Pavel: I am glad someone informed you of the ALAG option for handling your problem. My colleague w...@buffalo.edu<mailto:w...@buffalo.edu> 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: robert.ba...@iconplc.com<mailto:robert.ba...@iconplc.com> Web: www.iconplc.com<http://www.iconplc.com/> From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Pavel Belo Sent: Tuesday, January 14, 2014 1:45 PM 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 <br /><br /> ICON plc made the following annotations. ------------------------------------------------------------------------------ This e-mail transmission may contain confidential or legally privileged information that is intended only for the individual or entity named in the e-mail address. If you are not the intended recipient, you are hereby notified that any disclosure, copying, distribution, or reliance upon the contents of this e-mail is strictly prohibited. If you have received this e-mail transmission in error, please reply to the sender, so that ICON plc can arrange for proper delivery, and then please delete the message. Thank You, ICON plc South County Business Park Leopardstown Dublin 18 Ireland Registered number: 145835
