Approximate effect compartment

From: "Austin, Daren J" Subject: [NMusers] Approximate effect compartment Date: Thu, 21 Mar 2002 22:05:10 -0000 Dear all, not strictly a nonmem question but I would like to know whether this is either valid or been done before. I have some concentration-effect data which has some evidence of hysteresis. I can therefore use an effect compartment and fit the PK profiles then the PD. This has been done using a three-compartment model on IV data and a post-hoc fit of a PD model. I now have more data from inhaled, intranasal and IV and would like to fit the PD response. Unfortunately the concentrations are pretty sparse, and I don't really want all the hassle of fitting PK profiles to the three routes. What I propose is the following (sorry for all the maths): In a linear PK model with an effect compartment I can write the effect concentration ode as d(Ce)/dt = KEO(C(t) - Ce) Since the central compartment is a sum of exponentials of the form C(t) = Sum(i=1..n) A[i] Exp(-alpha[i].t) I can integrate to get (after rearranging) Ce(t) = Sum(i=1..n) (KEO/(KEO-alpha[i])) Exp(-alpha[i].t) (1-EXP(-(KEO-alpha[i]))t) For a 1-cpt IV bolus this is just Ce(t) = C(t) (KEO/(KEO-ke)) (1-EXP(-(KEO-ke)t) My question is can I use a similar tecnique in the various regions where time ~ 1/alpha[i] or just take some value for alpha[i] characteristic of the half life. Is this approximation likely to be any worse than trying to acount for variability using inter-subject PK parameters, for example, with sparse data? I have tried this by fitting an Emax model to my data (850 pts) and assume that the half life is known. Defining the approximate effect compartment and introducing KEO and its ETA reduced the likelihood function by about 200 compared to using the observed concentration! The KEO comes out at about 4/hr which is lower but consistent with earlier two-stage predictions. I get an excellent posthoc fit to the data with a largest weighted residual of 0.25 and no bias. All parameters are well defined with low CV's using METHOD=0 Can anyone point me to any references where this might have been discussed before? Kind regards, Daren Dr. Daren J. Austin Pharmacometrician Clinical Pharmacology Discovery Medicine GlaxoSmithKline daren.austin@gsk.com Tel: 7-711 2073 or +44 (0) 20 8966 2073 Fax: 7-711 2123 or +44 (0) 20 8966 2603