PD initialization

From: ABoeckmann <alison@c255.ucsf.edu> Subject: PD initialization Date: Mon, 9 Oct 2000 10:05:41 -0700 (PDT) There has been some discussion on how to initialize a baseline value for a PD compartment. I'll try to summarize what everyone has said on this. Basically, I agree with everyone. Different techniques were suggested, but they all can be used in this case. Atul's original question: > I am trying to PK/PD model a data set where the PD is explained by an > indirect response model with the production of the endogenous substance > suppressed by the drug. > > $DES > DADT(1)=-K*A(1) ; PK > CP=A(1)/S1 > EFF=1-CP/(CP+EC50) > DADT(2)=K0*EFF-KE*A(2) ; PD > > The value of the PD parameter is 10 ng/ml in the absence of the drug. > i.e at time zero > In the DV column, I put DV=10 with CMT=2. > > When we fit the data, why is it that the PD value at time zero starts at > zero instead of 10? > > I looked into page 331 in the help guide. It says that i should > initialize the system with a bolus dose into the PD compartment. > I don't exactly understand what is intended? I don't know what he means by the "PD parameter". People seem to think he means "the amount in compartment 2". Vladimir Piotrovsky and others suggested initializing CMT 2 by putting a dose record with AMT equal to 1 at time 0. In $PK, you must assign to F2 the baseline level of A(2). This causes PREDPP to multiply 1 by the the baseline level of A(2) when the "dose" is put into compartment 2. F2 can be modeled in different ways. Vladimir suggests using the steady state solution to the D.E. DADT(2)=K0*EFF-KE*A(2)=0, which is (when DADT(2)=0 and EFF=1) A(2)=K0/KE. He suggests: $PK ... F2 = K0/KE This seems quite correct. Bill Bachman writes: > What Vladimir is telling you to do is essentially to define the initials > condition for your differential equation for cmt=2 by putting a value in the > AMT column (not in DV). However, unless there is a scaling factor you did > not specify, I believe that amount should be 10 (not 1). Bill's suggestion (F2=10) is appropriate to Atul's original statement, if we assume that Atul wants to put exactly 10 in compartment 2. Jogarao Gobburu writes: > 1. Another way to code this is to include SS data item(=1 for > CMT=2,else =0 if pk is not at steady-state) to specify that PD is at > steady-state before dosing. You have to provide another data record for > your 'observation', as you do with most PK problems. AMT=0 indicates > steady-state with constant rate infusion (see help guide 'AMT'). eg: #ID TIME AMT SS CMT DV ... 1 0 0 1 2 . 1 0 . 0 2 10 1 0 100 0 1 . This is not incorrect - this should give the same result as Vladimir's suggestion. A steady state does is appropriate when there is no easy analytic solution, e.g., when there are more than 1 compartments to be initialized. Here, it is not necessary and will take more computer time. But now, Raj seems to want to do more: > The suggestion by Dr.Piotrovskij is that we add an AMT data at > time=0 for initializing the PD parameter. In fact myself and Atul > were attempting the same way and it has a bug in it. It does not > FIT the PD data at time=0. Instead, if we give a value of (say) > 3.5 (which is actually the concentration at t=0) as the AMT, the > PRED will be 3.5 (at t=0). In the second subject, if we give 4.5 as > AMT, PRED will return as 4.5. Is there any alternative way of > fitting E0? Atun said the baseline amount in A(2) (the PD value) was known and was constant. Now, it appears to be different for each subject. I think there are two ways to go. If the inter-subject difference is due to differences in K0 and/or KE, then F2 = K0/KE This allows NONMEM to estimate K0 and KE so to best fit both the baseline and the subsequent observations. If the baseline varies according to unknown influences, then a theta could be introduced. E.g., F2= THETA(x) Let NONMEM estimate this theta. Either way, each subject's data set needs both a dose record at time 0 (with CMT = 2 and AMT = 1), and an observation event record at time 0 (with CMT=2, DV= observed baseline value, e.g., 3.5 or 4.5), so that the baseline can be fit. eg: #ID TIME AMT CMT DV ... 1 0 1 2 . 1 0 . 2 3.5 1 0 100 1 .