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 email@example.com Tel: 7-711 2073 or +44 (0) 20 8966 2073 Fax: 7-711 2123 or +44 (0) 20 8966 2603 ******* From: "Bachman, William" Subject: RE: [NMusers] Approximate effect compartment Date: Fri, 22 Mar 2002 07:39:27 -0500 Daren, What you are proposing sounds like a lot of "hassle" to me. Why not just simultaneously fit all of your data from all routes of administration, particularly because the newer data is sparse. Just fit it all using an extravascular dosing model (e.g. ADVAN12). The original IV data (dense?) will stabilize the model and allow calculation of absolute F of the intranasal formulation. Am I missing something here? (seems to be a straight forward approach). Bill William J. Bachman, Ph.D. GloboMax LLC 7250 Parkway Dr., Suite 430 Hanover, MD 21076 Voice (410) 782-2212 FAX (410) 712-0737 firstname.lastname@example.org ******* From: "Kowalski, Ken" Subject: RE: [NMusers] Approximate effect compartment Date: Fri, 22 Mar 2002 08:15:48 -0500 Daren, You might want to take a look at my paper: Kowalski, K.G. and Karim, A. "A Semicompartmental Modeling Approach for Pharmacodynamic Data Assessment," JPB 23:307-322 (1995). In this paper I derive what I call a semicompartmental solution to the effect-site concentration (Ce) where the only kinetic parameter that is estimated is keo. I assume a piecewise linear model for Cp (like doing the trapezoidal AUC) and using the effect site link dCe/dt = keo(Cp - Ce), I derive a recursive solution for Ce that only requires "noncompartmental-like" calculations. Using this solution for Ce requires one to use the observed Cp as a covariate and then one can estimate, keo and the PD parameters without having to specify a compartmental model for Cp. Now the bad news. This approach was developed for single subject data with fairly dense sampling...enough for doing noncompartmental calculations. Since you have sparse population data I don't think this approach will work for you. Moreover, even if you had dense sampling, some very special programming using verbatim code would be needed if you wanted to implement this method in NONMEM and plan to put an eta on keo. It turns out that one cannot "simply" specify recursive models using $PRED if those recursive models involve etas because NONMEM won't calculate the derivatives properly. Nevertheless, my paper might give you some additional insight. Regards, Ken ******* From: Liping Zhang. [mailto:email@example.com] Subject: Re: [NMusers] Approximate effect compartment Date: Friday, March 22, 2002 3:51 PM The method will not work well when the PK data are sparse as expected. However if you want to use NONMEM and put an eta on Keo, NONMEM can do it. For example, go to NONMEM Users Repository and then check PKPD-Lew Sheiner and then look for the 2nd file named "SEQPOP". Best regards, Liping Zhang -- _/ _/ _/_/ _/_/_/ _/_/_/ Liping Zhang (firstname.lastname@example.org) _/ _/ _/ _/_ _/_/ 4th year Graduate student _/ _/ _/ _/ _/ Dr. Lewis Sheiner's group _/_/ _/_/ _/_/_/ _/ Biological and Medical Informatics Program Box 0626, UCSF, SF, CA, 94143-0626 415-502-1989 (v), 415-476-2796 (fax) ******* From: "Kowalski, Ken" Subject: RE: [NMusers] Approximate effect compartment Date: Fri, 22 Mar 2002 16:30:04 -0500 Liping, When I said that you can't easily put an eta on Keo (without verbatim code) I was referring to my semicompartmental recursive solution for Ce. If you use a fully compartmental solution for Ce where you specify a compartmental model for Cp then there are no issues with putting an eta on Keo even with sparse data. Ken ******* From:"Austin, Daren J" Subject: RE: [NMusers] Approximate effect compartment Date: Fri, 22 Mar 2002 19:41:06 -0000 > Do you mean to use this equation? > Ce(t) = C(t) (KEO/(KEO-alpha_i))*(1-EXP(-(KEO-alpha_i)t) > and substitute alpha_i with ka or kel in the absorption or elimination > phase > of the pk profile? > [Austin, Daren J] Yes > The equation below seems to be missing the A(i) coefficients. > Ce(t) = Sum(i=1..n) (KEO/(KEO-alpha[i])) Exp(-alpha[i].t) > (1-EXP(-(KEO-alpha[i]))t) > [Austin, Daren J] Yes, my solution was missing the A[i]. Essentially my point is that although a multicompartment model fits the dense PK data, I can generate very good PD fits by assuming the one-compartment model solution and estimating an approximte Ce from the observed plasma concentrations. It's really a question of how much the effect compartment needs to follow the central compartment. My approximation is that the dynamics of the effect compartment look one-compartment-like irrespetive of the multi-compartments needed for the plasma PK. When variability in KEO is added I wondered just how valid this approach would be. Thanks for the reference Ken. Daren