge, which is descrived by soome
futurists.  Stay tuned. 


Kind regards,





Hello Jacob,


Someone genious just helped me.  Tlag can be used.  How did I mis=
s 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 multiopl=
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=
adjusted if possible. 





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

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


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 ca=
lculate AUC

However, a moving average AUC would rarely be a mechanistic description
of effect delay. Leonid provide one possible solution (like an effect

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 abo=
ut single dose, multiple dosing, and in
the latter case is it sufficient to describe your endpoint at stead

·         And is the effect ap=
pearing 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 r=
each 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 mechanis=
ms for effect delay (i.e. the delay in on
and offset of effect that is not due to accumulation of PK at start of


Are you aware of the standard models for effect delay that one would
commonly consider and why did you dismiss these?


Best regards




From: owner-nmusers
On Behalf Of Pavel Belo
Sent: 14 January 2014 18:45
To: Bauer, Robert
Cc: nmusers
Subject: [NMusers] backward integration from t-a to t


Dear Robert,


Efficacy is frequently considered a function of AUC.  (AUC i=
s 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=
is irreversable because AUC of concentration can only increase; i=
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 calcula=
te 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 t=
integration routine? It seems like an easy thing to do.  =


Kind regards,



Received on Thu Jan 16 2014 - 11:40:40 EST

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