Guidance for Industry - Pharmanet
Guidance for Industry - Pharmanet
Guidance for Industry - Pharmanet
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<strong>Guidance</strong> <strong>for</strong> <strong>Industry</strong><br />
Population Pharmacokinetics<br />
DRAFT GUIDANCE<br />
This guidance document is being distributed <strong>for</strong> comment purposes only.<br />
Comments and suggestions regarding this draft document should be submitted within 60 days of<br />
publication in the Federal Register of the notice announcing the availability of the draft guidance.<br />
Submit comments to Dockets Management Branch (HFA-305), Food and Drug Administration,<br />
12420 Parklawn Dr., rm. 1-23, Rockville, MD 20857. All comments should be identified with<br />
the docket number listed in the notice of availability that publishes in the Federal Register. For<br />
questions regarding this draft document, contact Shiew-Mei Huang 301-594-5671.<br />
U.S. Department of Health and Human Services<br />
Food and Drug Administration<br />
Center <strong>for</strong> Drug Evaluation and Research (CDER)<br />
September 1997<br />
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TABLE OF CONTENTS<br />
I. INTRODUCTION ....................................................1<br />
II. BACKGROUND .....................................................2<br />
III. POPULATION METHODS ............................................4<br />
A. The Two-Stage Approach ........................................4<br />
B. The Population Approach ........................................4<br />
IV.<br />
WHEN TO PERFORM A POPULATION PHARMACOKINETIC STUDY AND<br />
ANALYSIS ..........................................................5<br />
V. STUDY DESIGN AND EXECUTION ....................................6<br />
A. Study Design ...................................................6<br />
B. Importance of Sampling Individuals on More Than One Occasion ........9<br />
C. Simulation .....................................................9<br />
D. Study Protocol ................................................10<br />
E. Study Execution ...............................................12<br />
VI. ASSAY ............................................................12<br />
VII. DATA HANDLING ..................................................13<br />
A. Data Assembly and Editing ......................................13<br />
B. Handling of Missing Data .......................................13<br />
C. Outliers ......................................................14<br />
D. Data Type ....................................................14<br />
E. Data Integrity and Computer Software ............................15<br />
VIII. DATA ANALYSIS ..................................................15<br />
A. Exploratory Data Analysis .......................................15<br />
B. Population Pharmacokinetic Model Development ....................16<br />
C. Model Validation ..............................................16<br />
IX. POPULATION ANALYSIS REPORT ...................................20<br />
A. Introduction ..................................................20<br />
B. Objectives, Hypotheses, and Assumptions ..........................20<br />
C. Assay ........................................................20<br />
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D. Data ........................................................20<br />
E. Data Analysis Methods .........................................21<br />
F. Results .......................................................21<br />
G. Discussion ....................................................21<br />
H. Application of Results ..........................................21<br />
I. Appendix ....................................................21<br />
J. Electronic Format Files .........................................22<br />
X. LABEL ............................................................22<br />
REFERENCES ...........................................................23<br />
GLOSSARY OF TERMS ...................................................28<br />
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GUIDANCE FOR INDUSTRY 1<br />
Population Pharmacokinetics<br />
I. INTRODUCTION<br />
Pharmaceutical industry scientists and the FDA have long been interested in the application of<br />
population pharmacokinetics to drug safety and efficacy evaluation. Reference is made to this<br />
subject in other FDA guidance documents such as General Considerations <strong>for</strong> the Clinical<br />
Evaluation of Drugs (FDA 77-3040), General Considerations <strong>for</strong> Pediatric Pharmacokinetic<br />
Studies, and in International Conference on Harmonisation (ICH) guidelines, including Dose-<br />
Response In<strong>for</strong>mation to Support Drug Registration (ICH- E4), and Studies in Support of<br />
Special Populations: Geriatrics (ICH-E7). These guidance documents support the application of<br />
special data analysis methodologies, such as the population pharmacokinetic approach, in the<br />
development and approval of new drugs with proper labeling in<strong>for</strong>mation <strong>for</strong> the safe and<br />
effective use of the drug.<br />
This guidance provides recommendations regarding the use of population pharmacokinetics in the<br />
drug development process. It summarizes scientific and regulatory issues that should be<br />
addressed during the conduct of population pharmacokinetic studies/analyses. It presents a<br />
comprehensive overview of population methods, including when to per<strong>for</strong>m a population<br />
study/analysis; how to design and execute a population pharmacokinetic study; how to handle and<br />
analyze population pharmacokinetic data; how to per<strong>for</strong>m internal and external validation of<br />
population pharmacokinetic models; and how to provide appropriate documentation <strong>for</strong><br />
population pharmacokinetic reports intended <strong>for</strong> submission to the FDA.<br />
Because the population approach is a rapidly evolving area of drug development and regulation,<br />
frequent communication throughout the entire process between the sponsor and the FDA review<br />
staff is encouraged.<br />
1<br />
This guidance has been prepared by the Population Pharmacokinetic Working Group of the Clinical<br />
Pharmacology Section of the Medical Policy Coordinating Committee in the Center <strong>for</strong> Drug Evaluation and Research<br />
(CDER) at the Food and Drug Administration. This guidance document represents the Agency's current thinking on<br />
population pharmacokinetics in drug evaluation. It does not create or confer any rights <strong>for</strong> or on any person and does not<br />
operate to bind FDA or the public. An alternative approach may be used if such approach satisfies the requirements of<br />
the applicable statute, regulations, or both.<br />
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II.<br />
BACKGROUND<br />
Population pharmacokinetics is the study of the sources and correlates of variability in plasma<br />
drug concentrations between individuals representative of those in whom the drug will be used<br />
clinically when relevant dosage regimens are administered (1). Certain patient pathophysiological<br />
features can regularly alter dose-concentration relationships. For example, renal failure usually<br />
causes steady state drug concentrations to be greater than those in patients with normal renal<br />
function receiving the same dosage of a drug eliminated mostly by the kidney. Population<br />
pharmacokinetics seeks to discover which measurable pathophysiologic factors cause changes in<br />
the dose-concentration relationship and to what degree so that the appropriate dosage can be<br />
recommended.<br />
A conceptual framework within which we can provide a more <strong>for</strong>mal definition of “population<br />
kinetics” is provided by a so-called hierarchical population model (also called a population model,<br />
a mixed effects model, or a random-effects model). At the first level of the hierarchy, such a<br />
model views pharmacokinetic observations in an individual (such as concentrations of drug<br />
species in biological fluids) as arising from an individual probability model, whose mean is given<br />
by a pharmacokinetic model (e.g., a biexponential) quantified by individual-specific parameters,<br />
which may vary according to the value of individual-specific time-varying covariates. The<br />
variance of the individual PK observations is also modeled, and the parameters of this model are<br />
additional individual-specific PK parameters.<br />
At the second stage of the hierarchy, the individual parameters are regarded as random variables<br />
and the probability distribution of these (often only the mean and variance) is modeled as a<br />
function of individual-specific covariates. These models and their parameter values are what we<br />
mean by “the population kinetics” of a given drug, while the use of study designs and data analysis<br />
methods designed to elucidate population PK models and their parameter values is what is meant<br />
by the population pharmacokinetic approach.<br />
The population pharmacokinetic approach in drug development offers the possibility of gaining<br />
integrated in<strong>for</strong>mation on pharmacokinetics not only from relatively sparse data, but also from<br />
dense data (or from a combination of dense and sparse data) obtained from subjects. The<br />
approach allows the analysis of data from a variety of unbalanced designs as well as from studies<br />
that are normally excluded because they do not lend themselves to the usual <strong>for</strong>ms of<br />
pharmacokinetic analysis, such as concentration data obtained from pediatric and elderly patients,<br />
or from data obtained during the evaluation of the relationships between dose or concentration<br />
and efficacy or safety.<br />
The subjects of pharmacokinetic studies are usually healthy volunteers or highly selected patients.<br />
Traditionally, the average behavior of a group (i.e., the mean plasma concentration-time profile)<br />
has been the main focus of interest. Interindividual variability in pharmacokinetics is viewed by<br />
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many incorrectly as a nuisance factor that has to be overcome, often through complex study<br />
designs and control schemes, and reduced through restrictive inclusion criteria. Study design and<br />
selection of volunteers that are rigidly standardized so that they are as homogeneous as possible<br />
are typical features of pharmacokinetic investigations. These studies, there<strong>for</strong>e, are often<br />
per<strong>for</strong>med under artificial conditions that do not represent the intended clinical use of the drug.<br />
In contrast to traditional pharmacokinetic evaluation, the population pharmacokinetic approach<br />
encompasses some or all of the following features(2):<br />
! It seeks to obtain relevant pharmacokinetic in<strong>for</strong>mation in patients who are representative of<br />
the target population to be treated with the drug.<br />
! It recognizes variability as an important feature that should be identified and measured during<br />
drug development or evaluation.<br />
! It seeks to explain variability by identifying factors of demographic, pathophysiological,<br />
environmental, or drug-related origin that may influence the pharmacokinetic behavior of a<br />
drug.<br />
! It seeks to quantitatively estimate the magnitude of the unexplained part of the variability in<br />
the patient population.<br />
The magnitude of the unexplained (random) variability is important because the efficacy and<br />
safety of a drug may decrease as unexplainable variability increases. Drug levels outside the<br />
target range become more likely, the greater the uncompensated variability in the relationship of<br />
dosage to steady state drug concentration. In addition to interindividual variability, the degree to<br />
which steady state drug concentrations in individuals typically vary about their long-term average<br />
is also important. Concentrations appear to vary due to inexplicable day-to-day or week-to-week<br />
kinetic variability and due to errors in concentration measurement. Estimates of this kind of<br />
variability (residual intrasubject, interoccasion variability) are important <strong>for</strong> therapeutic drug<br />
monitoring using the empiric Bayes approach. The knowledge of the relationship between<br />
concentrations, response, and physiology is essential to design dosing strategies <strong>for</strong> rational<br />
therapeutics that may not necessarily require therapeutic drug monitoring.<br />
A framework <strong>for</strong> defining optimum dosing strategies in a population, in a subgroup, or <strong>for</strong> the<br />
individual patient is provided by resolving the above issues. Recognizing the importance of<br />
resolving these issues in drug development has led to a surge in recent years in the application of<br />
population pharmacokinetics to new drug development and the regulatory process. In a recent<br />
survey of 206 new drug applications and supplements reviewed by the Office of Clinical<br />
Pharmacology and Biopharmaceutics of the FDA in fiscal years 1995 and 1996, it was found that<br />
over 23% (i.e., 47) of these submissions contained population pharmacokinetics and/or<br />
pharmacodynamic reports (3). The use of the population approach (population<br />
pharmacokinetics/pharmacodynamics) provided useful in<strong>for</strong>mation <strong>for</strong> the drug label in 83% of<br />
the 47 submissions on safety, efficacy and dosage optimization (3). However, in 17% of the 47<br />
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applications, the use of the approach did not yield any positive impact because the population<br />
approach was not integrated into the original plan of the drug development program (3).<br />
Population pharmacokinetics should, there<strong>for</strong>e, be integrated into drug development.<br />
III.<br />
POPULATION METHODS<br />
This discussion of population methods focuses on methods that provide estimates of some or all<br />
of the components of variability. There<strong>for</strong>e, the naive averaged data approach (see Glossary of<br />
Terms) will not be discussed.<br />
A. The Two-Stage Approach<br />
The usual method of pharmacokinetic data analysis is the two-stage approach. The first<br />
stage is the estimation of pharmacokinetic parameters through nonlinear regression using<br />
an individual’s experimental data (data rich situation). Individual estimates obtained in<br />
the first stage serve as input data <strong>for</strong> the second-stage calculation of descriptive summary<br />
statistics on the sample, typically mean vector and variance-covariance matrix. Analysis of<br />
dependencies between parameters and covariates using classical statistical approaches<br />
(linear stepwise regression, covariance analysis, cluster analysis) may be included in the<br />
second stage. The standard two-stage approach, when applicable, can yield adequate<br />
estimates of population characteristics. Mean estimates of parameters are usually unbiased,<br />
but the random effects (variance and covariance) are likely to be overestimated in all<br />
realistic situations (4 - 7). Refinements have been proposed to improve the standard twostage<br />
approach by bias correction <strong>for</strong> the random effects covariance and differential<br />
"weighting" of individual data according to its quality and quantity (7 - 9).<br />
B. The Population Approach<br />
The population approach in the context of drug evaluation developed from a recognition<br />
that, if pharmacokinetics and pharmacodynamics were to be investigated in patients,<br />
pragmatic considerations dictated that data should be collected under less stringent and<br />
restrictive design conditions. Considering the complete sample, rather than the individual<br />
as a unit of analysis, the population method of analysis (i.e., analysis according to a<br />
hierarchical random effect model) aims to estimate the distribution of the parameters and<br />
their relationships with covariates. The approach uses individual pharmacokinetic data of<br />
the observational (experimental) type, which are unbalanced and fragmentary, in addition<br />
to or instead of conventional pharmacokinetic data from traditional pharmacokinetic<br />
studies characterized by rigid and extensive design. Analysis according to a hierarchical<br />
(non-linear) random effects model (10) provides estimates of population characteristics<br />
that define the population distribution of the pharmacokinetic (and/or pharmacodynamic)<br />
parameters. In the mixed-effects modeling context, the collection of population<br />
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characteristics is composed of population typical values and population variability values<br />
(generally the variance-covariance matrix). In sparse data situations where estimates of<br />
individual parameters are, a priori, out of reach, an original one-stage or population<br />
estimation approach is required. A population analysis of pharmacokinetic data, there<strong>for</strong>e,<br />
consists of estimating directly the parameters of the population from the full set of<br />
individual concentration values. The individuality of each subject is maintained and<br />
accounted <strong>for</strong>, even when raw data are sparse.<br />
IV.<br />
WHEN TO PERFORM A POPULATION PHARMACOKINETIC STUDY AND<br />
ANALYSIS<br />
In drug development, the population approach can help increase knowledge of the quantitative<br />
relationships between drug input patterns, patient characteristics, drug disposition, and responses<br />
(11). The population approach may be used to estimate population parameters of a response<br />
surface model in phases 1 and 2B of clinical drug development, where in<strong>for</strong>mation is gathered on<br />
how the drug will be used in subsequent stages of drug development and after release (11). The<br />
population approach may increase the efficiency and specificity of drug development by<br />
suggesting more in<strong>for</strong>mative designs and analyses of experiments. Application of the population<br />
approach to phase 1 and perhaps much of phase 2B, where patients are sampled extensively, does<br />
not necessarily involve complex methods of data analysis. The two-stage methods can be used to<br />
analyze the data, and standard regression methods can be used to model dependence of<br />
parameters on covariates. Alternatively, the data from individual studies can be pooled and<br />
analyzed using the nonlinear mixed-effects modeling approach.<br />
The population approach can also be applied to phases 2A and 3 of drug development to gain<br />
in<strong>for</strong>mation on drug safety (efficacy) and to gather additional in<strong>for</strong>mation on drug<br />
pharmacokinetics (and pharmacodynamics) in special populations, such as the elderly (11, 12). It<br />
is also useful in postmarketing surveillance (phase 4) studies. Studies per<strong>for</strong>med in phase 3 and 4<br />
of clinical drug development lend themselves to the use of the full pharmacokinetic screen study<br />
design.<br />
V. STUDY DESIGN AND EXECUTION<br />
Certain preliminary pharmacokinetic in<strong>for</strong>mation should be known be<strong>for</strong>e any population<br />
pharmacokinetics study is undertaken. The drug’s major elimination pathways in humans should<br />
be known. Preliminary studies should have established the basic model describing the<br />
pharmacokinetics of the drug. The latter is important because the sparse data collected during<br />
population pharmacokinetic studies may not provide adequate in<strong>for</strong>mation <strong>for</strong> the deduction of a<br />
pharmacokinetic model. In addition, a sensitive and specific assay (see Assay section) capable of<br />
measuring all species (parent drug and metabolites) of clinical relevance should be available be<strong>for</strong>e<br />
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a population pharmacokinetic study is undertaken. When properly per<strong>for</strong>med, population<br />
pharmacokinetic studies in patients combined with suitable mathematical/statistical analysis (e.g.,<br />
using nonlinear mixed-effects modeling) is a valid approach and, on some occasions, an<br />
alternative to extensive studies.<br />
A. Study Design<br />
In the population pharmacokinetics context, there are two broad approaches <strong>for</strong> obtaining<br />
in<strong>for</strong>mation about pharmacokinetic variability: (a) trough screen (single or multiple)<br />
studies and (b) full pharmacokinetic screen (experimental population pharmacokinetic)<br />
studies. They yield an increasing amount of in<strong>for</strong>mation.<br />
1. Single-Trough Screen<br />
A single blood sample is obtained from each patient at or close to the trough of<br />
drug concentrations, shortly be<strong>for</strong>e the next dose (13), and a frequency distribution<br />
of plasma or serum levels in the sample of patients is calculated. Provided that the<br />
sample size is large, that assay and sampling errors are small, and that the dosing<br />
regimen and sampling times are identical <strong>for</strong> all patients, a histogram of such a<br />
trough screen gives a fairly accurate picture of the variability in trough<br />
concentrations in a target population. If these conditions are not met, such<br />
histograms do not represent strict pharmacokinetic variability because the data<br />
include many other sources of random fluctuation with significant contribution to<br />
the observed spread (14). When related with therapeutic outcome and occurrence<br />
of side effects, such histograms can be useful to improve the knowledge of the<br />
optimal concentration range of a given drug.<br />
The relationships of patient characteristics to the trough levels can be explored by<br />
simple statistical procedures such as multiple linear regression. Although simple,<br />
the trough (pharmacokinetic) screen will only yield in<strong>for</strong>mation about oral<br />
clearance and no other parameters of interest (e.g., apparent volume of<br />
distribution, half-life). Only qualitative, not quantitative, in<strong>for</strong>mation will be<br />
obtained. Components of variability — interindividual and residual variability —<br />
cannot be separated. This method will identify, qualitatively, pharmacokinetically<br />
relevant factors and their differences among subgroups (subpopulations). When<br />
implementing this sampling strategy, the difficulty of getting patients and<br />
physicians to adhere to the sampling strategy should be kept in mind. Compliance<br />
with at least the last two doses be<strong>for</strong>e trough level measurement is adequate <strong>for</strong><br />
this type of study, but the drug should be dosed to steady state. Because of<br />
uncertainty in doses and samples, the method can only reasonably be applied to<br />
drugs dosed at intervals less than or equal to one elimination half-life unless timing<br />
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of dose and of level can be assured, as in inpatient studies (15). Large numbers of<br />
subjects would be needed <strong>for</strong> this type of study because the data would be noisy.<br />
With this design, it is not advisable to contemplate measuring peak observations<br />
unless the drug is given intravenously or is a certain type of sustained release<br />
<strong>for</strong>mulation. The time <strong>for</strong> achieving maximum concentration depends on rates of<br />
all processes of drug disposition and may vary among subjects. Thus, the simple<br />
estimation of peak levels is subject to large uncertainty. Sampling peak levels also<br />
yields in<strong>for</strong>mation on variability of largely irrelevant kinetic processes <strong>for</strong> drugs <strong>for</strong><br />
which effects relate to steady-state mean concentrations, or the area under the<br />
concentration curve.<br />
2. Multiple-Trough Screen<br />
In this design, two or more blood samples are obtained near the trough of steadystate<br />
concentrations from most or all patients. In addition to relating blood<br />
concentrations to patient characteristics, it is possible now to separate<br />
interindividual and residual variabilities. Since patients are studied in greater detail,<br />
this design requires fewer subjects, and the relationships to patient characteristics<br />
can be evaluated with higher precision. To estimate interindividual variability of the<br />
oral clearance, nonlinear mixed-effects modeling should be used. When using<br />
pharmacokinetic models <strong>for</strong> parameter estimation, a sensitivity analysis (16) should<br />
be required to fix a parameter such as absorption rate constant to estimate other<br />
parameters and to determine the fixed parameter value that has the least effect on<br />
the estimation of the remaining parameters. The drawbacks of the single-trough<br />
screen design apply here. Although the estimates of intersubject and residual<br />
variability may or may not be biased, they may not be precise unless a large<br />
number of patients are studied.<br />
3. Full Pharmacokinetic Screen<br />
With this approach, blood samples are drawn from subjects at various times<br />
(typically 1 to 6 time points) following drug administration (6). The objective is to<br />
obtain, where feasible, multiple drug levels per patient at different times. This<br />
approach permits an estimation of pharmacokinetic parameters of the drug in the<br />
study population and an explanation of variability using the nonlinear mixed-effects<br />
modeling approach. The full pharmacokinetic screen (experimental population<br />
pharmacokinetic) study should be designed to explore the relationship between the<br />
pharmacokinetics of a drug and demographic/pathophysiological features of the<br />
target population (with its subgroups) <strong>for</strong> which the drug is being developed. A<br />
full pharmacokinetic screen study requires careful design considerations.<br />
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Population pharmacokinetic analysis is useful <strong>for</strong> looking at influences of<br />
pathophysiological conditions on parameters of a model with a well-established<br />
structure. The qualitative aspects of the model should be well known be<strong>for</strong>e<br />
embarking on a population study.<br />
The objective <strong>for</strong> carrying out a population pharmacokinetic study should be<br />
clearly defined since this will determine the study design. When designing a<br />
population pharmacokinetic study, the practical limitations of sampling times,<br />
number of samples/subject, and number of subjects should be considered.<br />
Preliminary in<strong>for</strong>mation on variability from pilot studies make it possible, through<br />
simulation, to anticipate certain fatal study designs as well as in<strong>for</strong>mative ones.<br />
Simulation studies can optimize design features <strong>for</strong> accurate and precise estimation<br />
of population pharmacokinetic parameters (17 - 22). Optimization of sampling<br />
design is critical to efficient experimental design when there are severe limitations<br />
on the number of subjects and/or samples/subject, as in pediatrics and the elderly<br />
(20). The use of in<strong>for</strong>mative study designs <strong>for</strong> population pharmacokinetic studies<br />
that yield in<strong>for</strong>mative data is encouraged (17, 19 - 22). The use of Bayesian<br />
designs <strong>for</strong> pediatric patients where adult data may serve as in<strong>for</strong>mative priors may<br />
be appropriate. Such a study should include enough patients in important<br />
subgroups to ensure accurate and precise parameter estimation and the detection<br />
of any subgroup differences.<br />
B. Importance of Sampling Individuals on More Than One Occasion<br />
The variance of an individual’s PK observations about the individual-specific PK model on<br />
a given occasion (i.e., the intra-individual variability; see Introduction) can conceptually be<br />
factored into two components: variability of PK observations due to variability of the PK<br />
model from occasion to occasion (inter-occasion variability), and variability of PK<br />
observations about the individual PK model appropriate <strong>for</strong> the particular occasion (noise;<br />
PK model misspecification). To be sure, some inter-occasion variability may be explained<br />
by inter-occasion variation in individual time-varying covariates, but to the extent that it is<br />
not, it represents, along with the noise, the irreducible uncertainty in predicting, and hence<br />
controlling drug concentrations. Drugs with narrow therapeutic indices and large interoccasion<br />
variability, <strong>for</strong> example, will be very difficult to control. If a population PK study<br />
consists of PK observations solely from individuals each studied on only a single occasion,<br />
the inter-occasion variability will appear incorrectly in the inter-individual variability term<br />
and not in the intra-individual variability term. This may lead to inappropriate optimism<br />
about the ability to control individual therapy within the therapeutic range by using<br />
feedback (e.g., therapeutic drug monitoring, or simply adjusting dose according to<br />
observed drug effects), and also to a fruitless search <strong>for</strong> inter-individual covariates that<br />
might explain the spuriously inflated) inter-individual variability. It is of utmost<br />
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importance to avoid this artifact by ensuring that at least a moderate subset of subjects<br />
contributing data to a population PK study contribute data from more than one occasion.<br />
Indeed if this is done, one may hope to separately estimate the components of intraindividual<br />
variability (23).<br />
C. Simulation<br />
Simulation of a planned study offers a powerful tool <strong>for</strong> evaluating and understanding the<br />
consequences of different study designs. Shortcomings in study design result in the<br />
collection of unin<strong>for</strong>mative data. Simulation can reveal the effect of input variables and<br />
assumptions on the results of a planned population pharmacokinetic study. Simulation<br />
allows study designers to assess the consequences of the design factors chosen and the<br />
assumptions made. Thus, simulation enables the pharmacometrician to better predict the<br />
results of a population study and to choose the study design that will best meet the study<br />
objectives. It is important to simulate a population pharmacokinetic study using alternative<br />
study designs to determine the most in<strong>for</strong>mative design, given the study objectives, be<strong>for</strong>e<br />
initiating such studies. Simulation is a useful tool to provide convincing objective evidence<br />
of the merits of a proposed study design and analysis (24).<br />
D. Study Protocol<br />
Two types of protocol may be considered depending on the setting in which a population<br />
pharmacokinetic study is to be per<strong>for</strong>med. If it is added on to a clinical trial (as can be<br />
envisaged in most situations), the population study should be carefully interwoven with the<br />
existing clinical protocol to ensure that it does not compromise the primary objectives of<br />
the study. Every ef<strong>for</strong>t should be made to convince investigators of the relevance of<br />
including a population pharmacokinetic study. Graphical displays of simulation results<br />
may help to achieve this objective. In addition, a population pharmacokinetic study<br />
protocol should be written since a population study can also be defined as evaluating data<br />
from existing data and/or data coming from more than one study. When a population<br />
study is a stand alone study, a comprehensive protocol should be prepared. The<br />
population pharmacokinetic study as part of the clinical protocol and the population<br />
pharmacokinetic study protocol are discussed briefly.<br />
1. Clinical Protocol<br />
The objectives of the population pharmacokinetic study should be clearly defined.<br />
These objectives, should be secondary to the primary clinical study objectives or<br />
primary when they would not compromise the study in question. The criteria <strong>for</strong><br />
sampling subjects and methods <strong>for</strong> data analysis (described in the population<br />
pharmacokinetic study protocol) should be clearly stated. The data to be used <strong>for</strong><br />
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population analysis should be defined, including patients and subgroups to be used<br />
and covariates to be measured. The sampling design should be specified and any<br />
subgroup stratification should be defined (25). In a multicenter trial, it may<br />
sometimes be necessary to obtain extensive data from some centers and sparse<br />
data from others (2). This type of data collection can be useful <strong>for</strong> in<strong>for</strong>mative<br />
data analysis protecting against model misspecification and it should be specified in<br />
the protocol. The data analysis plan should be described in advance in the protocol<br />
as accurately as possible. Statements such as “a pharmacokinetic screen will be<br />
per<strong>for</strong>med” or “data will be analyzed using NONMEM” are inappropriate because<br />
they do not convey in<strong>for</strong>mation on the study objective or how the analysis will be<br />
carried out.<br />
If possible, special case report <strong>for</strong>ms that can be easily understood by investigators<br />
should be designed to meet the needs of the pharmacokinetic evaluation.<br />
2. Population Pharmacokinetic Study Protocol<br />
The practical details of the pharmacokinetic evaluation should be described in a<br />
population pharmacokinetic study protocol, although the principles may be<br />
specified in the clinical study protocol in a general way. The primary (same as that<br />
in the clinical protocol) and secondary objectives should be clearly stated. The<br />
secondary objectives should be those that enable the data analyst to search <strong>for</strong> the<br />
unexpected, after the primary objectives have been addressed. The sampling<br />
design, data assembly, data checking procedure, and procedures <strong>for</strong> handling<br />
missing data and data anomalies should be clearly spelled out in the protocol. The<br />
data to be used <strong>for</strong> population analysis should be defined, including patients and<br />
subgroups to be used and covariates to be measured. The sampling design should<br />
be specified and any subgroup stratification should be defined (25). Real-time<br />
data assembly (see Data Assembly) would permit population pharmacokinetic data<br />
analysis to be per<strong>for</strong>med be<strong>for</strong>e the end of a clinical trial and would make it<br />
possible to include the results in the filing of the new drug application (NDA). If<br />
drug-drug interactions are to be characterized, the protocol should prespecify<br />
whether to determine (1) the effect of the presence or absence of a specific<br />
concomitant medication or (2) the total daily dose of the concomitant medication<br />
or (3) the plasma concentration of the potentially interacting medication. If food<br />
effect is to be evaluated, the time of sampling in relation to food intake, and the<br />
composition of food, should be specified in the protocol. Also, the procedure <strong>for</strong><br />
analyzing the data (and validation when appropriate) should be specified (see Data<br />
Analysis).<br />
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Distinguishing between clinically relevant and statistically significant covariates is<br />
important. Time variant covariates represent particular problems. In this case,<br />
several measurements should be made during the course of the study and, if this<br />
in<strong>for</strong>mation is found to be incomplete, model-based techniques may be used <strong>for</strong><br />
imputation between available data (See Handling of Missing Data). This also<br />
applies to time invariant covariates. Sensible methods of dealing with missing data<br />
should be predefined in the data analysis plan of the protocol. The issue of<br />
interoccasion variability (23) should be recognized and addressed in long-term<br />
studies. It is understandable that population pharmacokinetic data analysis, as a<br />
modeling exercise, cannot be planned to the fullest detail. However, the protocol<br />
should include study objectives; patient inclusion/exclusion criteria and<br />
pharmacokinetic evaluability criteria; sampling design; data handling and checking<br />
procedures; initial assumptions <strong>for</strong> modeling; a list of possible covariates to be<br />
investigated and the rationale <strong>for</strong> choosing them; and whether a sensitivity analysis<br />
and a validation procedure is envisaged.<br />
E. Study Execution<br />
A population pharmacokinetic study should be conducted according to current good<br />
clinical practice and good laboratory practice standards. The sampling strategy and the<br />
recording of samples should be part of good clinical practice and the handling of samples<br />
part of good laboratory practice. Error in recording sampling times relative to dosing<br />
history could result in biased and imprecise parameter estimates, depending on the nature<br />
and degree of the error (22).<br />
Every ef<strong>for</strong>t should be made to ensure that study subjects and clinical investigators comply<br />
with study protocol. To improve compliance, the protocol should not be overly<br />
complicated and blood sampling times should be convenient to both clinical staff and<br />
patients. The necessity of blood sampling should be carefully explained to patients and<br />
investigators. Instructions provided to the investigators should be clear and concise.<br />
These measures should be backed up by adequate monitoring by the sponsor while the<br />
study is ongoing. Adequate resources should be available <strong>for</strong> optimal sample preparation,<br />
storage at the investigator site, and transportation and storage of biological samples prior<br />
to analysis.<br />
Noncompliance with drug intake can be a source of confounding and lead to inappropriate<br />
interpretation of study results (26). Special care should be taken to use methodologies that<br />
are as objective as possible to reconstruct dosage history. Communication between all<br />
parties involved is essential <strong>for</strong> the successful conduct of a population study, especially if<br />
the study is part of a large scale clinical trial.<br />
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VI.<br />
ASSAY<br />
Correct evaluation of pharmacokinetic data depends on the accuracy of the analytic data obtained.<br />
Clinical investigators and their staff should be educated on the importance of sample timing,<br />
recording, proper labeling, and handling of samples.<br />
The accuracy of analytical data depends on the criteria used to validate the method. Consequently,<br />
drug and/or metabolite(s) stability, assay sensitivity, selectivity, recovery, linearity, precision, and<br />
accuracy should be carefully scrutinized be<strong>for</strong>e samples are analyzed. The importance of using<br />
validated assay methods <strong>for</strong> analyzing pharmacokinetic data cannot be over emphasized.<br />
VII.<br />
DATA HANDLING<br />
A. Data Assembly and Editing<br />
Real-time data assembly prevents the problems that generally arise when population<br />
pharmacokinetic data are stored until the end of a clinical trial. Real-time data assembly<br />
permits an ongoing evaluation of site compliance with the study protocol and provides the<br />
opportunity to correct violations of study procedures and policy. Evaluation of<br />
pharmcokinetic data can provide the data safety monitoring board with insights into drug<br />
exposure safety evaluations and drug-drug interactions. Adequate policies and procedures<br />
should be in place <strong>for</strong> study blind maintenance (27). Real-time data assembly creates the<br />
opportunity <strong>for</strong> editing the concentration-time data, drug dosing history, and covariate<br />
data necessary to meet the pharmacokinetic objectives of a clinical trial (28). Data<br />
assembly to create a population pharmacokinetic database after study completion may<br />
result in delays that are incompatible with the time course of the development program. It<br />
is important, there<strong>for</strong>e, to specify in the study protocol the use of real-time data analysis.<br />
Data editing means using a set of procedures <strong>for</strong> detecting and correcting errors in the<br />
data. The procedures should be planned be<strong>for</strong>e study initiation and predefined in the study<br />
protocol. Criteria <strong>for</strong> declaring data usable or unusable (e.g., time of blood sampling<br />
missing, dosing in<strong>for</strong>mation with no associated concentrations, concentrations with<br />
missing dosing in<strong>for</strong>mation) should be spelled out in the study protocol.<br />
B. Handling of Missing Data<br />
After assembling data <strong>for</strong> population analysis, the issue of any missing covariate data<br />
should be addressed. Missing data represent a potential source of bias. Thus, every ef<strong>for</strong>t<br />
should be made to fulfill the protocol requirements concerning the collection and<br />
management of data. Deletion of subjects with missing covariates can yield biased and<br />
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imprecise parameter estimates. Although caution should be taken when imputing missing<br />
values, it is usually better to estimate and impute a subject’s missing covariate data values<br />
than to delete that subject from the data set. Simple methods of imputation include the<br />
use of median, mean, or mode <strong>for</strong> missing values. These methods are biased and inefficient<br />
when predictors are correlated (29). Using maximum likelihood procedures (i.e., deriving<br />
regression models) <strong>for</strong> predicting each predictor from all other predictors is a better<br />
method. Alternatively, where imputation across a time series is possible, such a method<br />
should be used (30). Imputation procedures should be described, including a detailed<br />
explanation of how such imputations were done and of the underlying assumptions made.<br />
The sensitivity of the results of the analysis to the method of imputation of missing data<br />
should be tested, especially if the number of missing values is substantial. So-called<br />
multiple imputation, in which several imputed data sets are analyzed, can be used, where<br />
conclusions are of borderline significance, yet of clinical importance, to remove the<br />
optimistic bias from estimates of precision caused by imputing data and treating it as<br />
though it were actually observed (31).<br />
C. Outliers<br />
The statistical definition of an outlier is, to some extent, arbitrary. The reasons <strong>for</strong><br />
declaring a data point to be an outlier should be statistically convincing and prespecified in<br />
the protocol. Any physiological or study-related event that renders the data unusable<br />
should be explained in the study report. Because of the exploratory nature of population<br />
analysis, it may be that the study protocol did not specify a procedure <strong>for</strong> dealing with<br />
outliers. In such a situation, model building should be per<strong>for</strong>med on the reduced data set<br />
(i.e., data set without the outliers) as long as the conclusions are appropriately restricted<br />
to the limited population defined by the outlier-removal procedure. Including extreme<br />
outliers is not a good practice when using least-squares or normal-theory type estimation<br />
methods, as these inevitably have a disproportionate effect on estimates. Also, it is well<br />
known that <strong>for</strong> most biological phenomena, outlying observations are far more frequent<br />
than suggested by the normal distribution (i.e., biological distributions are heavy-tailed).<br />
Some robust methods of population analysis have recently been suggested, and these may<br />
allow outliers to be retained, without giving them undue weight (32-34).<br />
D. Data Type<br />
Two types of data can be used in population analysis: experimental data and observational<br />
(or population) pharmacokinetic data. Experimental data arise from traditional<br />
pharmacokinetic studies characterized by controlled conditions of drug dosing and<br />
extensive blood sampling. Population pharmacokinetic data are collected, most often, as a<br />
supplement in a study designed and carried out <strong>for</strong> another purpose. The data are<br />
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characterized by minimal control and few design restrictions: the dosing history is subject<br />
specific, the amount of pharmacokinetic data collected from each subject varies, the timing<br />
of blood sampling in relation to drug administration differs, and the number of samples per<br />
patient, typically 1 to 6, is small.<br />
E. Data Integrity and Computer Software<br />
Data management activities should be based on established standard operating procedures.<br />
The validity of the data analysis results depends on the quality and validity of methods and<br />
software used <strong>for</strong> data management (data entry, storage, verification, correction, and<br />
retrieval), and pharmacostatistical processing. Documentation of testing procedures <strong>for</strong><br />
the computer software used <strong>for</strong> data management should be available. It is crucial that the<br />
software used <strong>for</strong> population analysis be adequately supported and maintained.<br />
VIII.<br />
DATA ANALYSIS<br />
Population modeling can potentially be used in several phases of new drug development, including<br />
the planning, design, and analysis of studies in the exploratory and confirmatory stages of new<br />
drug development. Thus, the protocol should describe the pharmacokinetic models to be tested.<br />
Careful documentation of modeling ef<strong>for</strong>ts, data visualization, model validation (when<br />
appropriate), and data listing should be provided.<br />
Population pharmacokinetic data analysis can be carried out in three interwoven steps: (a)<br />
exploratory data analysis, (b) population pharmacokinetic model development, and (c) model<br />
validation. The data analysis plan should be clearly defined in the study protocol.<br />
A. Exploratory Data Analysis<br />
Exploratory data analysis isolates and reveals patterns and features in the population data<br />
set using graphical and statistical techniques. It also serves to uncover unexpected<br />
departures from familiar models. An important element of the exploratory approach is its<br />
flexibility, both in tailoring the analysis to the structure of the data and in responding to<br />
patterns that successive analysis steps uncover.<br />
Most population analysis procedures are based on explicit assumptions about the data, and<br />
the validity of the analyses depends upon the validity of assumptions. Exploratory data<br />
analysis techniques provide powerful diagnostic tools <strong>for</strong> confirming assumptions or, when<br />
the assumptions are not met, <strong>for</strong> suggesting corrective actions. Without such tools,<br />
confirmation of assumptions can be replaced only by hope. Exploratory data analysis<br />
should be coupled with more sophisticated population modeling techniques in the analysis<br />
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of population pharmacokinetic data (35). Exploratory data analysis per<strong>for</strong>med should be<br />
well described in the population report.<br />
B. Population Pharmacokinetic Model Development<br />
1. Objectives, Hypotheses, and Assumptions<br />
The objectives of the analyses should be clearly stated. The hypotheses being<br />
investigated should be clearly articulated. It is recommended that all known<br />
assumptions inherent in the population analysis be explicitly expressed.<br />
2. Population Model Development<br />
The steps taken (i.e., sequence of models tested) to develop a population model<br />
(35-37) should be clearly outlined to permit the reproducibility of the analysis. The<br />
criteria and rationale <strong>for</strong> model building procedures dealing with confounding,<br />
covariate, and parameter redundancy should be clearly stated. The criteria and<br />
rationale <strong>for</strong> model reduction to arrive at the final population model should also be<br />
clearly explained.<br />
3. Reliability of Results<br />
The reliability of the analysis results should be checked using diagnostic plots;<br />
confidence intervals (standard errors) <strong>for</strong> key parameters should be checked using<br />
nonparametric techniques (such as the jackknife (35)) and the profile likelihood<br />
plot (mapping the objective function (38)). This is appropriate because the<br />
possibility of biased results is increased by the complexity of the population models<br />
and by the sparse individual data available. The nonlinearity of the statistical<br />
model and ill-conditioning of a given problem can produce numerical difficulties<br />
and <strong>for</strong>ce the estimation algorithm into a false minimum. Because the maximum<br />
likelihood procedure is sensitive to bizarre observations, it may be necessary to<br />
check the stability of the model (39). It is important to evaluate the quality of the<br />
results of a population study/analysis <strong>for</strong> robustness. Evaluation <strong>for</strong> robustness<br />
may be approached by sensitivity analysis (38); the use of case deletion diagnostics<br />
(35, 37) is also encouraged. Evidence of robustness renders the results reasonable<br />
and independent of the analyst.<br />
C. Model Validation<br />
Validation can be defined as the evaluation of the predictability of the model developed<br />
(i.e., the model <strong>for</strong>m together with the model parameter estimates) with a learning or<br />
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index data set on a validation data set not used <strong>for</strong> model building and estimation. A<br />
model may be valid <strong>for</strong> one purpose and not valid <strong>for</strong> another. The objective of validation<br />
is to examine whether the model is a good description of the validation data set in terms of<br />
its behavior and of the application proposed.<br />
Validation depends on the objective of the analysis. Not all population models may need to<br />
be validated. Population models developed <strong>for</strong> explaining variability (which does not<br />
require dosage adjustment recommendation) and <strong>for</strong> providing descriptive in<strong>for</strong>mation <strong>for</strong><br />
labeling may be tested <strong>for</strong> stability only (39). Also, population pharmacokinetic models<br />
developed as part of a population pharmacokinetic /pharmacodynamic model may not<br />
need to be validated. However, the predictive per<strong>for</strong>mance of a population<br />
pharmacokinetic model developed <strong>for</strong> dosage recommendation as part of labeling should<br />
be tested. In such a situation, model validation procedure should be an integral part of the<br />
protocol.<br />
1. Types of Validation<br />
There are two types of validation: external and internal. External validation is the<br />
application of the developed model to a new data set (validation data set) from<br />
another study. Internal validation refers to the use of data-splitting and resampling<br />
techniques (cross-validation and bootstrapping) <strong>for</strong> validation purposes. External<br />
validation provides the most stringent method <strong>for</strong> testing a developed model.<br />
! Data-splitting<br />
For testing predictive per<strong>for</strong>mance, data-splitting is an effective method of model<br />
validation when it is not practical to collect a new set of data to test the model.<br />
The disadvantage of this method is that, in the area of linear regression, the<br />
predictive accuracy of the model is a function of the sample size resulting from the<br />
data-splitting (40). To maximize the predictive accuracy, it is recommended that<br />
the entire sample be used <strong>for</strong> model development and assessment (40). Datasplitting<br />
may not validate the final model if one desires to recombine the index and<br />
validation data sets to derive a refined model <strong>for</strong> predictive purposes. However, if<br />
data-splitting is to be used, a random subset of the data (two-thirds, i.e., the index<br />
data set) should be used <strong>for</strong> model building and the remaining data should be used<br />
<strong>for</strong> model validation. At the end of the exercise, the index and validation data sets<br />
should be pooled and the final population model fitted to the data to determine the<br />
appropriateness of each covariate retained in the final model.<br />
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! Cross-validation<br />
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Cross-validation is repeated data-splitting. The benefits of cross-validation over<br />
data-splitting are that (1) the size of the model development database can be much<br />
larger so that less data are discarded from the estimation process and (2) not<br />
relying on a single sample split reduces variability. Due to high variation of<br />
accuracy estimates, cross-validation is inefficient when the entire validation<br />
process is repeated (41).<br />
! Bootstrapping<br />
Bootstrapping, an alternative method of internal validation, has the advantage of<br />
using the entire data set <strong>for</strong> model development. Sample size is critical in pediatric<br />
settings where ethical and medical concerns limit recruitment into studies. The<br />
bootstrap resampling procedure can be useful <strong>for</strong> evaluating the per<strong>for</strong>mance of a<br />
population model when there is no test data set (39).<br />
2. Validation Methods<br />
The issue of validation of population models remains unresolved. The advantages<br />
and disadvantages of methods addressed in the literature and of methods used in<br />
applications have been discussed above. The data analyst should justify the<br />
method he/she chooses. Although the science of validation of population models<br />
is still evolving, consideration will be given to well-described innovative methods<br />
of model validation.<br />
! Prediction Errors on Concentrations<br />
This is calculated as the difference between observed and model-predicted<br />
concentrations. The mean prediction error is calculated and used as a measure of<br />
accuracy and the mean absolute error (or root mean square error) is used as a<br />
measure of precision.<br />
This method can be used when only one sample per subject is obtained. When<br />
more than one observation is obtained per subject, the method is inadequate<br />
because prediction errors are not independent if several concentrations per subject<br />
are available (42). The method does not take into account the correlation of<br />
observations within subjects.<br />
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! Standardized Prediction Errors<br />
This method (43) takes into account variability and correlation of observations<br />
within an individual. The mean standardized prediction error and the variance are<br />
calculated, and a t-test (appropriately a z-test) per<strong>for</strong>med to determine whether the<br />
mean is significantly different from zero and the standard deviation approximates<br />
1. Confidence intervals about the standard deviation of the standardized prediction<br />
errors can be constructed. This test per<strong>for</strong>med on the mean of the standardized<br />
prediction errors incorrectly assumes that the estimates <strong>for</strong> the population<br />
parameter values are given without error. The use of the approach is discouraged.<br />
! Validation through Parameters<br />
This method (44) avoids the problems encountered in prediction error of<br />
concentrations by per<strong>for</strong>ming validation with model parameters. Model parameters<br />
are predicted from the validation data set with or without covariates and bias and<br />
precision are calculated <strong>for</strong> the predictions.<br />
! Plot of Residuals Against Covariates<br />
A simple plot of residuals obtained by freezing the final model and predicting into<br />
a validation data set against covariates can yield in<strong>for</strong>mation on the clinical<br />
significance of the model in terms of a covariate or subpopulation (45).<br />
! A Plot of Residuals Against Covariates and Validation through<br />
Parameters.<br />
These methods are useful approaches <strong>for</strong> examining the predictive per<strong>for</strong>mance of<br />
population models. When there is no test data set, the bootstrap approach should<br />
be used: the mean parameter values obtained by repeatedly fitting the final<br />
population model to at least 200 bootstrap replicate data sets are compared to the<br />
final population model parameter estimates obtained without bootstrap replication<br />
(39).<br />
! Posterior Predictive Check<br />
A new technique, the so-called Posterior Predictive Check, may prove useful in<br />
determining whether important clinical features of present and future data sets are<br />
faithfully reproduced by the model (46)<br />
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IX.<br />
POPULATION ANALYSIS REPORT<br />
The report should contain the following: (a) introduction, (b) objectives, hypotheses, and<br />
assumptions (c) assay, (d) data, (e) data analysis methods, (f) results, (g) discussion,<br />
(h) application, (I) appendix, and (j) electronic <strong>for</strong>mat files.<br />
A. Introduction<br />
The introduction should briefly state the general intent of the analysis. It should include<br />
enough background in<strong>for</strong>mation to place the analysis in its proper context within the<br />
drug’s clinical development and to indicate any special features of a population<br />
pharmacokinetic study.<br />
B. Objectives, Hypotheses, and Assumptions<br />
The objectives of the analysis, and study where applicable, should be stated. In addition to<br />
the primary objective, any secondary objectives should be explicitly stated. If the analysis<br />
was per<strong>for</strong>med as a result of the implementation of a study protocol, the report should<br />
note whether the objectives were preplanned or were <strong>for</strong>mulated during or after study<br />
completion. This is not necessary <strong>for</strong> the analysis of pooled data. The assumptions made<br />
and the hypotheses tested should be clearly stated in the report (see section VIII B.1).<br />
C. Assay<br />
This section should contain a description of the assay method(s) used in quantitating drug<br />
concentrations. Assay per<strong>for</strong>mance (quality control samples) should also be included.<br />
The validity of the method(s) should also be described.<br />
D. Data<br />
Where data are pooled <strong>for</strong> analysis, the report should state the studies from which the data<br />
were pooled. The data set should be part of the appendix to the report. The report<br />
should contain the response variable and all covariate in<strong>for</strong>mation and explain how they<br />
were obtained. The report should include a description of the sampling design used to<br />
collect the plasma samples and a description of the covariate, including their distributions<br />
and the accuracy and precision with which they were measured. An electronic copy of the<br />
data set should be submitted. Data quality control and editing procedures should be<br />
described in this section.<br />
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This section should contain a description of the treatment of outliers and missing data<br />
(where applicable), and a detailed description of the criteria and procedures <strong>for</strong> model<br />
building and reduction incorporating exploratory data analysis. A flow diagram(s) of the<br />
analysis per<strong>for</strong>med and representative control/command files <strong>for</strong> each significant model<br />
building/reduction step should be provided.<br />
F. Results<br />
The key results of the analysis should be compiled into comprehensible tables and plots.<br />
To aid interpretation and application, a thorough description of the results should be<br />
provided. Complete output of results obtained <strong>for</strong> the final population model and key<br />
intermediate steps should be included.<br />
G. Discussion<br />
The report should include a comprehensive statement of the rationale <strong>for</strong> the model<br />
building and reduction procedures, interpretation of the results, protocol violations, and<br />
any other relevant in<strong>for</strong>mation.<br />
H. Application of Results<br />
A discussion of how the results of the analysis will be used (e.g., to support labeling,<br />
individualize dosage, support safety, or define additional studies) should be provided.<br />
In addition, the use of graphics to communicate the application of a population model<br />
(e.g., <strong>for</strong> dosage adjustment) is recommended.<br />
I. Appendix<br />
The appendix should contain the data set(s) used in population analysis. The output table<br />
from the final model should be in this section, as well as any additional plots that are<br />
deemed important. Where the analysis was per<strong>for</strong>med as a result of a clinical study or a<br />
population pharmacokinetic study, the study protocol should be included in the appendix.<br />
J. Electronic Format Files<br />
Data set and representative command files used <strong>for</strong> population analyses may be submitted<br />
as ASCII files and/or PDF files with the filing of a new drug application. It is understood<br />
that data <strong>for</strong>mat may be software specific. The Agency may, on some occasions, request<br />
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that the data be <strong>for</strong>matted in a manner that is compatible with another type of software.<br />
An electronic copy of the report may also be a part of the submission. However, the<br />
submission of these data and reports in electronic <strong>for</strong>m does not eliminate the need to<br />
submit a paper copy.<br />
X. LABEL<br />
Where population model parameter estimates are included in the label, the total number of<br />
subjects used <strong>for</strong> the analysis and the precision with which the parameters were estimated should<br />
be included in the report. Where the results of the population analysis provide descriptive<br />
in<strong>for</strong>mation <strong>for</strong> the label, it should be stated that the in<strong>for</strong>mation was obtained from a population<br />
analysis. In<strong>for</strong>mation from population analyses used to characterize subpopulations should include<br />
the total sample size used <strong>for</strong> the analysis and the proportion of subjects belonging to the<br />
subpopulation.<br />
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REFERENCES<br />
1. Aarons L. "Population Pharmacokinetics: Theory and Practice." Br J Clin Pharmacol<br />
1991; 32: 669 - 670.<br />
2. Steimer, J.L., S. Vozeh, A. Racine-Poon, et al., "The Population Approach: Rationale,<br />
Methods, and Applications in Clinical Pharmacology and Drug Development" (Chapter<br />
15), in: Welling, P.G. and L.P., Balant (eds.) Pharmacokinetics of Drugs. (Handbook of<br />
Experimental Pharmacology) Berlin- Heidelberg: Springer-Verlag. Vol 110: pp 404 - 451<br />
(1994).<br />
3. Ette, E.I., R. Miller, W. R. Gillespie, et al., "The Population Approach: FDA Experience,"<br />
in Balant, L.P. and L.Aarons (eds.), The Population Approach: Measuring and Managing<br />
Variability in Response, Concentration and Dose, Commission of the European<br />
Communities, European Cooperation in the field of Scientific and Technical Research,<br />
Brussels, 1997, in Press.<br />
4. Sheiner, L.B.and S.L. Beal, "Evaluation of Methods <strong>for</strong> Estimating Population<br />
Pharmacokinetic Parameters. I. Michelis-Menten Model: Routine Clinical Data." J<br />
Pharmacokinet Biopharm 1980; 8: 553 - 571.<br />
5. Sheiner, L.B.and S.L. Beal, "Evaluation of Methods <strong>for</strong> Estimating Population<br />
Pharmacokinetic Parameters. I. Biexponential Model and Experimental Pharmacokinetic<br />
Data," J Pharmacokinet Biopharm 1981; 9: 635 - 651.<br />
6. Sheiner, L.B. and S.L. Beal, "Evaluation of Methods <strong>for</strong> Estimating Population<br />
Pharmacokinetic Parameters. I. Monoexponential Model and Routine Clinical Data," J<br />
Pharmacokinet Biopharm 1983; 11: 303 - 319.<br />
7. Steimer, J.L., A. Mallet, J.L. Golmard, et al., "Alternative Approaches to the Estimation<br />
of Population Pharmacokinetic Parameters: Comparison with the Nonlinear Mixed Effects<br />
Model," Drug Metab Rev 1984; 15: 265 - 292.<br />
8. Prevost, G., "Estimation of a Normal Probability Density Function from Samples<br />
Measured with Non-negligible and Non-constant Dispersion," Internal Report 6-77,<br />
Adersa-Gerbios, 2 avenue du 1er mai, F-91120 Palaiseau.<br />
9. Racine-Poon and Smith A.M.F., "Population Models. In: Berry DA (ed), Statistical<br />
Methodology in Pharmaceutical Sciences. Dekker, New York, p 139 - 162 (1990).<br />
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10. Beal, S.L. and L.B. Sheiner, "Estimating Population Pharmacokinetics." CRC Critical Rev<br />
Biomed Eng 1982; 8: 195 - 222.<br />
11. Sheiner, L. B., "Learning vs Confirming in Clinical Drug Development," Clin Pharmacol<br />
Ther 1997; 61: 275 -291.<br />
12. Vozeh, S., J.L. Steimer, M. Rowland et al., "The Use of Population Pharmacokinetics in<br />
Drug Development," Clin Pharmacokinet 1996; 30: 81 - 93.<br />
13. E7 Studies in Support of Special Populations: Geriatrics, (ICH <strong>Guidance</strong>).<br />
14. Steimer, J.L., F. Mentre, A. Mallet, "Population Studies <strong>for</strong> Evaluation of<br />
Pharmacokinetic Variability: Why? How? When?" In Aiache JM, Hirtz J (eds) 2nd<br />
European Congress on Biopharmaceutics and Pharmacokinetics, vol. 2: Experimental<br />
Pharmacokinetics, Lavoisier, Paris, pp 40 - 49.<br />
15. Sheiner, L.B. and L.Z. Benet, "Postmarketing Observational Studies of Population<br />
Pharmacokinetics of New Drugs" Clin Pharmacol Ther 1985; 38: 481 - 487.<br />
16. Wade, J.R., A.W. Kelman, C.A. Howie, and B. Whiting, "Effect of Misspecification of the<br />
Absorption Process on Subsequent Parameter Estimation in Population Analysis," J<br />
Pharmacokinet Biopharm 1993; 21: 209 - 222.<br />
17. Hashimoto, Y. and L.B. Sheiner, "Designs <strong>for</strong> Population Pharmacodynamics: Value of<br />
Pharmacokinetic Data and Population Analysis," J Pharmacokinet Biopharm 1991; 19:<br />
333 - 353.<br />
18. Al-Banna, M.K., A.W. Kelman, and B. Whiting, "Experimental Design and Efficient<br />
Parameter Estimation in Population Pharmacokinetics," J Pharmacokinet Biopharm 1990;<br />
18: 347 - 360.<br />
19. Ette, E.I., H. Sun, and T.M. Ludden. Design of Population Pharmacokinetic Studies,"<br />
Proc Am Stat Assoc (Biopharmaceutics Section) 1994; pp 487 - 492.<br />
20. Jones, C.D., H. Sun, and E.I. Ette, "Designing Cross-sectional Pharmacokinetic Studies:<br />
Implications For Pediatric and Animal Studies," Clin Res Regul Affairs 1996; 13 (3&4):<br />
133-165.<br />
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21. Johnson, N.E., J.R. Wade, and M.O. Karlson, "Comparison of Some Practical Sampling<br />
Strategies <strong>for</strong> Population Pharmacokinetic Studies," J Pharmacokinet Biopharm 1996; 24<br />
(6): 245 - 172.<br />
22. Sun, H., E.I. Ette, and T.M. Ludden. "On Error in the Recording of Sampling Times and<br />
Parameter Estimation from Repeated Measures Pharmacokinetic Data," J Pharmacokinet<br />
Biopharm 1996; 24 (6): 635 - 648.<br />
23. Karlson, M. O. and L.B. Sheiner. "The Importance of Modeling Interoccasion Variability<br />
in Population Pharmacokinetic Analyses," J Pharmacokinet Biopharm 1993; 21 (6): 735 -<br />
750.<br />
24. Hale, M., W.R. Gillespie, S.K. Gupt, et al., "Clinical Simulation: Streamlining Your Drug<br />
Development Process," Applied Clin Trials 1996; 5: 35 - 40.<br />
25. Aarons, L., P.L. Balant, F. Mentre, et al., "Practical Experience and Issues in Designing<br />
And Per<strong>for</strong>ming Population Pharmacokinetic/pharmacodynamic Studies," Eur J Clin<br />
Pharmacol 1995; 49: 251 - 254.<br />
26. Girard, P., L.B. Sheiner, H. Kastrissios, et al., "Do We Need Full Compliance Data <strong>for</strong><br />
Population Pharmacokinetic Analysis," J Pharmacokinet Biopharm 1996; 24: 265 - 282.<br />
27. Rombout, F, "Good Pharmacokinetic Practice (Gpp) and Logistics a Continuing<br />
Challenge," In Balant, L.P. and L.Aarons (eds), The Population Approach: Measuring<br />
and Managing Variability in Response, Concentration and Dose, Commission of the<br />
European Communities, European Cooperation in the field of Scientific and Technical<br />
Research, Brussels, 1997. In Press<br />
28. Fiedler-Kelly, J.D., D.J. Foit, D.W. Knuth, et al., "Development of a Real-time,<br />
Therapeutic Drug Monitoring System," Delavardine Registration Trials. Pharm Res.<br />
1996: 13:Supp: S454.<br />
29. Donner, A., "The Relative Effectiveness of Procedures Commonly Used in Multiple<br />
Regression Analysis <strong>for</strong> Dealing with Missing Values," Am Stat 1982; 36: 378 - 381.<br />
30. Higgins, K.M., M. Davidian, and D.M. Giltinan, "A Two-step Approach to Measurement<br />
Error in Time-dependent Covariates in Nonlinear Mixed Effects Models, with Application<br />
to Igf-1 Pharmacokinetics" J Am Stat Assoc 1997; 92: 436 - 448.<br />
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31. Rubin, D.B., "Multiple Imputation after 18+ Years" J Am Stat Assoc 1996; 91: 473 - 489.<br />
32. Fattinger, K.E., L.B. Sheiner, and D. Verotta, "A New Method to Explore the<br />
Distribution of Interindividual Random Effects in Non-linear Mixed Effects Models."<br />
Biometrics 1996; 51: 1236 - 1251.<br />
33. Mallet, A., "A Maximum Likelihood Estimation Method <strong>for</strong> Random Coefficient<br />
Regression Models," Biometrika1986; 73: 645-656.<br />
34. Wakefield, J., "The Bayesian Analysis of Population Pharmacokinetic Models," J Am Stat<br />
Assoc 1996; 91: 62 - 75.<br />
35. Ette, E.I. andT.M. Ludden, "Population Pharmacokinetic Modeling: the Importance of<br />
In<strong>for</strong>mative Graphics," Pharm Res 1995; 12 (12): 1845 - 1855.<br />
36. Mandema, J.W., D. Verotta, and L.B. Sheiner. "Building Population Pharmacokinetic-<br />
Pharmacokinetic Models. I. Models <strong>for</strong> Covariate Effects," J Pharmacokinet Biopharm<br />
1992; 20: 511 - 528.<br />
37. Mandema, J.W., D. Verotta, and L.B. Sheiner, "Building Population Pharmacokinetic-<br />
Pharmacodynamic Models," In D’Argenio, D.Z. (ed) Advanced Pharmacokinetic and<br />
Pharmacodynamic Systems Analysis, New York: Plenum Press, p 69 - 86 (1995).<br />
38. Sheiner, L.B., "Analysis of Pharmacokinetic Data Using Parametric Models. II.<br />
Hypothesis Tests and Confidence Intervals." J Pharmacokinet Biopharm 1986; 14: 539-<br />
555.<br />
39. Ette, E.I., "Population Model Stability and Per<strong>for</strong>mance," J Clin Pharmacol, 1997; 37:<br />
486 - 495.<br />
40. Roecker, E.B., "Prediction Error and its Estimation <strong>for</strong> Subset-Selected Models,"<br />
Technometrics, 1991; 33; 459 - 468.<br />
41. Efron, B., "Estimating the Error Rate of a Prediction Rule: Improvement on Crossvalidation,"<br />
J Am Stat Assoc 1983; 78: 316 - 331.<br />
42. Mentre, F., and M. E. Ebelin, "Validation of Population<br />
Pharmacokinetic/pharmacodynamic Analyses: Review of Proposed Approaches," In<br />
Balant, L.P., and L. Aarons ( eds), The Population Approach: Measuring and Managing<br />
Variability in Response, Concentration and Dose, Commission of the European<br />
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Communities, European Cooperation in the field of Scientific and Technical Research,<br />
Brussels, 1997. In Press<br />
43. Vozeh, S., P.O. Maitre, and D.R. Stanski. "Evaluation of Population (NONMEM)<br />
Pharmacokinetic Parameter Estimates." J Pharmacokinet Biopharm 1990; 18: 161 - 173.<br />
44. Bruno, R., N. Vivier, J.C. Vergniol, et al., "A Population Pharmacokinetic Model <strong>for</strong><br />
®<br />
Docetaxel (Taxotere ): Model Building and Validation," J Pharmacokinet Biopharm<br />
1996; 24: 153 - 172.<br />
45. Beal, S.L., "Validation of a Population Model. E-mail to NONMEM Usersnet<br />
Participants," February 2, 1994.<br />
46. Gelman et al., Bayesian Data Analysis, 1995, Chapman and Hall: New York.<br />
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GLOSSARY OF TERMS<br />
Accuracy: A state characterized by measurements or estimates clustering tightly about the true<br />
value.<br />
Bias: The degree to which the typical prediction is either too high or too low.<br />
Bootstrapping: A computer-based resampling method <strong>for</strong> estimating sampling variances,<br />
confidence intervals, stability of regression models, and other properties of statistics.<br />
Covariates: A set of explanatory variables.<br />
Cross-validation: A statistical method <strong>for</strong> estimating prediction error.<br />
Data assembly: The merging of covariate in<strong>for</strong>mation, dosing history, sample times relative to<br />
dosing history, and concentration measurements to <strong>for</strong>m the population pharmacokinetic<br />
database.<br />
Data editing: A set of procedures <strong>for</strong> detecting and correcting errors in the data.<br />
Data-splitting: The act of partitioning available data into two portions — estimation or index<br />
data set and validation data set.<br />
Exploratory data analysis: A method of data analysis that emphasizes the use of graphical and<br />
statistical techniques to isolate patterns and features in a data set, revealing these <strong>for</strong>cefully to the<br />
data analyst.<br />
External validation: The application of the developed model to a new data set (validation data<br />
set) from another study.<br />
Fixed effects: The population average values of pharmacokinetic parameters that may in turn be<br />
a function of various patient demographic or pathophysiological variables (Whiting B, Kelman<br />
AW, Grevel J. Population pharmacokinetics: theory and clinical application. Clin Pharmacokinet<br />
1986; 11: 387 - 401).<br />
Full pharmacokinetic screen: A sampling design in which blood samples are drawn from<br />
subjects at various times (typically 1 to 6 time points) following drug administration.<br />
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Imputation: The filling in of plausible and consistent values <strong>for</strong> missing data.<br />
Interoccasion variability: Random variability in individual pharmacokinetic parameters between<br />
study occasions.<br />
Intersubject variability: The variation of response (e.g., concentration) from one subject to<br />
another to a given treatment regimen; measures the magnitude of random individual variability in<br />
relation to fixed effects.<br />
Internal validation: The use of data-splitting and resampling techniques (cross-validation and<br />
bootstrapping) <strong>for</strong> validation purposes.<br />
Jackknife technique: A statistical method <strong>for</strong> reducing bias in parameter estimates and<br />
calculating realistic variances.<br />
Model stability: The choice of variables included in the population model.<br />
Model validation: The evaluation of the predictability of the model (i.e., the model <strong>for</strong>m<br />
together with the model parameter estimates) developed with learning or index data set on a<br />
validation data set not used <strong>for</strong> model building and estimation.<br />
Multiple-trough screen: A sampling design in which two or more blood samples are obtained<br />
near the trough of steady state concentrations, at least from most patients.<br />
Nonlinear mixed-effects modeling: A nonlinear regression technique that accounts <strong>for</strong> both<br />
fixed and random effects, hence mixed effects.<br />
Naive averaged data approach: A method of estimating mean (population) pharmacokinetic<br />
parameters by first averaging the concentration at each time point and fitting a model to the<br />
averaged data.<br />
Outlier: Collective term used to refer to either a contaminant or a discordant observation<br />
(Beckman & Cook, 1983; Beckman RJ, Cook RD. Outlier…..s. Technometrics 1983; 25:<br />
119 - 149 ). A discordant observation is any observation that appears surprising or discrepant<br />
to the investigator; a contaminant observation is any observation that is not realized from the<br />
target distribution (Beckman & Cook, 1983; Beckman RJ, Cook RD. Outlier..…..s.<br />
Technometrics 1983; 25: 119 - 149).<br />
Population: A group of subjects studied, usually 30 or more.<br />
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Population approach: A model-based approach to drug development.<br />
Population pharmacokinetics: The study of variability in plasma drug concentration between<br />
individuals when standard dosagte regimens are administered.<br />
Precision: A description of how sets of measurements or estimates cluster about some value.<br />
Prediction error: The difference between an observed value and a model predicted value.<br />
Random effects: The intersubject variability and residual intrasubject variability<br />
Residual intrasubject variability: The variation in response (e.g., concentration) due to<br />
inexplicable day-to-day kinetic variability and response (concentration) measurement error.<br />
Single-trough screen: A sampling design in which a single blood sample is obtained from each<br />
or some patients in a study at or close to the trough (steady-state minimum) of drug<br />
concentrations shortly be<strong>for</strong>e the next dose (13).<br />
Simulation: A numerical technique <strong>for</strong> conducting experiments with certain types of<br />
mathematical models describing the behavior of the system under study.<br />
Standard two-stage approach: A method of estimating population pharmacokinetic parameters<br />
in which a pharmacokinetic model is fitted to each subject's data in the first step, and in the second<br />
step estimates of population characteristics of each parameter is computed as the empirical mean<br />
(arithmetic or geometric) and variance of the individual parameter estimates.<br />
Traditional pharmacokinetic study: A pharmacokinetic study in which subjects are sampled<br />
intensively.<br />
Unbalanced design: A study design (in the context of this guidance) in which all subjects<br />
participating in a study do not supply the same number of observations.<br />
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