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 =

to

build a comprehensive, beautiful and fully-mechanistic model. A

pragmatic and working model is needed. Such pragmatic model alre=

ady

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=

t

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 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=

e

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 ca=

lculate 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 abo=

ut single dose, multiple dosing, and in

the latter case is it sufficient to describe your endpoint at stead

state?

· 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

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-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=

effect

is irreversable because AUC of concentration can only increase; i=

t

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=

he

integration routine? It seems like an easy thing to do. =

Kind regards,

Pavel

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

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 =

to

build a comprehensive, beautiful and fully-mechanistic model. A

pragmatic and working model is needed. Such pragmatic model alre=

ady

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=

t

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 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=

e

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 ca=

lculate 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 abo=

ut single dose, multiple dosing, and in

the latter case is it sufficient to describe your endpoint at stead

state?

· 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

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-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=

effect

is irreversable because AUC of concentration can only increase; i=

t

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=

he

integration routine? It seems like an easy thing to do. =

Kind regards,

Pavel

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