Guidance for Industry

Population

Pharmacokinetics

U.S. Department of Health and Human Services

Food and Drug Administration

Center for Drug Evaluation and Research (CDER)

Center for Biologics Evaluation and Research (CBER)

February 2022

Clinical Pharmacology

Population

Pharmacokinetics

Guidance for Industry

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U.S. Department of Health and Human Services

Food and Drug Administration

Center for Drug Evaluation and Research (CDER)

Center for Biologics Evaluation and Research (CBER)

February 2022

Clinical Pharmacology

Contains Nonbinding Recommendations

TABLE OF CONTENTS

INTRODUCTION ...................................................................................................... 1

II. BACKGROUND ........................................................................................................ 2

III. APPLICATION OF POPULATION PK ANALYSIS ............................................... 2

A. Application of Population PK Analysis in Drug Development ........................................... 3

B. Application of Population PK Analysis to Inform Drug Use in Labeling ............................ 5

IV. DATA USED FOR POPULATION PK ANALYSIS ................................................. 7

A. Study Subjects and Covariates ....................................................................................... 7

B. PK Sampling Schedule .................................................................................................. 7

V. DATA ANALYSIS ..................................................................................................... 8

A. Preliminary Examination of the Data ............................................................................. 9

B. Model Development ...................................................................................................... 9

C. Model Validation .........................................................................................................10

D. Simulations Based on Population PK Models .................................................................12

VI. LABELING BASED ON THE RESULTS OF POPULATION PK ANALYSIS ..... 14

VII. POPULATION PK STUDY REPORTING ............................................................. 14

A. Format and Content of the Population PK Study Report ................................................14

B. Submitting Electronic Files to the Agency ......................................................................17

VIII. GLOSSARY OF SELECTED TERMS .................................................................... 19

IX. REFERENCES......................................................................................................... 20

Contains Nonbinding Recommendations

Population Pharmacokinetics

Guidance for Industry

This guidance represents the current thinking of the Food and Drug Administration (FDA or Agency) on

this topic. It does not establish any rights for any person and is not binding on FDA or the public. You

can use an alternative approach if it satisfies the requirements of the applicable statutes and regulations.

To discuss an alternative approach, contact the FDA office responsible for this guidance as listed on the

title page.

I. INTRODUCTION

This guidance is intended to assist sponsors and applicants

of new drug applications (NDAs),

biologics license applications (BLAs), abbreviated new drug applications (ANDAs), and

investigational new drugs (IND) applications in the application of population pharmacokinetic

(PK) analysis. Population PK analysis is frequently used to guide drug

development and inform

recommendations on therapeutic individualization (e.g., through tailored dosing) (Marshall et al.

2015; Lee et al. 2011; Bhattaram et al. 2005). Adequate population PK data collection and

analyses submitted in marketing applications have in some cases alleviated the need for

postmarketing requirements or postmarketing commitments.

This guidance includes common applications of population PK analysis to inform drug

development and drug use. This list of applications is not meant to be comprehensive, but rather

provides illustrative examples. This guidance also includes the FDA’s current thinking on the

data and model submissions to support regulatory decisions, recommendations on how to

incorporate information from population PK analyses in labeling, and the general expectations

regarding the format and content for population PK reports submitted to the Agency.

The contents of this document do not have the force and effect of law and are not meant to bind

the public in any way, unless specifically incorporated into a contract. This document is

intended only to provide clarity to the public regarding existing requirements under the law.

FDA guidance documents, including this guidance, should be viewed only as recommendations,

This guidance has been prepared by Office of Clinical Pharmacology in the Center for Drug Evaluation and

Research (CDER) and the Center for Biologics Evaluation and Research (CBER) at the Food a nd Drug

Administration.

Herea fter, the term sponsor will be used to refer to both sponsors and applicants.

For purposes of this guidance, references to drugs and drug and biological products includes drugs approved

under section 505 of the Federal Food, Drug, and Cosmetic Act (the FD&C Act) (21 U.S.C. 355) and biological

products licensed under 351 of the Public Health Service Act (PHSA) (42 U.S.C. 262) that are drugs.

Contains Nonbinding Recommendations

unless specific regulatory or statutory requirements are cited. The use of the word should in

Agency guidances means that something is suggested or recommended, but not required.

II. BACKGROUND

Population PK analysis is a well-established, quantitative method that can explain some of the

variability in drug concentrations among individuals (Sheiner, Rosenberg, and Marathe 1977;

Grasela Jr and Sheiner 1991). The focus of this guidance is on the use of this approach in

explaining the variability in drug concentrations observed among human trial subjects from

intrinsic factors, extrinsic factors, differences in dosing, and routes of administration. Drug

concentrations can vary significantly among individuals who are following the same dosing

regimen. This variability can be attributed to intrinsic factors, such as differences in body weight,

presence and extent of liver or renal impairment, or the presence of genetic polymorphisms, or to

extrinsic factors, such as effects of food on drug absorption or concomitant medications that can

interact with the administered drug’s absorption and/or metabolism. In some cases, intrinsic or

extrinsic factors lead to clinically relevant changes in drug concentrations that require clinical

management strategies, such as a change in the dose or dosing regimen.

Intrinsic and extrinsic factors that commonly influence drug exposure are often investigated in stand-

alone clinical pharmacology studies.

Stand-alone studies are well controlled and can provide a

robust assessment of these interactions. However, stand-alone studies are usually designed to

focus on intrinsic and extrinsic factors with the highest potential to affect drug exposure, leaving

many possible interactions unstudied. Such stand-alone studies also typically have a limited

number of subjects, are designed as single-dose studies, and might not be conducted in the target

patient population. Population PK analysis typically includes data directly collected from both

patients and healthy volunteers, allowing for an assessment of multiple intrinsic and extrinsic

factors that are not otherwise evaluated in a single trial or population. In addition, the relatively

large numbers of patients included in population PK analysis can improve the precision of the

estimated effect of the factors that affect drug exposures and confirm which factors do not

change drug exposures.

Population PK analysis has the potential to integrate all relevant PK information across a range

of doses and populations to identify factors that can affect a drug’s exposure. Such information

can come from studies with rich or sparse PK sampling, after a single dose or multiple doses,

and/or at steady state, and from healthy individuals, subjects with organ impairment, or the

patient population. These analyses, in turn, can inform strategies to select initial dosage

regimens, manage dosing and administration for a given subpopulation, plan subsequent studies,

or support labeling.

III. APPLICATION OF POPULATION PK ANALYSIS

See section IX for references for specific FDA guidances for industry that address stand-alone clinica l

pha rmacology studies.

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Sponsors seeking advice on the use of population PK analysis for drug development decisions

are encouraged to do so at appropriate milestone meetings with the Agency. While this guidance

focuses on typical applications of population PK analysis, it is recognized there are many novel

applications of population PK analyses beyond those described in this guidance. For example,

application of population PK, model-based approaches can be an alternative for evaluating the

bioequivalence of long-acting injectables, products with sparse PK sampling, or other scenarios

when non-compartmental analysis (NCA) becomes challenging (Zhao et al. 2019). For such

applications, the model’s intended use and its regulatory impact determine the level of robustness

needed for model evaluation. As an example, the model-integrated approach used should be

expected to reliably control the error rate for confirmatory bioequivalence applications.

Sponsors are encouraged to contact the Agency to discuss such novel applications of population

PK analyses to inform drug development and use.

Confidence in a given population PK analysis to support an intended objective is increased by

the following:

• Understanding of the drug’s PK properties

• Prespecified questions in the population PK data analysis plan that will be addressed by a

population PK analysis

• PK data of sufficient quantity and quality (Bonate et al. 2012) from subjects who

represent the indicated population and subpopulations of interest

• Good model performance (i.e., the model should describe the data with acceptable

accuracy and precision and should be evaluated for model misspecification) and validity

for the intended objective

A. Application of Population PK Analysis in Drug Development

1. Selecting Dosing Regimens To Be Tested in Clinical Trials

Population PK analyses are capable of identifying intrinsic and extrinsic factors that can

significantly impact the pharmacokinetics of the drug and inform dosing regimens for testing in

clinical trials to help minimize the variability of treatment response in patients. For example, an

observed strong relationship between body weight and drug exposure can provide support for

body weight-based dosing schemes (e.g., mg/kg dosing or categorical dosing based on body

weight cut points). Such analyses should be combined with a robust understanding of the

relationship between drug exposure and drug effect (e.g., by using pharmacodynamic biomarkers

or clinical endpoints), target engagement (e.g., receptor occupancy), or drug toxicity to inform

the clinical relevance and further refine dosing.

Population PK models can also be used to simulate drug exposures that are expected to occur

following doses or dosing regimens that have not been directly investigated in prior clinical

studies (see section V.D for a discussion on simulation strategies). For example, a population

PK analysis can be used to predict PK changes resulting from the inclusion of a loading dose,

Contains Nonbinding Recommendations

changing the dose, or altering the dosing frequency of a dosing regimen for later trials in the drug

development program. When appropriately justified, such analyses, in conjunction with

exposure-response data, have been used to approve dosing regimens that have not been directly

evaluated in the clinical trials (Kimko and Peck 2010). In such cases, sponsors are encouraged

to seek Agency input in advance of performing the analyses.

2. Deriving Sample Size and Sampling Scheme Requirements

Simulations and optimal design methods can maximize the utility of population PK data

collection and analyses. For example, the trial sample size and PK sampling schedule can be

optimized so that the PK parameters and the estimates for major covariate (bolded terms are

defined in section VIII upon first use) effects of interest can be estimated with a defined degree

of precision (see section IV.B for a discussion on various sampling schedules). Simulations with

population PK models can help determine the number of patients in a subpopulation that

achieves sufficient power to detect a significant covariate given a defined covariate effect size

(e.g., the number of patients receiving a concomitant medication that should be included in an

analysis to detect a significant drug-drug interaction (DDI); see section III.B.2).

3. Deriving Exposure Metrics for Conducting Exposure-Response Analysis

The importance and application of exposure-response (E-R) relationships for new drugs are

outlined in the FDA guidance entitled Exposure-Response Relationships — Study Design, Data

Analysis, and Regulatory Applications (May 2003).

Population PK analysis can be used to

derive patient PK exposure metrics that are appropriate for sequential E-R analyses. When

relevant, the derivation of exposure metrics should account for: (1) dose interruptions or

modifications; and (2) variations in the pharmacokinetics of a drug over time due to intrinsic or

extrinsic subject factors (e.g., time-varying exposure due to disease state or anti-drug antibodies

for some monoclonal antibodies).

Population PK models can predict individual patient exposures at specific time points regardless

of the spread in sampling times (e.g., trough concentrations can be predicted for all subjects).

When PK data are missing in a small number of subjects, population PK models can predict the

most likely concentration-time profile based on individual covariates including both time-

varying and subject-level covariates (e.g., body weight, genetic polymorphism, sex) (Wählby U

2004). Such predictions are useful, assuming that the residual error and the between-subject

variability are low, and the effect of observed covariates on the PK characteristics of the drug is

considerably larger (see section V.D).

Individual patient exposure metrics are generated based on Empirical Bayes Estimates (EBEs).

When parameter shrinkage is high (i.e., the standard deviation-based shrinkage is usually

greater than 20 to 30 percent), EBEs might be considered less reliable (Savic and Karlsson

2009). The informativeness of individual data (e.g., in cases with sparse data) should be

assessed using individual shrinkage estimates. In addition to parameter shrinkage, the reliability

We update guidances periodically. For the most recent version of a guidance, check the FDA guidance web page

at https://www.fda.gov/regulatory-information/search-fda-guidance-documents.

Contains Nonbinding Recommendations

of individual PK patient exposure metrics is dependent on the nature of the collected PK data and

the validity of model assumptions. See section V.C for discussions on model validation and

section IV for discussions regarding the adequacy of the data used for population PK analysis.

4. Pediatric Trial Designs

The use of modeling and simulation can help evaluate potential trial designs and optimize dose

selection for pediatric patients.

Additional sample size considerations for pediatric studies have

been presented in the literature (Wang et al. 2012). Population PK analysis is especially

appropriate in children because it allows the use of infrequent (i.e., sparse) sampling compared to

the rich sampling associated with traditional PK analyses, thus minimizing the total volume of

blood sampled.

Selecting a dosing regimen for pediatric studies can be based on simulations using a population

PK model developed with adult PK data and incorporating the following when scientifically

justified: (1) principles of allometry; (2) knowledge of developmental changes that can influence

the pharmacokinetics of a drug (ontogeny); and (3) data on the bioavailability of the pediatric

formulation (Holford, Heo, and Anderson 2013; Barbour, Fossler, and Barrett 2014; Zhang et al.

2015; Mahmood I 2014). Incorporating the latest understanding in the population PK model on

the effect of maturation of physiology in pediatric patients across various ages, especially in

those less than 2 years old, can further improve the ability to identify appropriate pediatric

dosing. Dose selection should also consider information on disease similarity and dose- and

exposure-response relationships in adults and pediatrics.

B. Application of Population PK Analysis to Describe Drug Use in Labeling

Population PK analysis using data from early- and late-stage clinical trials, together with results

from stand-alone clinical pharmacology studies, can be used to support the absorption,

distribution, and elimination (metabolism and excretion) (ADME) information in the labeling of

the drug.

In addition, population PK analysis, together with relevant information from stand-alone studies,

nested studies, or other sources, is routinely used to evaluate the effects of covariates on the PK

parameters of a drug and its relevant metabolites to support dosing recommendations. The need

for dose adjustments due to the effect of a covariate on the exposure of the drug should be

evaluated in the context of all available data, including the known E-R relationships for efficacy

and safety. The E-R relationships should be used to establish concentration boundaries within

which dose adjustments are not clinically relevant (i.e., covariate effects within these boundaries

might not warrant a dose alteration; however, covariate effects outside these boundaries could

require a dose modification to optimize the benefit-risk profile of the drug).

For more information, see the FDA guida nce entitled General Clinical Pharmacology Considerations for

Pediatric Studies for Drugs and Biological Products (December 2014). When final, this guida nce will represent the

FDA’s current thinking on this topic.

Contains Nonbinding Recommendations

1. Specific Populations

Results from population PK analyses can be incorporated into drug product labeling to describe

the PK properties in general patient populations or specific populations, as appropriate. Whether

a covariate analysis supports labeling statements depends on multiple factors, such as the number

of subjects with the covariate included in the analysis, the distribution of the covariate (for

continuous covariates), and the amount of available PK data (see section IV.A).

Some examples of these situations are listed below:

• Stand-alone renal or hepatic impairment studies in the general population might not be

ethical with some drugs (e.g., highly toxic agents). In such cases, adequate representation

of patients in clinical trials with the intrinsic factor of interest, as well as adequate PK

sampling to reliably characterize the effects of the intrinsic factor, can allow for the use

of population PK analysis to characterize the exposure of the drug and its relationship to

response and thus support dosing recommendations in that population.

• Some defined specific populations are traditionally not studied in stand-alone, clinical

pharmacology studies because of the lack of an expected clinically meaningful effect on

the drug’s pharmacokinetics due to prior knowledge of the drug’s ADME characteristics.

Instead, factors such as the influence of sex, age, body weight, or race on the

pharmacokinetics of the investigational drug are often studied without stand-alone trials.

Population PK analysis can be used to describe the pharmacokinetics of a drug in these

subgroups.

• Simulations from population PK models established from pediatric and adult data can be

used to compare the exposure of the drug in pediatric patients and adults, and then derive

the recommended pediatric doses.

2. DDIs

Clinical DDIs (e.g., nested studies as part of a phase 3 trial) can be evaluated using population

PK analysis. General design considerations for nested DDI studies are found in the FDA

guidance entitled Clinical Drug Interaction Studies - Cytochrome P450 Enzyme- and

Transporter-Mediated Drug Interactions (January 2020). Using population PK approaches to

characterize the DDI potential of a drug is not without limitations, and methodological

considerations for using population PK analysis to evaluate DDIs have been described elsewhere

(Bonate et al. 2016; Wang et al. 2017). Specific considerations for the use of a population PK

approach to evaluate DDIs include the following:

• DDIs should be characterized for individual drugs and not for therapeutic classes of

drugs, although exceptions are possible (e.g., multiple proton pump inhibitors can be

pooled if the interaction mechanism is pH-dependent).

• Multiple perpetrators can be pooled to form one covariate category provided that the

perpetrators belong to the same class of index inhibitors/inducers (i.e., weak, moderate,

Contains Nonbinding Recommendations

or strong) as identified by the Agency. The pooled perpetrators should all have the same

mechanism of interaction with similar specificity for their respective metabolizing

enzymes. In cases where a clear classification is not recognized by the Agency (i.e.,

transporter inhibitors), pooling should be prespecified whenever possible and is

considered on a case-by-case basis.

• An adequate number of subjects with the concomitant medication should be included in

the trial. The PK sampling schedule should allow for appropriate characterization of the

PK parameters of interest. Adequate information on the dose, timing of administration,

and duration of treatment for the interacting drugs should be available. Simulations can

determine the number of subjects needed to detect an interaction of a defined magnitude

within a given trial design.

• Interactions should be investigated on all physiologically plausible structural elements of

the PK model (e.g., apparent clearance (CL/F), relative bioavailability (F

rel

), rate of

absorption) based on the mechanism of the interaction.

IV. DATA USED FOR POPULATION PK ANALYSIS

Sponsors are encouraged to use all relevant data to support the population PK model. The

sponsor should justify the omission of data from certain studies, certain individuals, or certain

time points and prespecify such omissions in the population PK data analysis plan or study

protocol whenever possible. The sponsor should demonstrate that the data are adequate for the

purpose of the analysis in their report. For example, sponsors can conduct model-based power

analyses showing that the given study design has sufficient power to detect clinically meaningful

covariate relationships under the proposed population PK model (see section III.B).

A. Study Subjects and Covariates

Determining if the data are adequate to address the intended study question is a vital step in any

population PK analysis (see section V.C). The dataset should include a sufficient number of

subjects with an adequate number of PK samples at informative time points. Covariates cannot

be claimed to be influential or not influential on the exposure of a drug if the covariate

distribution is narrow (for continuous covariates) or if the number of subjects in the category is

inadequate (for categorical covariates). Many continuous covariates have established cutoff

values that define category levels. If dosing recommendations are proposed for these categories,

the range of the continuous covariates should preferably span the entire category and not just the

upper or lower ends. An increase in the range and frequency of the covariates tends to increase

the likelihood of finding a true clinically significant covariate relationship and decreases the

likelihood of finding false-positive relationships (Wählby et al. 2002; Wählby, Jonsson, and

Karlsson 2001).

B. PK Sampling Schedule

Contains Nonbinding Recommendations

The precision and bias of model-derived PK parameters are dependent on multiple factors,

including the complexity of the model, the number of subjects, the number of samples per

subject, and the sampling schedule. As the number of samples per subject decreases, the

importance of the timing of PK samples increases. For example, if the purpose of an analysis is

to match the maximum concentration (C

max

) observations across populations or dosage forms,

then a sufficient number of PK samples should be collected in the absorption phase. Sponsors

are encouraged to prospectively plan the PK sampling schedule so that the population PK model

is maximally informative.

The methodology and available software for the optimal design of the population PK model are

covered in multiple reviews in the literature (Dodds, Hooker, and Vicini 2005; Nyberg et al.

2015; Ogungbenro and Aarons 2007; Ogungbenro and Aarons 2008). The list below shows

some examples of sampling schedules. Depending on the purpose of the analysis, one or a

combination of the listed strategies can be employed:

• Patients are randomly assigned sampling windows that are derived based on optimal

design methods. The number of samples per patient and the number of sampling

windows are also determined based on optimal design methods.

• Patients randomly contribute two or more samples that, when combined, cover the entire

dosing interval.

• Most patients contribute one sample at a specified time point, often immediately before

the next dose when there is sufficient prior PK knowledge about the study drug.

Sponsors are encouraged to use all relevant PK data for the intended use. However, the extent of

sampling per individual patient and the percentage of sampled patients should ultimately depend

on the intended use of the data. For example, if the C

max

will be used in subsequent E-R

analyses, then there should be adequate sampling around the time to the maximum concentration

max

) (see section III.A.3). In any situation, it is important to verify that patients with missing

PK data do not differ from other patients. For example, patients with missing PK data should not

have higher dropout rates because of a lack of effect or adverse events. If between-occasion

variability will be estimated, the design should be sufficient to assess the presence and

magnitude of effect, requiring at least multiple samples per individual at more than one occasion.

Ignoring large between-occasion variability can lead to biased population parameter estimates

(Karlsson and Sheiner 1993). Similarly, multiple samples per individual should be collected if

time-varying covariates, such as the influence of anti-drug antibodies on drug exposure, are

expected.

V. DATA ANALYSIS

This section of the document provides some guiding principles on the methodological aspects of

population PK analysis. Further methodological considerations and good practices, including

topics not covered here, have been described by others (Ette and Williams 2007; Bonate PL

Contains Nonbinding Recommendations

2011; Mould and Upton 2013; Byon et al. 2013; Tatarinova et al. 2013; Lunn et al. 2002;

Schmidt and Radivojevic 2014).

A. Preliminary Examination of the Data

Population PK analysis often begins with a visual examination of the observed data. Preliminary

examination of the data reveals patterns and features in the population dataset using graphical

and statistical techniques and can provide powerful diagnostic tools for confirming assumptions

or, when the assumptions are not met, for suggesting corrective actions (Tukey 1977; Ette and

Ludden 1995). For example, strong correlations between covariates can preclude the ability to

make inferences about individual covariate effects and have implications for the choice of

covariate modeling approach. The scientific (i.e., pharmacologic, biologic, pathophysiologic, or

clinical) merits of including highly correlated covariates should be assessed. This scenario is

often the case with, for example, body weight and creatinine clearance as calculated by the

Cockcroft-Gault Equation. Relevant preliminary examination of the data should be concisely

described in the population PK analysis report.

B. Model Development

Model development methods and best practice recommendations are constantly evolving.

Specific advice on how to develop population PK models is beyond the scope of this guidance.

However, to facilitate the regulatory review of population PK models, sponsors should explicitly

describe their model development procedures (see section VII for more discussion on population

PK reporting). Some aspects of model development that are important for regulatory review are

provided below:

• Model development issues can be addressed through several valid approaches, each with

its own benefits and drawbacks. For example, covariate analysis can be performed based

on several approaches or their possible combinations (e.g., stepwise covariate analysis,

full covariate model approach, the Lasso) (Wählby, Jonsson, and Karlsson 2002;

Gastonguay 2004; Ribbing et al. 2007). In such cases, sponsors should justify why a

particular approach was used.

• The choice of the structural model should be informed from exploration of the observed

data, previous modeling results (when applicable), and a common scientific rationale.

Otherwise, an inappropriate structural model (e.g., missing the covariance between

clearance and volume of distribution in the structural model) could result in incorrect

covariate identification.

• Covariate-parameter relationships can be formulated based on the current knowledge of

biology, physiology, or allometric principles,

and should take into account any data-

driven information on the covariate-parameter relationship (e.g., time-dependent

covariates). Correct identification of the true covariate-parameter relationship is essential

when applying a population PK model to describe drug exposure in patients based on

covariates included in the population PK analysis or when applying the population PK

model to untested scenarios.

Contains Nonbinding Recommendations

• Issues regarding missing data, including missing covariates and data below the limit of

quantification (LOQ), should be addressed with appropriate analysis methods (Beal 2001;

Bergstrand and Karlsson 2009; Johansson and Karlsson 2013; Keizer et al. 2015). The

sponsor should justify their methodological approach with regard to missing data using

approaches such as sensitivity analysis.

• The sponsor should distinguish between outlying individuals and outlier data points.

Individual data points that are suspected outliers could be omitted during the model

development process. However, the sponsor should investigate the influence of the

outliers on the final parameter estimates by refitting the final model to the complete

dataset. Removal of suspected outlying individuals is generally discouraged unless the

reason for the outlier is a protocol violation or other human error. Sponsors should

specify how outliers are identified and handled in the analysis. The reasons for declaring

a data point to be an outlier should be prespecified in the data analysis plan. For

example, data points with a normalized weighted residual greater than five could be

considered outliers in some cases. The number of excluded outliers should be kept to a

minimum and clearly documented in reports and datasets.

C. Model Validation

Model validation is a critical step for any population PK analysis and should be conducted to

examine whether the developed model can sufficiently characterize the observed data and

generate reliable modeling and simulation results to meet the needs of the analysis. No single

model validation method is generally sufficient to evaluate all components of a model. Several

methods are generally used so that the relative strengths and weaknesses of each method can

complement each other. In general, models should describe the data with an acceptable level of

bias and an acceptable degree of precision.

Model validation depends on the objective of the analysis and should follow a fit-for-purpose

approach. In some cases, a model can be valid for one purpose but not for another. When

parameter shrinkage is high (standard deviation-based shrinkage: usually greater than 20-30

percent), EBEs might be less reliable (Savic and Karlsson 2009). The informativeness of

individual data should be assessed using individual shrinkage estimates, and the reliability of

individual drug exposure levels to be used in a sequential E-R analysis (see section III.A.3)

needs to be carefully evaluated. However, such a model can still be useful for a covariate

analysis provided that the method for covariate modeling is insensitive to shrinkage (Mould and

Upton 2013).

Submissions to the Agency should contain a detailed description of the model validation

methods used, an explanation of why those methods were selected, model diagnostics supporting

use of the model, and sensitivity analyses, as needed, to demonstrate the impact of assumptions

on the conclusions (see section VII.A). Sponsors are encouraged to discuss model validation

approaches with the Agency, particularly if the population PK analyses are critical for

understanding and supporting proposed dosing.

Contains Nonbinding Recommendations

1. Common Approaches for Model Validation

Procedures for conducting a thorough model validation are continuously evolving, and the

Agency welcomes innovations in this field. Several common methods of model validation are

reported in the literature (Karlsson and Savic 2007; Byon et al. 2013, Nguyen et al. 2017) and are

discussed in the sections below.

Basic goodness-of-fit (GOF) plots illustrate how well the model describes the observed data.

GOF plots are also used to evaluate model assumptions (e.g., normality of the random effects)

and to guide model development. Although GOF plots can show that the overall fitting is

acceptable, additional evaluation of the model in subgroups of patients is often necessary

depending on the context of use. For example, if the model will be used to predict drug

exposures in pediatric patients, model validation should be conducted for all relevant age groups.

GOF plots that are stratified for important patient characteristics (e.g., stratified by age group or

cytochrome (CYP) polymorphisms), trial design (e.g., dose or formulation), sampling design

(e.g., sparse versus full), or other important variables are often more convincing of the adequate

performance of a model than GOF plots of the full dataset. Because few patients could be

included in some analysis subgroups, the sponsor should include justifications, as needed,

regarding the sufficiency of the available data to support its intended use.

The following is a list of some of the GOF plots that are considered informative:

• The dependent variable (DV) versus the individual predictions (IPRED)

• The DV versus population predictions (xPRED), where ‘x’ could be nothing, C

(conditional), or P (simulation-based)

• The absolute individual weighted residuals (|IWRES|) versus IPRED or time

• The appropriate form of weighted residuals (xWRES) versus xPRED or time, where ‘x’

is defined as above

• A representative sample of IPRED, xPRED, and observations versus time (one plot per

subject)

• A histogram or Quantile-Quantile (Q-Q) plot of random effects

• The correlations between random effects

• The random effects versus covariates

Time should be evaluated as continuous time and as time after dose.

This plot is most informative when it is compared before and after the inclusion of covariates.

Contains Nonbinding Recommendations

The individual parameters, IPRED and IWRES, tend to shrink towards the population estimate in

individuals with few observations. When shrinkage is high (the standard deviation-based

shrinkage is usually greater than 20-30 percent), diagnostic plots that rely on EBEs, IPRED, or

IWRES can become uninformative, and correlations between random effects and covariates can

be obscured (Savic and Karlsson 2009, Xu et al. 2012, Lavielle and Riba 2016). Furthermore,

high shrinkage can limit the value of using individual post hoc estimates for E-R analysis (see

section III.A.3). However, simulation-based, diagnostic plots are not affected by shrinkage in a

similar manner and can be more informative for diagnostic purposes when shrinkage is high.

Model selection based on parameter shrinkage is not necessary. There are several available

simulation-based diagnostics, including but not limited to, Visual Predictive Check (VPC), the

prediction corrected VPC (pcVPC), the Numerical Predictive Check (NPC), and Normalized

Prediction Distribution Errors (NPDE) (Bergstrand et al. 2011, Brendel et al. 2006).

GOF criteria can also be reflected by some numerical metrics, such as the estimate of the

precision of a parameter. Estimates of parameter precision can provide valuable information

regarding the adequacy of the data to support that parameter. Parameter uncertainty can be

estimated through several methods, such as bootstrap procedures, sampling importance

resampling, log-likelihood profiling, or using the asymptotic standard errors of parameter

estimates. In addition to parameter uncertainty, it is important to compare parameter point

estimates with previous analyses and to evaluate the physiological plausibility of the point

estimates. Another useful numerical metric to evaluate models is the condition value. A large

condition number (the ratio of the largest and the smallest eigenvalue), typically interpreted as

values greater than 1000) indicates that the observed data cannot support the estimation of one or

several parameters (Montgomery, Vining, and Peck 2012). Over-parameterized models can be

simplified and updated as additional data from well-designed clinical trials become available.

An appropriate model should be biologically plausible, consistent with current knowledge, and

have mathematically identifiable parameters. Performance of the model can be checked against

a set of test data, either internal or external. A validation approach relying on the data used for

model building is considered as internal validation. External validation, on the other hand, relies

on the data not used for model building. Data collected in a drug development program can be

split into a model building dataset and a testing dataset. The testing dataset is commonly used

for external validation. Data splitting is a powerful method for model checking. However,

before deciding on a data splitting approach, sponsors should consider the potential impact of the

loss of data on the model’s power to detect covariate relationships and estimate parameters with

an acceptable degree of precision.

There is an additional level of uncertainty when the purpose of the model is to simulate PK

profiles for scenarios that are beyond those that have been clinically studied. Such uncertainty

can be addressed by a sensitivity analysis of the parameter estimates and their impact on the

metric used to inform a decision (Kimko and Peck 2010).

D. Simulations Based on Population PK Models

Simulations should be based on protocols that outline the simulation study to be performed. The

level of detail in the protocol should correspond to the complexity and impact of the question the

Contains Nonbinding Recommendations

simulation addresses. Models used for simulations should be validated to address the specific

question the simulation study is trying to answer. Although a model could have been previously

used and validated, it needs to be revalidated if the new purpose is different from the original

purpose. Depending on the purpose of the model, various levels of uncertainty and variability

can be added to the simulations. Some examples are discussed below.

1. Simulations Based on Fixed-Effect Estimates

In their simplest form, simulations are used to illustrate the drug-concentration profile for a

typical individual. Such simulations are based on the typical estimates of the fixed-effect

parameters. Note that predictions based on typical parameter estimates do not correspond to

mean predictions. Mean predictions are obtained by calculating the mean concentration-time

profiles based on simulations with between-subject variability in population PK parameters and

residual error.

2. Simulations Based on Uncertainty of Fixed-Effect Estimates

Uncertainty in parameter estimates can be accounted for if the desire is to illustrate the

probability of the typical subject’s drug exposure to reach or stay above a specific cutoff point or

if one wishes to illustrate the effect of covariates. The choice, if uncertainty of fixed effects is

considered, should be objective driven. For example, forest plots that illustrate the effect of

covariates on the area under the concentration time curve (AUC) or other parameters can be

generated based on simulations with uncertainty in fixed-effect parameters, thereby facilitating

the interpretation of the relative importance of covariates on exposure. Alternatively, if the

effect on exposure estimates is the objective, the uncertainty of all fixed effects should be

considered.

These types of simulations are also useful to evaluate the performance of new

dosing regimens for testing in future trials. Additionally, simulations with parameter uncertainty

can be used to graphically illustrate the effect of parameter precision on PK profiles.

3. Simulations Based on Estimates of Between-Subject Variability

Between-subject variability in PK parameters is accounted for in simulations when the purpose is

to show the range of individual predictions of concentrations in the studied population. Residual

error is added to the individual prediction when the range of observed concentrations is the main

interest.

If the purpose is to predict the observed concentration range of a future population, then

uncertainty in the between-subject variability should be accounted for in addition to the fixed-

effect parameters and residual error.

The correlation between random effects should be accounted for to avoid unrealistic parameter

combinations in subjects. Simulations that account for between-subject variability and include

covariate effects should be conducted in a population with realistic demographic variables.

Demographic variables can be obtained from databases or generated by resampling with

replacement of the individuals in the original study or by sampling the covariate distributions and

their correlations in the target population.

Contains Nonbinding Recommendations

VI. LABELING BASED ON THE RESULTS OF POPULATION PK ANALYSIS

Results from population PK analysis can be presented in the CLINICAL PHARMACOLGY

section and summarized in other sections of labeling, as appropriate. Other relevant labeling

sections should not repeat this detailed information but rather provide a succinct description or

recommendation based upon these results followed by a cross-reference to the CLINICAL

PHARMACOLGY section, as appropriate. In general, there is no need to explicitly state in

labeling that the information is based on population PK analysis. Recommendations for

developing the CLINICAL PHARMACOLOGY section are discussed in the FDA guidance for

industry entitled Clinical Pharmacology Labeling for Human Prescription Drug and Biological

Products — Content and Format (December 2016).

VII. POPULATION PK STUDY REPORTING

This section outlines the recommended format and content for a sponsor to submit a population

PK analysis in support of its drug’s clinical pharmacology program. Population PK analyses can

be appropriate at multiple points in the drug development process, for example in the IND, NDA,

BLA, ANDA, or postmarketing stages. The depth and breadth of population PK analyses at each

stage can vary because of the availability or quality of clinical data.

Population PK study reports that are important for regulatory decisions should be included in the

electronic common technical document (eCTD) module 5.3.3.5 and the corresponding programs,

datasets, and define files under the datasets folder within eCTD module 5.

A. Format and Content of the Population PK Study Report

To enable the efficient and consistent review of population PK analyses, the FDA recommends

that the results from population PK analyses should be accompanied with a structured population

PK report. The report should contain the following sections: (1) executive summary, (2)

introduction, (3) materials and methods, (4) results, (5) discussion, (6) conclusions, and (7)

appendix (if applicable). Expected information and elements to be included in these sections are

discussed briefly in Table 1. Sections of the annotated labeling that contain information based

on population PK analysis should include hyperlinks to the population PK report. Additional

discussion regarding reporting is available in the scientific literature (Dykstra et al. 2015).

Contains Nonbinding Recommendations

Table 1: Expected Content in Each Section of the Population PK Study Report

Sections

Expected Content

Executive

Summary

• The purpose of the analysis

• The key findings that affect drug use or labeling

• A plain language summary of objectives, data, methodology, and conclusions

• Results presented as their effect on clinically relevant drug exposures, not

model parameters

• Visual presentations of relevant exposure metrics to illustrate how identified

subpopulations differ from the typical population

Introduction

• The background to place the population PK study in the context of the overall

clinical development program

• The objectives for the population PK analysis

• The PK characteristics of the drug

Materials

and Methods

• A description of the trials and the trial data included in the population PK

analysis with information on:

o Dose, including the frequency and duration of dosing, as well as the

number of subjects, number of samples, and number of below the level

of quantification (BLOQ) samples

o Reasons for not including trials with available and potentially

informative data, if applicable

o A distinction between all available relevant data versus final data used

for model building and evaluation

• Hyperlinks to the original trial reports of data used for the analysis and the

bioanalytical evaluation reports for each trial

• Detailed demographic information and other covariate information

• Planned criteria, table of assumptions, and procedures for model building and

evaluation, including:

o Handling of outliers and missing data (e.g., methods of imputation)

o Model-estimation method

o Equations for all model structures and covariate relationships

o Equations for parameter transformations, if parameters are presented in

dimensions other than those in the model output file

Continued

Contains Nonbinding Recommendations

Table 1 continued: Expected Content in Each Section of the Population PK Study Report

Sections

Expected Content

Materials

and Methods

o Equations for parameter transformations, if parameters are presented in

dimensions other than those in the model output file

o The method for incorporating variability or parameter uncertainty or

for deriving confidence intervals or prediction intervals

• Detailed descriptions of planned simulations and sensitivity analyses used to

support conclusions and recommendations

• Software and version used for the analysis and simulation*

* Note: The FDA does not recommend or require the use of particular

software for conducting population PK analysis. The sponsor should report

the software used and submit the electronic files supporting the analysis and

simulations (see section VII.B below). If necessary, consult the FDA

regarding the submission of certain file types.

Results

• Summary of the data and data exploration, with adequate graphical and tabular

displays

• A description of the final model, model building steps, validation, final

parameter estimates, and deviations from planned analyses, if applicable

• Application of the model to the objectives, including the relevance of

covariates on PK parameters and simulations of alternative dosing, if

applicable

• Accompanying tables and figures to place findings into context

• Typically, tables and figures should include the following, with other tables

and figures included in the Appendix and cross-referenced in the report body,

as applicable:

o Key modeling building steps, including a description of the structural

and covariate models and objective function changes

o A comparison of parameter estimates from the base to the final model

o Parameter estimates and their associated uncertainty, with variability

reported as the coefficient of variation (CV%) and precision reported

as the percent relative standard error (RSE%) or the 95 percent

confidence interval. Shrinkage should be included in the parameter

estimates table.

o Key diagnostic plots

o GOF plots stratified by the relevant covariates to illustrate model

performance in specific subgroups

Continued

Contains Nonbinding Recommendations

Table 1 continued: Expected Content in Each Section of the Population PK Study Report

Results

o Results of model evaluations/validation, such as VPCs,

pcVPCs, NPCs, and NPDEs, etc., should also be included

• A description of simulation results or scenarios, if applicable

Discussion

• An interpretation of the modeling results, including discussions on:

o The adequacy or limitation of the data and model to support

conclusions and recommendations

o The rationale for the modeling approach, assumption

verification, and assessment of uncertainty

o Consistency or inconsistency between the results from

population PK and stand-alone clinical pharmacology studies

and/or previously completed related population analyses

• An assessment of the clinical relevance of the results, including

physiological plausibility and clinical significance of the identified

relationships

• An assessment of any alternative dosing regimens in the context of E-R

analyses for safety and efficacy

Conclusions

• A short summary of major findings from the analysis written in plain

language

Appendix

Additional materials should be included in the Appendix, as needed. The

Appendix does not need to contain full line listings from datasets. Materials

from the Appendix should be cross-referenced in the report body, as

appropriate. Appropriate materials for the Appendix include but are not limited

to:

• Supplemental tables and figures for summaries and analyses included

in the report that support model development or conclusions but are not

critical to the primary purpose of the report

• Methods and codes for generating the key figures and tables

(preferably, codes are submitted as separate files from the study report)

• Listing of samples removed from the analysis and reasons for removal

• A run record describing the steps during model development

• A diagram showing the connection between input datasets,

codes/control streams, and output datasets presented in the E-R report

B. Submitting Electronic Files to the Agency

Contains Nonbinding Recommendations

Sponsors should refer to the FDA web page

for general advice on submitting data and related

files (e.g., coding scripts). It is critical that datasets and model files submitted for the base, final,

and key intermediate models are the same as those used for generating the model outputs in the

appendices of the report. In addition, FDA staff should be able to identify the source data for

any dataset constructed using output files or postprocessed results from population PK analyses.

For example, if exposure metrics from population PK analyses are included in datasets for E-R

analyses, the sponsor should ensure the traceability between the population PK model output and

any postprocessing steps involved in the construction of the dataset. This can be accomplished

by providing definition files, reviewer guides, and/or codes utilized for dataset assembly.

All conclusions drawn from the population PK analysis should be reproducible by the Agency

with the available codes and data. It is also important to include the unique subject identifier

information for each subject in the population PK dataset and ensure that the identifiers are the

same in the individual clinical trial datasets. This information is vital if data integration is

required between the individual-level outputs (e.g., individual, post hoc estimates for clearance

or volume of distribution generated from the population PK model) and the efficacy or safety

datasets from the individual clinical study reports.

The FDA web page on submitting data can be accessed at https://www.fda.gov/about-fda/center-drug-evaluation-

and-research-cder/modeldata-format.

Contains Nonbinding Recommendations

VIII. GLOSSARY OF SELECTED TERMS

Covariate

An observed factor that correlates with drug exposure in patients (e.g.,

renal function, body weight, age, sex, genetic polymorphism)

Dependent variable (e.g., drug plasma concentrations)

EBE

Empirical Bayes Estimates, or individual parameter estimates in a

mixed-effects model

GOF

Goodness of fit, a collection of diagnostic criteria used to evaluate

model performance

IPRED

Individual Predicted Data, based on Individual Empirical Bayes

parameter estimates

IWRES

Individual Weighted Residuals, a type of residual

Model validation

The use of various methods to validate model performance for a

specific purpose

NPC

Numerical Predictive Check, a GOF method related to VPC

pcVPC

Prediction corrected VPC, a type of GOF plot related to VPC

Q-Q

Quantile-quantile, a type of GOF plot

Residual

The difference between the predicted and the observed value

Residual error

An estimate of the remaining unexplained variability

Shrinkage

A measure of the extent to which EBE depends on the population

parameters versus the individual observed data

VPC

Visual predictive check, a type of GOF plot

xPRED

Predicted data, based on population parameter estimates, where ‘x’ can

be nothing, C (conditional), or P (simulation-based)

xWRES

Weighted Residuals, a type of diagnostic, where ‘x’ can be nothing, C

(conditional), or P (simulation-based)

Contains Nonbinding Recommendations

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FDA guidances for industry:

Clinical Pharmacology Labeling for Human Prescription Drug and Biological Products —

Content and Format (December 2016)

Clinical Drug Interaction Studies—Cytochrome P450 Enzyme- and Transporter-Mediated Drug

Interactions (January 2020)

Exposure-Response Relationships — Study Design, Data Analysis, and Regulatory Applications

(May 2003)

In Vitro Drug Interaction Studies – Cytochrome P450 Enzyme- and Transporter-Mediated Drug

Interactions (January 2020)

Pharmacokinetics in Patients With Impaired Hepatic Function — Study Design, Data Analysis,

and Impact on Dosing and Labeling (May 2003)

See also the following FDA guidances: (1) Assessing the Effects of Food on Drugs in INDs and NDAs —

Clinical Pharmacology Considerations (February 2019); (2) General Clinical Pharmacology

Considerations for Pediatric Studies for Drugs and Biological Products (December 2014); and (3)

Pharmacokinetics in Patients With Impaired Renal Function — Study Design, Data Analysis, and Impact

on Dosing and Labeling (September 2020). When final, these guidances will represent the Agency’s

current thinking on these topics.