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| EXOGENOUS SUPPLEMENTATION EXAMPLE |
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DISCUSSION:
In this example, an oral "drug" is given exogenously, and it also
exists as an endogenous substance. There is an unknown dosing history
prior to the observation period (i.e., prior to time zero). This
example illustrates how three sources of drug can be modeled: pre-
existing endogenous drug, pre-existing drug from an unknown prior dos-
ing history, and drug from known doses. Any combination of the three
could be modeled without the others.
The rate of endogenous drug production is assumed to be constant, with
no feedback control of production. Thus endogenous drug is at steady-
state, and, with linear kinetics, its effect is simply to add a con-
stant increment to exogenous drug in the sampled compartment (the
increment is modeled as theta(7)).
For the drug with unknown dosing history, it is assumed that the sub-
ject is at steady state with respect to this drug. This part of total
drug is modeled by a steady state infusion dose into the depot com-
partment, ending at time 0, and having an unknown rate. The result of
the SS dose is to introduce drug into all compartments of the system
(not just the central compartment) because it is distributed
throughout the system and is subject to elimination from the system.
The unknown rate is modeled as theta(5). NONMEM will adjust theta(5)
to best fit not only the "baseline" observation at time 0, but also
the later observations.
Note that if samples are not taken sufficiently long after the time of
the last dose ( > 4 half-lives), then theta(7) and theta(5) may not be
separately identifiable. Note that the value of theta(7) may be
determined by the residual concentration after all exogenous drug has
disappeared.
A combined additive and ccv error model is used. Theta(8) is the ratio
of the C.V. of the proportional component to the standard deviation of
the additive component.
Any ADVAN/TRANS combination could be used. Population data could also
be modeled in this manner, with eta variables in the $PK block.
$PROBLEM Example of pre-existing drug.
$INPUT ID TIME DV AMT SS II RATE
$DATA DATA1
$SUBROUTINES ADVAN4 TRANS5
$PK
AOB=THETA(1)
ALPHA=THETA(2)
BETA=THETA(3)
KA=THETA(4)
R1=THETA(5)
S2=THETA(6)
$ERROR
FP=THETA(7)+F ; adds endogenous component
W=(1+THETA(8)*THETA(8)*FP*FP)**.5
Y=FP+W*ERR(1)
Note that, if there are other doses into the depot compartment with
modeled rates, it is necessary to assign a value to R1 conditionally.
E.g.,
IF (TIME.EQ.0) THEN
R1=THETA(5) ; rate for SS infusion record at time 0
ELSE
R1=....; rate of other kind of dose
ENDIF
Note also that the combined additive and ccv error model can also be
modeled using two random variables:
Y = F*(1+ERR(1)) + ERR(2)
A fragment of the data follows. Record 1 specifies the SS infusion
for the pre-existing drug, which ends at time 0. Record 2 gives the
baseline observation. Record 3 specifies an oral bolus dose. Record
4 gives an observation.
1 0 . 0 1 0 -1
1 0 62.2 . . . .
1 0.01 . 95 . . .
1 0.50 235.93 . . . .
REFERENCES: Guide V Section 8
REFERENCES: Guide VI Section III.F.5
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