residual error model, endogeneous drug

From: Paul.Tanswell@bc.boehringer-ingelheim.com Subject: residual error model, endogeneous drug Date: Thu, 3 May 2001 09:46:45 +0200 NONMEM users: I am modeling single dose, 2-compartment i.v. pharmacokinetics of a drug X which exhibits endogenous plasma levels, in >100 individuals. In each subject, the baseline concentration of X was measured in one pre-dose sample, and multiple samples were subsequently measured for X post dose. The baseline levels are low compared to Cmax after exogenous dosing, but not negligible compared to the plasma levels measured at later time points. I followed the procedure suggested for such data in the NONMEM help guide (p312) and used the following code for the residual error (power model; was better than the additive + proportional model) $ERROR FTOT=F+CBAS W=FTOT**THETA(6) Y=FTOT+W*(EPS(1)) IPRED=FTOT IRES=CP-IPRED IWRES=IRES/W THETA(6) is the exponent in the power model. FTOT is the total plasma concentration estimate, comprising the sum of the exogenous (F) and endogenous (CBAS) drug concentrations. CBAS was allowed to vary between individuals in the $PK block (CBAS=THETA(5)*EXP(ETA(4)). The PK model is ADVAN 3 TRANS 4 with ETAs for CL, Q and V1, and a block structure for OMEGA. THE PROBLEM: 1. Although the model ran well and the plots of PRED vs DV and IPRED vs DV were satisfactory, the individual values of CBAS, which are a small cluster of values at the lower end of the DV range, were systematically underestimated by about 30%. A plot of IPRED (y) vs DV (x) just for the CBAS yielded an approximately linear relationship but with slope 0.68. 2. The code does not seem quite right to me. Considering CBAS, which is a single pre-dose endogenous measurement per subject, it seems logical to give it an ETA, but it does not seem reasonable to allow an EPS additionally. However, in the code as written, the estimate for the sum of the endogenous and exogenous drug (FTOT) allows both levels of random variability. When FTOT decreases to near CBAS or equals CBAS, then CBAS will effectively have both an ETA and an EPS assigned to it. My questions to the group: - is there a method of coding such that F but not CBAS is allowed to have an EPS assigned to it - would this remove the bias in the estimation of CBAS, - can one still get correct values for W and IWRES? Thanks for any help and best regards Paul Tanswell