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 (<t) from the integration routine? It seems like an easy thing to do. Kind regards, Pavel
