**Design of Pediatrics Population Pharmacokinetic Studies: Study Power,
Precision, and Accuracy**

**(Draft ****10/16/03****)**

Peter
I. Lee, He Sun, Larry Lesko

Office
of Clinical Pharmacology and Biopharmaceutics

Center
for Drug Evaluation and Research

II.
Study Design Factors

III.
Methodology

This
document is intended to provide general concepts and technical basis for
developing a study design template of pediatrics population pharmacokinetics
studies. Population pharmacokinetics
studies can be used in NDA submissions for identifying pharmacokinetics changes
due to intrinsic factors, such as age, body weight, body surface area, and
gender. For pediatrics
pharmacokinetics studies, the sparse sampling design is specially justified by
the need of minimizing the blood volume taken from each child, and by a better
study feasibility to take less samples in outpatient settings.

The
quality of the results and conclusions from population pharmacokinetic studies
depend very much on the quality of the study design and conduct. This document is intended to address the
influence of the study design factors on the results of population
pharmacokinetics studies.

The
quality of a population pharmacokinetic (PPK) study design can be measured by
the statistical power to achieve the study objectives, which may include (1)
identifying a difference in pharmacokinetics between adults and pediatrics, and
(2) accurately estimating pharmacokinetic parameters in pediatrics without
bias. The results of the first objective
will support whether a dose adjustment is needed for pediatrics, and the
results of the second objective will provide the basis for estimating the
required dose adjustment in pediatrics.
This document discusses some of the key study design factors that
influence the study power and prediction errors of a population pharmacokinetic
study. Study simulation is an
established methodology for examining the design of population pharmacokinetic
studies. This document briefly describes
the simulation methodologies that will be used for constructing the pediatrics
PPK study design template.

**Due to the complexity and
interplay between different design factors, no single standard study design is
recommended for all scenarios. Study
simulation should be conducted on the case-by-case basis to ensure the quality
of the study design and outcomes.**

The contents of this document should be
considered in light of the “FDA Guidance for Industry: Population Pharmacokinetics”.

II. Study Design Factors

The
main objective of a pediatric pharmacokinetics (bridging) study is to provide
pharmacokinetics information as a basis, in conjunction with known
exposure-response relationship, for dose adjustment in the pediatric population. A decision process for recommending dose
adjustment in special populations was proposed in the Clinical Pharmacology
Subcommittee (CPSC) Meeting on

To
provide sufficient information for a decision on recommending a dose adjustment
for the pediatric patients, a pediatric population pharmacokinetic (PPK) study
should be designed to determine whether there is a clinical significant
difference in pharmacokinetics between pediatrics and adults, and to accurately
estimate the pharmacokinetic parameters of the pediatric population.

Many
study design factors may influence the experimental outcomes of the population
pharmacokinetic (PPK) studies and their analysis results. Important PPK study design factors include
the number of subjects (total and sub-population), sampling scheme (number of
samples per subject, nominal sampling time, variability of actual sampling
time, and whether extensive samples are taken in some subjects). In addition, the study design should also
account for study conduct factors such as compliance of the patients (the
variability of dosing time, whether the variability is recorded and accounted
for in the analysis, consistent dosing pattern, missing doses, and whether the
missing doses are recorded and accounted for in the analysis). Other non-design, drug-specific factors may
also affect the quality of the study result.
They include inter-subject and intra-subject variability of the
pharmacokinetics.

Due
to the complexity and many varieties of study designs, it is not realistic to
recommend a one-size-fit-all design.
However, there are some basic points for general consideration during
the study design.

· The study performance should
be estimated in terms of the specific study objectives, which may include (1)
identifying if there is a clinical significant difference in pharmacokinetics
between adults and pediatrics, and (2) accurately estimating pharmacokinetic
parameters in pediatrics without bias.

· Dosing time and sampling
time should be recorded during the study conduct and accounted for in the data
analysis. If the deviations from the nominal times might be non-ignorable,
analysis plans to deal with this are particularly important.

· Compliance is an important
factor that influences the study outcomes.
It should be considered in the study design and simulation, and if
compliance is to be used in the analysis of the study, the latter should
include consideration of the possibility that compliance is a confounder.

· More samples per subject,
and more importantly, more subjects usually provide better study performance if
the study design remains otherwise the same.

· Studies with greater intra-
or inter- subject variability require more samples per subject or more subjects
per age group to achieve similar performance.

· Distribution of the sampling
times among subjects should cover the full dosing interval as much as possible
to describe the concentration-time profile.

· Fixing sampling time among
subjects (ie, same sampling time for all subjects) may be inferior to
randomizing sampling times, especially when the number of samples permitted per
subject is insufficient to fully identify each subject’s full structural model.

· Unbalanced design (ie,
different number of samples per subject or sampling time between
sub-populations), if these design differences are not randomly assigned (i.e.
may be informative), may bias study results.

· One-sample-per-subject
design does not allow intra-subject variability and inter-subject variability
to be distinguished, and may result in biased estimates of either. At least some subjects (preferably most or
all) should be studied with an intra-subject design adequate to fully identify
their individual model.

· To obtain good estimations
of Ka, Cl and their variability, samples in the absorption and elimination
phases, respectively, should be collected.
Concentration of sampling times in a particular region of the dosing
interval (eg, troughs in all subjects) may result in poor study outcomes.

· Study simulation is
recommended as a best practice to determine study performance (power,
precision, and accuracy). All relevant
study design factors should be considered in the simulation.

Figure
1. The revised decision tree for
recommending dose adjustment in special populations (to be presented at the
CPSC Meeting on

III. Methodology

Commonly
used population pharmacokinetic models were described in the literature
[Sheiner & Grasela, J Pharmcokinetics and Biopharmaceutics, 19(3):11S,
1991].

For
example, a general pharmacokinetic structural model can be expressed in the
following equation:

_{} (1)

where C_{ij} is the plasma
concentration of subject i at measurement j, p_{i,k} is the k-th
pharmacokinetic parameters of subject i, and e_{ij} is the intra-subject variability
. The individual PK parameters can be expressed in terms of population typical
parameters and inter-subject variability.

_{} (2)

where q_{k } is the typical population value of p_{k},
and h_{i,k} is the inter-subject
variability of the parameters for subject i.

When a pharmacokinetic parameter (say,
clearance) changes in a sub-population that is defined by covariate *G*, a covariate model can be used to
describe the typical population parameter as a function of the covariate or the
treatment group. For example:

_{} (3)

where q_{k } is the
typical value of pharmacokinetics parameters for the population, G is the
covariate defining the sub-population, and q_{n} are
the parameters determining the relationship between the typical population
parameter value and the covariate

Study Performance - Identifying clinically significant difference in pharmacokinetics between pediatrics and adults

_{}Ho: DCl=0 (4)

where
DCl is the difference in clearance between the
pediatric and the adult populations. The
alternative hypothesis can be that DCl_{ }is equal to a
value that is considered clinically significant.

H_{1}: DCl/ Cl_{typical}
= x% (5)

where
x% is the minimum difference in clearance that is considered clinically
significant. The selection of the
alternative hypothesis will depend on the pharmacokinetics/pharmacodynamics
relationship to identify the clinical significant change in clearance. Assuming the pharmacokinetics follow Equation
(1)-(3), the significance of DCl can be tested by fitting
two models to the pharmacokinetic data: Model 1 is represented by Equations
(1)-(2) and Model 2 is represented by Equations (1)-(3). The values of DCl is considered different
from 0 by performing the likelihood ratio test between the two models.

Study
simulations can be conducted to estimate the PPK study power based on the above
hypotheses. A number of replicate
studies and analyses are simulated with the assumption of either the null or
the alternative hypotheses. The false
positive and false negative rates are then estimated by counting the percentage
of the replicates that show opposite results than the assumed hypothesis. The common study simulation procedure for
power estimation is described later in this document.

It
should also be recognized that if the null hypothesis (Equation 4) is found
statistically significant based on the study outcomes, it does not necessarily
indicate that the difference is clinically significant even if the study has
been designed (with the alternative hypothesis, Equation 5) to detect such a
difference. However, the pharmacokinetic
parameter estimation should be reasonable accurate based on the study that is
designed to detect a significant difference in pharmacokinetics. The second objective for the pediatric PPK
study is to further ensure an accurate estimation of pharmacokinetic parameters
in pediatrics, so that the dose in the population can be adequately selected.

The second
key information to be provided by a pediatric PPK study is the estimated
pharmacokinetic parameters in pediatrics (Figure 2). There are several ways for
examining the precision and accuracy of parameter estimation from population
pharmacokinetics studies. Since the
"true" parameter values were known in the simulations, the accuracy
and precision of parameter estimation could be quantified. Both the degree of
bias and the precision of estimates relative to true values are of interest and
were computed.

To express bias and precision on the same scale, percentage prediction errors are computed. For each run and for each parameter, the difference between the true value

q_{k}
and the estimated value _{} was expressed as a
percentage of the true value (i.e., percentage prediction error, %PE).* *Thus,

_{} (6)

where *k* denotes the k-th parameters. A number of replicate studies can be
simulated to estimate PE%. The mean %PE
of all replicate studies can be used as a measure of accuracy, and SD of all
%PE as a measure of precision of parameter estimation.

Precision can
also be computed using:

_{} (7)

and bias can
be defined as

Generating PK Parameters

The
basic pharmacokinetic model, e.g., Equations 1-3, used to simulate the data is
first assumed based on prior knowledge of the drug. Typically, only the
pharmacokinetic model in adults is available at the time of designing a
pediatric PPK study. A hypothesis, e.g.,
Equation (5), can be made to assume the minimum scenario to be identified by
the PPK study, in which the pharmacokinetics of the pediatric population is
clinically significantly different from that of adults.

The following factors should be considered in
the simulations: (1) study design: e.g., the number of subjects, number of
samples, sampling time(s), [lbs1] variability of actual
sampling time, whether full profile is taken in some subjects, and (2)
deviation from protocol design [Sheiner & Steimer, Annu. Rev. Pharmacol.
Toxicol, 40:67, 2000]: e.g., the variability of dosing time, consistent dosing
pattern, and missing doses.
Pharmacokinetics covariates
should also be considered in the simulation: e.g., inter-subject variability of
pharmacokinetics.

Simulating Study Conduct

In
addition to the above factors considered in the simulation process for study
design, the following should also be considered for study conduct: whether the
actual dosing time is recorded and accounted for in the analysis, and whether
the missing doses are recorded and accounted for in the analysis.

Generating Population PK Data

The population pharmacokinetics data can be
generated by accounting for pharmacokinetic variability and study design and
study conduct factors, using the pharmacokinetic model (1)-(3). Study-related variables in individual
subjects, including sampling time, concentration, dosing time, and compliance
pattern, can also be generated via simulation for different study design
scenarios.

For each study design factor considered, a
large number of replicates are simulated and fitted to the models. To estimate the study power, standard methods
(such as likelihood ratio test) for estimating significance of DCl (Equation 3) can be used to test the
Hypothesis (6) for each replicate. The
number of replicates (Np) is counted for those that resulted in significant
sub-group effect. The ratio of this
number (Np) to the total number of replicates is the estimated power of the
study.

The prediction errors are usually estimated
by examining the mean and SD (among replicates) of %PE, bias, or precision
defined in Equations (6) – (8).

[lbs1] What does this mean?