Re: backward integration from t-a to t

On 18/01/2014 5:30 a.m., Pavel Belo wrote: > Thank you Nick. > > We see the advantage and disadvantages this approach clear and understand the difference between the modeling and the curve fitting exercise. On the other hand, out motto is to keep an open mind and to keep trying. There are scenarios where the approach may work and where it will not work. In any case, it is useful to study it and keep it in the library even if it is classified as a rare case. It is easier to provide critique than to suggest something constructive. Lets phrase Leonid for doing the constructive part and being innovative. Lets thank Robert for providing the algorithm! > > Take care, > Pavel > On Thu, Jan 16, 2014 at 07:48 PM, Nick Holford wrote: > > Pavel, > Unless your drug is an alkylating agent the use of AUC will always > be mechanistically wrong. > I hope you also considered the possibility of disease progression > (i.e. changing baseline) and also the possibility of changing C50 > due to potentiation or physiological changes. > Nick > > On 17/01/2014 1:29 p.m., [email protected] wrote: > > > Hi Pavel, > > You mentioned that the effect compartment did not help, and the model I > > suggested is identical to the effect compartment. May be try something like > > transit compartment model: > > > > DADT(2)=C-K0*A(2) > > DADT(3)=K0*A(2)-K0*A(3) > > ... > > DADT(X)=K0*A(X-1)-K0*A(X) > > > > AUCapprox=A(2)+...+A(X) > > > > This will prolong the shape of AUCapprox(t). It could be a bit simpler and > > smoother than tlag implementation > > Leonid > > > > Original email: > > ----------------- > > From: Pavel [email protected] > > Date: Thu, 16 Jan 2014 13:05:54 -0500 (EST) > > To:[email protected],[email protected] > > Subject: RE: [NMusers] backward integration from t-a to t > > > > Hello Leonid, > > > > Thank you bein helpful. You got the main point. AUC is a better > > predictor than concentration, but it has to disppear very slowly but > > surely. > > > > A potential challenge is biological meaning of this approach. It will > > be necessary to explain it to the biologists, who ask question like "Why > > do you use 2 compartment in PK model while human body has so many > > compartments?". > > > > We will see! > > > > Thanks, > > Pavel > > > > On Wed, Jan 15, 2014 at 01:19 AM,[email protected] wrote: > > > > > 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 [email protected] > > > Date: Tue, 14 Jan 2014 13:45:18 -0500 (EST) > > > To:[email protected],[email protected] > > > Subject: [NMusers] backward integration from t-a to t > > > > > > Dear Robert, > > > > > > Ã, > > > > > > Efficacy isÃ, frequently considered aÃ, function of AUC.Ã, (AUC is just > > > an integral. It is obvious how to calculate AUC any software which can > > > solve ODE.)Ã, A disadvantage of this model of efficacyÃ, is that the > > > effect is irreversable becauseÃ, AUC of concentration can only > > > increase;Ã, it cannot decrease.Ã, In many cases, a more meaningful model > > > is a model where AUC is calculated form time tÃ, -a to t (kind of > > > "moving average"), where t is timeÃ, in the system of differential > > > equations (variable T in NONMEM).Ã, Ã, There are 2 obvious ways to > > > calculate AUC(t-a, t).Ã, The first is to do backward integration, which > > > looks like a hard and resource consuming way for NONMEM.Ã, The second > > > one is to keep in memory AUC for all time pointsÃ, usedÃ, during theÃ, > > > integrationÃ, 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.Ã, > > > > > > Ã, > > > > > > Is there a way toÃ, access AUC forÃ, the past time points (> integration > > > routine?Ã, It seems like an easyÃ, thing to do.Ã, Ã, Ã, > > > > > > Ã, > > > > > > Kind regards, > > > > > > PavelÃ, Ã, > > > > > > -------------------------------------------------------------------- > > > mail2web - Check your email from the web at > > > http://link.mail2web.com/mail2web > > > > -------------------------------------------------------------------- > > myhosting.com - Premium Microsoft® Windows® and Linux web and application > > hosting - http://link.myhosting.com/myhosting > > -- Nick Holford, Professor Clinical Pharmacology > > Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A > University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand > office:+64(9)923-6730 mobile:NZ +64(21)46 23 53 > email:[email protected] > http://holford.fmhs.auckland.ac.nz/ > > Holford NHG. Disease progression and neuroscience. Journal of > Pharmacokinetics and Pharmacodynamics. > 2013;40:369-76 http://link.springer.com/article/10.1007/s10928-013-9316-2 > Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and > adults. J Pharm Sci. > 2013: http://onlinelibrary.wiley.com/doi/10.1002/jps.23574/abstract > Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. > 2013;2: http://www.nature.com/psp/journal/v2/n5/full/psp201318a.html > Holford NHG. Clinical pharmacology = disease progression + drug action. > British Journal of Clinical Pharmacology. > 2013: http://onlinelibrary.wiley.com/doi/10.1111/bcp.12170/abstract -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand office:+64(9)923-6730 mobile:NZ +64(21)46 23 53 email: [email protected] http://holford.fmhs.auckland.ac.nz/ Holford NHG. Disease progression and neuroscience. Journal of Pharmacokinetics and Pharmacodynamics. 2013;40:369-76 http://link.springer.com/article/10.1007/s10928-013-9316-2 Holford N, Heo Y-A, Anderson B. A pharmacokinetic standard for babies and adults. J Pharm Sci. 2013: http://onlinelibrary.wiley.com/doi/10.1002/jps.23574/abstract Holford N. A time to event tutorial for pharmacometricians. CPT:PSP. 2013;2: http://www.nature.com/psp/journal/v2/n5/full/psp201318a.html Holford NHG. Clinical pharmacology = disease progression + drug action. British Journal of Clinical Pharmacology. 2013: http://onlinelibrary.wiley.com/doi/10.1111/bcp.12170/abstract