From: Rebecca Wrishko <wrishko@unixg.ubc.ca>
Subject: Predicted Concetration derivations
Date: Wed, 17 Nov 1999 11:54:12 -0800

The assistance of the group would be greatly appreciated in solving the following question, how does NONMEM generate the predicted serum concentrations at the times for which there is a corresponding event record? Implementing Advan1 Trans2 (NMTRAN control stream below) and Advan3 Trans3 (NMTRAN control stream below) subroutines for the pk modeling of vancomycin in a small pediatric population, I was able to obtain final parameter estimates of CL, V and etas (One-Compartment) and Cl, V, Vss, and etas (Two-Compartment). I have attempted using the final PK parameter one- and two-compartment estimates of CL and Vss, obtained from the modeling routines to calculate expected drug concentrations and do not derive the same values as those generated from the NONMEM execution. How are the fixed (theta) and random (eta) parameters incorporated into the formulae for calculating the predicted serum concentrations?

Thank you
Rebecca

NM-TRAN 1:
\$SUBROUTINES ADVAN1 TRANS2; One Compartment Linear Model
\$PK
CL=THETA(1)*EXP(ETA(1)) ; mean clearance
V=THETA(2)*EXP(ETA(2)) ; mean central volume
K=CL/V ;reparameterization required
S1=V
\$THETA (0,4.) ; clearance estimate
(0,10.) ; volume estimate

\$OMEGA .04 .04 ; twenty percent cv

\$SIGMA .02 ; ten percent cv

\$ERROR
Y=F+ERR(1)

\$ESTIMATION MAXEVAL=450 SIGDIGITS=4

\$COVARIANCE

NM-TRAN 2:
\$SUBROUTINES ADVAN3 TRANS3; Two Compartment Linear Model
\$PK
CL=THETA(1)*EXP(ETA(1)) ; mean clearance
V=THETA(2)*EXP(ETA(2)) ; mean central volume
VSS=V+THETA(3)*EXP(ETA(3))
Q=THETA(4)

K=CL/V; reparameterization lines
K12=Q/V
K21=Q/(VSS-V)
S1=V

\$THETA (0,3)
(0,5)
(0,10)
(0,3)

\$OMEGA .25 .25 .25 ; fifty percent cv

\$SIGMA .04 ; twenty percent cv

\$ERROR
Y=F+ERR(1)

\$ESTIMATION MAXEVAL=450 SIGDIGITS=4

\$COVARIANCE

Rebecca Wrishko
Division of Clinical Pharmacy
Faculty of Pharmaceutical Sciences
University of British Columbia
Email: wrishko@unixg.ubc.ca

*****

Date: Wed, 17 Nov 1999 13:57:22 -0800 (PST)
From: ABoeckmann <alison@c255.ucsf.edu>
Subject: Re: Predicted Concetration derivations

I don't think the group can help with this. I'll respond only to the question about the 1st. control stream because the kinetics are so simple. Maybe this will be sufficient.

Because Rebecca included the reparameterization from CL and V to rate constant K, she does not need to use TRANS2. It simply repeats the reparameterization. She could save some run time using ADVAN1 TRANS1, but this should not affect the outcome of the run.

She does not show us her dosing records. Suppose there is only a single bolus dose AMT at T0. THen the calculation of A0, A1, A2 at event times T0, T1, T2, etc. is:

A0=AMT
A1=A0*EXP(-K*(T1-T0))
A2=A1*EXP(-K*(T2-T1))

The predictions PRED0, PRED1, PRED2, etc. at these event times are
PRED0=A0/S1
PRED1=A1/S1
PRED2=A2/S1

With the default method of estimation, etas are 0. In the above,

K=theta(1)/theta(2)
S1=theta(2)

If there are multiple bolus doses, they are added when appropriate. E.g., if there is a dose AMTi at time Ti, then Ai=Ai (from above)+AMTi

If there are infusions, the equations are more complicated.

I do not know why she cannot get the same values from "the modeling routines". But make sure that the thetas are the same. If REbecca is plugging in thetas derived from other routines into NONMEM, then DO NOT RUN THE ESTIMATION STEP!!

>From Rebecca:

NM-TRAN 1:
\$SUBROUTINES ADVAN1 TRANS2; One Compartment Linear Model
\$PK
CL=THETA(1)*EXP(ETA(1)) ; mean clearance
V=THETA(2)*EXP(ETA(2)) ; mean central volume
K=CL/V ;reparameterization required
S1=V

\$THETA (0,4.) ; clearance estimate
(0,10.) ; volume estimate

\$OMEGA .04 .04 ; twenty percent cv

\$SIGMA .02 ; ten percent cv

\$ERROR
Y=F+ERR(1)

\$ESTIMATION MAXEVAL=450 SIGDIGITS=4

\$COVARIANCE