In this example, an oral "drug" is given exogenously, and it also exists as an endogenous substance. Additionally there is an unknown dosing history prior to the observation period (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.

The rate of the endogenous drug production is assumed to be constant, with no feedback control of production. Thus the endogenous drug is at steady-state, and, assumed with linear kinetics, its effect is an additive constant (THETA(7) in the model) to the exogenous drug in the sampled compartment.

For the drug with unknown dosing history, it is assumed at steady state, modeled by a steady state infusion dose into the depot compartment, ending at time 0, and having an unknown rate (THETA(5) in the model). 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 through-out the system and is subject to elimination from the system. Thus the THETA(5) estimate takes account of both the "baseline" observation at time 0 as well as 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. In the model THETA(8) is the ratio of the coefficient of variable of the CCV component to the standard deviation of the additive component.

Any ADVAN/TRANS combination could be used. Though for implementation is for single subject, the approach is equally applicable to population data.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15

 $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)

In the model the reserved variable R1 is the infusion rate in the depot compartment (see $PK). If there are additional doses into the depot compartment with modeled rates, it is necessary to assign a value to R1 conditionally, e.g.

1
2
3
4
5

  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

The combined additive and CCV error model can also be modeled using two random variables:

1

  Y = F*(1+ERR(1)) + ERR(2)

Below is a fragment of the data. 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
2
3
4

  1       0       .      0       1       0      -1
  1       0    62.2      .       .       .       .
  1    0.01       .     95       .       .       .
  1    0.50  235.93      .       .       .       .