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 (<t) from the 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
