A SASIML program for simulating pharmacokinetic data 51
Table 2
Influence of subject number on bioequivalence determinations Between-subject parameter values
K
a
h
− 1
V
c
Lkg F
K
el
h
− 1
a Simulation conditions for treatments 1 and 2 one-compartment model
a
Treatments 1 and 2 2.0 30
1.0 15 0.50 20
0.327 15 Subjtrt
10 15
20 24
30 40
100 1000
b Simulation output Reject AUC
0.519 0.435
0.355 0.305
0.268 0.216
0.035 Reject C
max
0.398 0.315
0.236 0.206
0.173 0.117
0.11 Accept both
0.389 0.495
0.594 0.639
0.687 0.762
0.961 1.0
a
Results if one considers the entire subject population. AUC 162 g hmL, 29 CV; C
max
= 35 mgmL, 26 CV; parameter values for treatments 1 and 2 are identical.
equivalent. However, the ability to confirm equiva- lence under these conditions is generally limited by
traditionally small number of observations included in these trials. Therefore, we modified the num-
ber of subjects included per treatment, increas- ing study size from 10 to 1000. We conducted one
thousand iterations of each run, and the propor- tion of successful runs where equivalence was con-
firmed were assessed
Table 2 . As expected, the
power of the study to confirm bioequivalence in- creased as the number of subjects tended towards
infinity.
4.4. Dosing schedule
We simulated the two examples described previ- ously in Section
3 . For the example of the profiles
resulting from sporadic input, either 12 or 21 doses were administered. Due to the rapid terminal elim-
ination half-life used in these simulations, the re- sults obtained on each dosing day was identical. The
results of a 12 or 21 dose input schedule is provided over 2 dosing days in
Fig. 5 .
We also simulated a random input schedule where the total dose is 100.0 mg and that this dose
is administered once daily for three consecutive days or 33.3 mg per day. Each daily dose is ran-
domly administered five times during the 24 h in- terval. The results of this simulation simulated in
four animals, using a one-compartment open body model with rapid input K
a
∼ 2 h
− 1
and elimination T
12
∼ 2 h is provided in
Fig. 6 .
4.5. Analytical noise
This simulation is based upon the identical one com- partment body model previously described, sim-
ulated without noise and without subpopulations. Using the pharmacokinetic parameter values de-
scribing treatment 1 of the one-compartment open body model, the error about each simulated con-
centration was defined by an 80 confidence that
Fig. 5
Graph of two multiple input schedules 12 or 21 scheduled inputs that may be used to mimic some known rate of drug consumption when administered in food or in water.
52 E. Russek-Cohen et al.
Fig. 6 Simulation of four subjects receiving five random inputs over a 3-day dosing interval. Dose amount = 33 mgday,
T
12
∼ 2 h.
the assayed values will fall within 70 and 143 of the true value. An example of the effect of assay
noise on the distribution of observed concentrations e.g., the hour 2 sample is provided in
Fig. 7 . To
show the impact of model specification normally distributed untransformed input parameters versus
ln-normal distribution of input parameter and as- say noise on the means and variances of the con-
centrations at each sampling time considered for the 1000 replications of 24 subjects per treatment,
the resulting concentration versus time profiles are compared in
Table 3 mean and CV for treatment 1.
Fig. 7
Example of the effect of adding assay noise to the simulated concentrations: frequency plots of the hour 2 drug concentrations are provided when simulated without Graph A and with Graph B assay noise. Concentrations
are based upon parameters used to simulate the treatment 1 values for the one-compartment body model. The error was defined by 80 confidence that the assayed values fall within 70 and 143 of the true value.
A SASIML program for simulating pharmacokinetic data 53
Table 3
Impact of assay noise on drug concentrations gmL and population variance expressed as CV Time h
Untransformed parameters no noise
Untransformed parameters with noise
ln-Transformed parameters no noise
Mean CV
Mean CV
Mean CV
0.25 19.02
0.32 19.76
0.44 19.00
0.32 0.5
28.85 0.29
30.17 0.42
28.85 0.29
1 35.00
0.26 36.33
0.39 35.00
0.26 1.5
33.79 0.25
35.18 0.39
33.79 0.25
2 30.38
0.25 31.50
0.38 30.38
0.25 3
22.92 0.27
23.79 0.40
22.92 0.27
4 16.85
0.30 17.63
0.43 16.85
0.30 6
8.99 0.37
9.40 0.48
8.99 0.37
8 4.82
0.46 5.00
0.55 4.82
0.46 12
1.42 0.66
1.48 0.74
1.42 0.65
16 0.43
0.90 0.45
0.98 0.43
0.91 24
0.05 1.51
0.05 1.57
0.05 1.51
36 0.0019
2.85 0.0020
3.00 0.0019
2.89 48
0.0001 4.77
0.0001 5.00
0.0001 5.00
4.6. Varying parameter constraints and population characteristics
