44 E. Russek-Cohen et al.
Fig. 2 Simulation decision tree: options provided in this
SAS program.
of caution, an important limitation is that random number generators can potentially repeat a number
sequence if the quantity of values to be generated exceeds 2
31
. By using different seeds to generate data for each treatment or any subset of the data,
the time until repeats occur can be substantially increased.
3.2. Study design
At this point in time, the programmer can only spec- ify a parallel study design. However, a future iter-
ation of this program will allow for the simulation of crossover trials.
3.3. Pharmacokinetic model
Either a one- or two-compartment open body model can be selected:
1. ncompart = 1: this indicates that a one-
compartment model is selected. The user must define the mean and coefficient of variation for
four parameters: K
a
, V
c
, F, and K
el
. In this case, the equation for a two-compartment model is
used, but the values for k
pc
, k
cp
, and ˛ are set to zero.
2. ncompart = 2: this indicates the use of a two-
compartment model. The user must define means and coefficients of variation for K
a
, k
pc
, V
c
, ˛, F, and ˇ. The value of k
cp
is automatically defined based upon Eq.
13 .
Output parameters e.g., AUC and C
max
can be evaluated as if they followed a normal or a log-
normal distribution, and statistical tests can be run on the transformed or untransformed values.
As currently written, the ln-transformed param- eter values are used for estimating the confi-
dence intervals about the ratio of treatment means. Should the use of untransformed param-
eter values be preferred, coding will need to be revised to accommodate corresponding changes
in the equation for calculating confidence in- tervals about the difference in treatments ex-
pressed relative to the reference mean
[1] .
3.4. Constraints on F
In most situations, it is biologically inappropriate for values of F bioavailability to exceed 100 of
the administered dose. Therefore, the user has the option of using the following command to constrain
the simulated output of F for the test preparation:
Note: F = paramt[i, 3]
if paramt[i, 3] = 1 then paramt[i, 3] = 1; if paramt[i, 3] = .001 then paramt[i, 3] = .001;
This command needs to be specified separately for the test and reference groups. The same state-
ment can be used for the reference formulation by substituting paramr in place of paramt. This op-
tion is included as a command within the SAS code. By inserting an asterisk immediately prior to these
comments
Note: F = paramt[i, 3], the output will
not constrain F to fall between 0.001 and 1.0. If this parameter is simulated under the condi-
tion of a lognormal distribution, the code can be modified to read as follows:
Note: log F = paramt[i, 3]
if paramt[i, 3] = 0 then paramt[i, 3] = 0; if paramt[i, 3] = .001 then paramt[i, 3] = .001;
Note that an asterisk is placed before the last state- ment above because back transformed values equal
to or less than 0 cannot be generated when using a log scale.
A SASIML program for simulating pharmacokinetic data 45
3.5. Population considerations
Randomly generated pharmacokinetic parameters can follow either a normal, a ln-normal, or a mix-
ture of two normal distributions. While there are examples of simulated bioequivalence studies that
are based upon normally distributed parameters
[20,21,31] , many investigators argue that pharma-
cokinetic parameters such as clearance and vol- ume of distribution more closely follow a ln-normal
distribution [32—34]
. Differences in the simulation output resulting from the use of normal versus ln-
normal parameter distributions is provided else- where
[35] . Further arguments suggest that due to
the presence of subpopulations, neither a normal nor a ln-normal distribution can accurately describe
the pharmacokinetic parameters within a popula- tion. Jelliffe et al.
[36] notes that many patient
populations are composed of clusters of subpopu- lations, in which case neither the assumption of a
normal nor ln-normal parameter distribution is ap- propriate.
The user is asked to define parameter distribu- tion characteristics as follow:
1. PARMTYPE = 0: single multivariate normal distri-
