A SASIML program for simulating pharmacokinetic data 49
Table 1
Example of the program’s summation of sim- ulation results
The means procedure Variable
Mean Sum
Std Error rejauc
0.9980000 998.0000000
0.0014135 rejcmax
1.0000000 1000.00
bothacc
h. simulated sampling times. 2. Treatment summary:
a. parameter correlation coefficients; b. computed parameter standard deviations;
c. covariance matrix; d. expected versus observed parameter means
and standard deviations. 3. Output summary:
a. mean concentration versus time profiles, mean and standard deviation for AUC, C
max
, and T
max
; b. proc univariate output for all parameters and
concentrations at each sampling time; c. schematic plots comparing treatment popu-
lation characteristics for the input parame- ters, drug concentrations at each sampling
time, and bioavailability parameters; d. to facilitate the evaluation of the results over
a large number of replicates, the number of trials and proportion of the total number of
replications that fail or succeed in meeting the bioequivalence criteria are summarized
at the end of the simulation output. A sample output summary is featured is
Table 1 .
Under the column titled ‘‘Mean’’, this table pro-
vides a synopsis of the fraction of the total number of replicates that failed to have confidence inter-
vals contained within the bounds defining equiva- lence with respect to AUC rejauc and C
max
rejc- max
. The proportion of simulated replicates when both AUC and C
max
are contained within the bioe-
quivalence criteria bothacc is also provided. The output also indicates the total number of replicates
that fall within each of these categories Sum, and the standard error about the mean ratio Std Error.
4. Typical sample runs of the program
Identical seeds were used for all simulations in the following examples so that the output can be iden-
tical except for changes specified by the coded pa- rameters.
4.1. One-compartment open body model
To demonstrate the data generation potential of this program, the various attributes are variants
of the output generated with a one-compartmental open body model.
Model specifications 1. Subject per treatment = 24.
2. Number of replications = 1000. 3. Total dose = 100 mg.
4. Reference product parameter mean values:
K
a
= 2 h
− 1
; V
c
= 1 Lkg; F = 0.50; K
el
= 0.327 h
− 1
. To demonstrate product inequivalence, the test
product parameter values are K
a
= 1.0 h
− 1
and F
= 0.35. 5. Correlation coefficients: The parameter output
for the test and reference products will be based upon the identical correlation matrix, where the
correlation coefficients for each contrast are set to 0.1. This minimizes the constraints about the
resulting parameter values. Clearly, in some sit- uations e.g., hepatic disease there can be con-
comitant changes in drug clearance and there- fore K
el
and volume of distribution as the con- centrations of serum albumin decrease
[43] . Al-
ternatively, there may be a relationship between K
a
and F, particularly if the drug is associated with a limited window of absorption within the
small intestine. In these cases, F and K
a
may be highly correlated
[44] . Consequently, the in-
vestigator needs to consider these physiological and pharmacokinetic properties when establish-
ing the correlation coefficients. 6. Variability estimates: The relative standard de-
viation of the reference product are as follow: K
a
= 0.25; V
c
= 0.15; F = 0.20; K
el
= 0.15. For the test product, the relative standard deviation are
K
a
= 0.35; V
c
= 0.15; F = 0.30; K
el
= 0.15. Parame- ters are normally distributed.
7. Measurement error: Under the basic simula- tion conditions, there was no assay error, no
pre-selected LOQ, and no subpopulations. Since the various dosing options have already been
demonstrated, all other simulations were con- ducted as a single bolus administration.
The mean concentrationtime profile for this simulation is shown in
Fig. 3 .
4.2. Two-compartment open body model
To demonstrate the data generation potential of this program, the various attributes are variants of
the output generated with the one-compartmental open body model.
50 E. Russek-Cohen et al.
Fig. 3 Mean and standard deviation of concentrations at each sampling time. Data are based upon a one-compartment
open body model, using untransformed parameters, no assay noise and no specified lower limit of quantification.
Model specifications 1. Subject per treatment = 24.
2. Number of replications = 1000. 3. Total dose = 100 mg.
4. Reference product parameter mean values:
K
a
= 2 h
− 1
; V
c
= 1 Lkg; F = 0.50; ˇ = 0.135 h
− 1
; k
cp
= 0.9 h
− 1
; ˛ = 2 h
− 1
. To demonstrate product inequivalence, the test product parameter val-
ues are K
a
= 1.0 h
− 1
and F = 0.35. 5. Correlation coefficients: The parameter output
for the test and reference products are based upon the identical correlation matrix, where the
correlation coefficients for each contrast are set to 0.1.
6. Parameter variability estimates: The relative standard deviations of the reference product are
K
a
= 0.25; V
c
= 0.15; F = 0.20; ˇ = 0.15; k
pc
= 0.20; ˛
= 0.20. For the test product, the relative stan- dard deviations are identical to those of the
reference product, except that K
a
= 0.35 and F
= 0.30. All input parameters are normally dis- tributed.
7. Measurement error: All simulations are per- formed without any addition of analytical error.
The mean concentration versus time profiles generated under these simulation conditions are
provided in Fig. 4
.
4.3. Relative bioavailability determinations
To provide an example of the program’s ability to confirm product comparability, we simulated
two treatments containing pharmacokinetic param- eters associated with large intersubject variabil-
ity. The two treatments were identical with respect to mean and variance values, and thus were truly
Fig. 4
Mean and standard deviation of concentrations at each sampling time. Data are based upon a two-compartment open body model, using untransformed parameters, no assay noise and no specified lower limit of quantification.
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
