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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5195_Библиотеки_им_академика_М_И_Перельмана.pdf
Whereas these equations predict drug concentrations after intravenous
bolus administration, they can also approximate drug concentrations following
oral administration if bioavailability, F, is added to the numerator and drug
absorption is much more rapid than drug elimination (KA much greater than
K). If the absorption rate does not greatly exceed the elimination rate, use of
these equations will result in overestimating the true peak and underestimating
the true trough concentrations. To characterize drug concentrations following
a single-dose oral administration using a one-compartment model with firstorder absorption, the following equation can be used:
SIZE AND AGE EFFECTS ON
PHARMACOKINETICS
Size is a critical element in understanding, analyzing, and applying principles
of PK in pediatrics. Weight (WT) can range more than 100-fold between
premature infants and adolescents and correlates strongly with age and other
clinical characteristics that may also impact a drug’s disposition. Pediatric
PK parameters are most often scaled by body weight. This scaling approach
has the advantage of being easy to calculate and apply to dosing resulting in
milligram per kilogram dosing. However, many physiologic functions that
affect drug clearance (renal function, cardiac output, and hepatic blood flow)
do not scale directly to weight in a linear manner. Estimated body surface
area (BSA) is an alternative scalar for many physiologic processes that affect
drug disposition. Using BSA rather than weight to scale for size in children
has been found empirically to provide a more linear relationship with
clearance for many drugs. However, scaling volume of distribution with BSA
may not be as linear as it is with weight. The use of BSA requires height
measurements to estimate, is prone to calculation errors, and is primarily
reserved for antineoplastic and other agents with very narrow therapeutic
indices. A third approach to scaling clearance is the allometric method.
Allometric scaling is used extensively in evaluating physiologic and
preclinical PK data across animal species. Since the 1940s, it has been
applied to adjusting drug doses in humans and is based on relating
physiologic functions and morphology to body size. This approach suggests
that WT
0.75
be used to scale clearance, and this scalar correlates closely with
percentage of liver weight relative to body weight during the first 18 years of
life (Fig. 2.10). It also suggests Vd be scaled by WT
1.0
, which results in shorter
half-lives in smaller, younger individuals, which is consistent with what is
results to scaling by BSA without requiring a height measurement. However,
like BSA, this method is prone to calculation errors and has limited clinical
application for estimating dosage in individual children. It is important to
recognize that these sizing approaches do not account for additional
maturational effects on processes that impact PK during human development.
Thus, in addition to these size effects, additional components that account for
developmental PK differences are necessary, especially in younger
populations. Linked allometric scaling with maturation models for
development of elimination pathways may be helpful to describe pediatric
PK.
Figure 2.10 Liver size as function of age. The relative liver weight (WT) as percentage of total body
weight shows decrease during infancy and childhood. This relationship closely mirrors the shape of the
allometric scaling factor WT
0.75
/WT (adjusted by a scalar to superimpose the two curves).
A more mechanistic approach can be used to describe pediatric PK based
on changes in body composition through physiologic-based PK (PBPK). This
approach incorporates organ sizes and tissue-specific drug partitioning along
with organ blood flows to describe drug disposition in the human body as a
system of blood flows and tissue partitioning. These models require a large
number of differential equations to characterize the drug concentration-versustime profile and thus cannot be used to estimate PK parameters based on
individual patient’s PK data. However, the PBPK approach is very useful for
predicting the impact of physiologic and maturational changes on drug
exposure in plasma and tissues. PBPK modeling is widely used in
environmental toxicology to predict the disposition of chemicals in pediatric
populations.
PHARMACODYNAMICS
A number of different PD models are used to describe drug action, and most
include a monotonic component linking drug exposure and action. The most
common are the E
max
and related sigmoid E
max
models, which are represented
mathematically as
where E
max
is the maximum effect, EC50 is the concentration that produces
half-maximal effect, and γ is a shape constant. When γ equals 1, the sigmoid
E
max
simplifies to the E
max
model. This model has its origins in receptor–ligand
binding relationships and predicts that effects increase nearly in proportion to
drug concentrations at low concentrations (well below EC50), and effects
increase in proportion to the logarithm of drug concentrations around EC50. In
situations in which drug concentrations greatly exceed EC50, drug effects can
be maintained despite relatively dramatic changes in drug concentrations (Fig.
2.11).
Figure 2.11 The pharmacokinetic–pharmacodynamic relationship of a sigmoid E
max
model. Although
the drug concentrations fall rapidly (t
1/2
= 4 hours), the pharmacodynamic effect persists and drops more
slowly when the concentrations are well above the EC50. At 12 hours postdose, the concentration is only
12.5% of the peak value, yet only 50% of the effect has been lost if the 12-hour concentration equals
EC50. If the 12-hour concentration is higher (three times the EC50), less than 15% of the effect is lost in
this interval. This persistence of effect allows dosing less frequently than half-life.
In some situations, E
max
and related models can be directly linked to serum
concentrations to describe rapidly occurring drug effects. However, a lag or
hysteresis between serum drug concentrations and effects often exists. This
can be due to two separate phenomena. The first type of lag can be due to
distribution. This can be encountered with central nervous system–active
drugs, which require distribution into the brain to produce their effects. The
second delay occurs when the effects of drugs are mediated through synthesis
or metabolism of endogenous moieties. In the latter situation, drug effects can
occur through a cascade of processes, and overall homeostasis is altered only
after the drug has caused endogenous intermediaries of effects to be
synthesized or depleted. A group of indirect response PD models with E
max
equation components can be used to describe these processes. Examples of
drugs that have delayed effects through this mechanism include antiinflammatory effects of glucocorticoids and anticoagulant effects of warfarin.
PD effects may also be related to total drug exposure. In these situations,
either very slow accumulation or irreversible changes accrue with continued
exposure. This PD relationship commonly describes toxic effects, including
those from heavy metals and antineoplastic agents that irreversibly bind to
DNA.
Determining the PD parameters for a drug requires selection of
appropriate effect measurements and mechanistically plausible models. PD
parameter estimates are most robust when the effects are relatively direct and
reproducible. The range of drug concentrations used to determine the PD
parameters is also important. The use of a narrow range of concentrations may
limit the ability to fully characterize the concentration–response relationship.
A single paired drug concentration and associated response can be described
by a variety of E
max
–EC50 value combinations, so broad concentration–
response measurements are desired. Although this broad dose range approach
is used in the early phases of drug development for adults, PD studies in
pediatrics typically have limited concentration–effect ranges. In addition, the
use of indirect markers of drug effects, such as surrogate or biomarkers, can
result in different PD parameter values based on the specific biomarker
measured. Whereas methods to determine drug concentration are typically
consistent across the age continuum studied, biomarkers appropriate in one
age group may not be appropriate in another or may change with human
development. These potential confounders should be addressed when
calculating pediatric PD parameters. Lastly, even with high-quality surrogate
markers, disease presentation and progression differences in pediatric
subpopulations can lead to PD changes, particularly when the organ system
affected undergoes significant development during infancy and childhood.
POPULATION
PHARMACOKINETICS/PHARMACODYNAMIC
S
Whereas detailed description of PK in individual subjects is determined for
regulatory and research purposes, in most clinical circumstances precise
determination of an individual’s PK to optimize therapy is impractical.
Summary data generated from intensive phase 1 PK studies are used to infer
individual patient’s PK characteristics and drug exposure from a specific
dosing regimen. However, most of these studies are performed in relatively
healthy and homogeneous populations with limited age ranges and are
conducted under tightly controlled environments. Although this approach
results in rapid generation of PK data, the patients studied may not reflect
subpopulations that will frequently receive the drug clinically. Concomitant
drugs, diseases, and patient characteristics encountered clinically with drug
use, but avoided in intensive studies, may alter a drug’s PK and PD. Thus, the
dosing derived from tightly controlled phase 1 and phase 2a clinical trials
may provide biased estimates of the larger population of subjects that will
ultimately receive therapy. In addition, these studies provide little insight into
the extreme PK/PD responses likely to be encountered on a given dose to the
larger population. Accordingly, most phase 1 PK studies focus on average or
median CL and Vd values with little attention directed to variability and
sources of variability.
The use of sparse PK sampling in larger pediatric populations has been
emphasized to better describe PK and PD using population analysis
approaches. In this approach, the precision in the PK parameter estimates for
individual participants is reduced by taking fewer evaluations per subject.
However, less intensive sampling allows inclusion of a wider spectrum of
participants likely to receive the drug clinically. Although reduction in
frequency and number of samples has obvious appeal in pediatric
populations, the ability of population methods to analyze unbalanced data
collected at various times is also attractive in these populations. This method
allows pooling of data across studies to provide a uniform, robust, single PK
analysis rather than attempting to compare results of separate, smaller studies
that are complicated by significant analysis methodology differences. The
population PK method also regards variability differently than does the
traditional intensive approach. Instead of avoiding variability by design, one
goal of the population approach is to quantify both within- and betweenparticipant variability and examine clinical characteristics that can explain
between-participant variability to indicate alternative dosing requirements for
specific subpopulations. It is a robust method and can be used to characterize
the impact of age and development on drug PK (Fig. 2.12).
Figure 2.12 A comparison of intensive two-stage and population pharmacokinetic (PK) methods for
detecting sources of PK variability such as age. This represents a typical simulation using 240
concentrations. In the intensive evaluation, 15 samples were used to precisely calculate the clearance in
each of 16 subjects. In the population analysis, three samples collected in 80 subjects were used to
describe the population PK. Individual clearance estimates were generated for graphical comparison by a
Bayesian method. The size of the symbols is proportional to the relative error of the parameter estimate
in each subject. Having fewer samples reduced individual subject parameter precision in the population
analysis, but the population analysis was robust in detecting the age effect on clearance.
The population PK approach in pediatrics has been most widely applied
in the newborn population, although there has been growing use in older
pediatric populations. The ability to accommodate unbalanced designs allows
one to incorporate both longitudinal and cross-sectional elements to assess
maturation within a study. Whereas traditional PK studies have uniformly
been unable to distinguish differences between in utero and postnatal
maturation, appropriately designed population studies are able to tease out
these different influences. The population method is also particularly useful
for drugs with long half-lives or for drugs whose steady-state PK may be
difficult to predict from a single-dose PK evaluation (autoinduction or
inhibition of metabolism or excretion). In these instances, the logistics and
ethical constraints of waiting for the drug to “wash out” to capture AUC
0−inf
following a single dose for a traditional PK analysis may preclude its study.
Although clearance can be estimated from classically intensive steady-state
data collected over a dosage interval, the resulting analyses assume dosing
and collection times that are performed exactly on schedule. Even in
experienced pediatric study environments, these assumptions can be violated.
Although the classical intensive analysis has difficultly accounting for these
variations, even when they are known, the population approach does not need
to make the assumption of steady state if an exact dosing history is collected.
The study of drug interactions is another area where population PK methods
have significant value in pediatrics. The logistics of conducting traditional PK
drug interaction studies is extremely difficult in pediatric populations, and
these studies can often be more easily done using population approaches.
However, potential drug interactions identified by population methods must
be interpreted cautiously. Unless randomized, the relationship between
concomitant therapies and altered PK is not causal and may serve only as a
marker for other patient characteristics that may be responsible for the PK
differences.
Whereas the primary goal of most population PK analyses is to describe
the overall PK of the study group, estimates of individual subjects’ PK
parameters can be obtained through Bayesian post hoc analyses. This allows
population PK studies to be nested into traditional phase 3 efficacy studies
and provide estimates of individual drug exposure that can be used for
exploratory analysis of potential PD relationships. This paradigm is being
extensively used for regulatory purposes to look at drug exposure in subjects
who experience toxicity or lack clinical benefit. Another outcome from
population PK studies is the ability to get more accurate estimates of PK
variability. Accurate estimates of the variance and covariance of PK
parameters are essential for realistic simulations to evaluate the impact of
various dosing strategies on drug exposure and ultimately clinical outcome.
Like other analysis methods, the population PK approach has limitations.
It requires a high degree of expertise to perform these analyses, and the
analysis process can be time-consuming. The underlying mathematical
principles are complex, and if the data are not appropriate for the complexity
of the drug, adequate characterization may not be possible. Thus, PK samples
that are informative of all of the PK parameters to be estimated must be
collected. Random samples or only trough samples may not be sufficient.
Frequently, these samples are taken in outpatient settings, so there are
additional assumptions of adherence to therapy that are not encountered in
single-dose intensive studies. Assessing adherence in younger pediatric
populations, where multiple caregivers may be involved, is challenging.
Although population analyses allow collection of fewer samples per
individual, this reduction of information per subject is compensated by
collecting information from a larger number of subjects. As pediatric studies
try to maximize the information generated, there is temptation to perform
population PK studies from sparse samples in a small number of subjects. The
results from these small studies must be viewed critically because they can
generate unreliable parameter estimates.
The population method attempts to determine the sources of betweenparticipant variability. As age, size, and many laboratory measures are highly
correlated, it is important that pediatric population–based models have a
mechanistic basis. Maturational changes may impact multiple PK parameters
simultaneously and can be nonlinear. Thus, standard correlation screens of
potential covariates and PK parameters may underappreciate important
factors that drive pediatric PK variability. Even after accounting for age,
gender, size, renal function, and pharmacogenomic differences, unexplained
pediatric between-participant variability may still be largely due to
unidentifiable causes.
SUMMARY
Understanding the PK and PD behavior of a drug for its use in the intended
patient population is needed for rational and optimal drug therapy.