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Guidance for Industry: Population Pharmacokinetics
DRAFT GUIDANCE
This guidance document is being distributed for comment purposes only.
Comments and suggestions regarding this draft document should be submitted within 60 days of publication in the Federal Register of the notice announcing the availability of the draft guidance. Submit comments to Dockets Management Branch (HFA-305), Food and Drug Administration, 12420 Parklawn Dr., rm. 1-23, Rockville, MD 20857. All comments should be identified with the docket number listed in the notice of availability that publishes in the Federal Register. For questions regarding this draft document, contact Shiew-Mei Huang 301-594-5671.
U.S. Department of Health and Human Services
Food and Drug Administration
Center for Drug Evaluation and Research (CDER)
September 1997
TABLE OF CONTENTS
I. INTRODUCTION
II. BACKGROUND
III. POPULATION METHODS
A. The Two-Stage Approach
B. The Population Approach
IV. WHEN TO PERFORM A POPULATION PHARMACOKINETIC STUDY AND ANALYSIS
V. STUDY DESIGN AND EXECUTION
A. Study Design
B. Importance of Sampling Individuals on More Than One Occasion
C. Simulation
D. Study Protocol
E. Study Execution
VI. ASSAY
VII. DATA HANDLING
A. Data Assembly and Editing
B. Handling of Missing Data
C. Outliers
D. Data Type
E. Data Integrity and Computer Software
VIII. DATA ANALYSIS
A. Exploratory Data Analysis
B. Population Pharmacokinetic Model Development
C. Model Validation
IX. POPULATION ANALYSIS REPORT
A. Introduction
B. Objectives, Hypotheses, and Assumptions
C. Assay
D. Data
E. Data Analysis Methods
F. Results
G. Discussion
H. Application of Results
I. Appendix
J. Electronic Format Files
X. LABEL
REFERENCES
GLOSSARY OF TERMS
GUIDANCE FOR INDUSTRY
Population Pharmacokinetics
I. INTRODUCTION
Pharmaceutical industry scientists and the FDA have long been interested in the application of population pharmacokinetics to drug safety and efficacy evaluation. Reference is made to this subject in other FDA guidance documents such as General Considerations for the Clinical Evaluation of Drugs (FDA 77-3040), General Considerations for Pediatric Pharmacokinetic Studies, and in International Conference on Harmonisation (ICH) guidelines, including Dose-Response Information to Support Drug Registration (ICH- E4), and Studies in Support of Special Populations: Geriatrics (ICH-E7). These guidance documents support the application of special data analysis methodologies, such as the population pharmacokinetic approach, in the development and approval of new drugs with proper labeling information for the safe and effective use of the drug.
This guidance provides recommendations regarding the use of population pharmacokinetics in the drug development process. It summarizes scientific and regulatory issues that should be addressed during the conduct of population pharmacokinetic studies/analyses. It presents a comprehensive overview of population methods, including when to perform a population study/analysis; how to design and execute a population pharmacokinetic study; how to handle and analyze population pharmacokinetic data; how to perform internal and external validation of population pharmacokinetic models; and how to provide appropriate documentation for population pharmacokinetic reports intended for submission to the FDA.
Because the population approach is a rapidly evolving area of drug development and regulation, frequent communication throughout the entire process between the sponsor and the FDA review staff is encouraged.
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1. This guidance has been prepared by the Population Pharmacokinetic Working Group of the Clinical Pharmacology Section of the Medical Policy Coordinating Committee in the Center for Drug Evaluation and Research (CDER) at the Food and Drug Administration. This guidance document represents the Agency's current thinking on population pharmacokinetics in drug evaluation. It does not create or confer any rights for or on any person and does not operate to bind FDA or the public. An alternative approach may be used if such approach satisfies the requirements of the applicable statute, regulations, or both.
II. BACKGROUND
Population pharmacokinetics is the study of the sources and correlates of variability in plasma drug concentrations between individuals representative of those in whom the drug will be used clinically when relevant dosage regimens are administered (1). Certain patient pathophysiological features can regularly alter dose-concentration relationships. For example, renal failure usually causes steady state drug concentrations to be greater than those in patients with normal renal function receiving the same dosage of a drug eliminated mostly by the kidney. Population pharmacokinetics seeks to discover which measurable pathophysiologic factors cause changes in the dose-concentration relationship and to what degree so that the appropriate dosage can be recommended.
A conceptual framework within which we can provide a more formal definition of Apopulation kinetics@ is provided by a so-called hierarchical population model (also called a population model, a mixed effects model, or a random-effects model). At the first level of the hierarchy, such a model views pharmacokinetic observations in an individual (such as concentrations of drug species in biological fluids) as arising from an individual probability model, whose mean is given by a pharmacokinetic model (e.g., a biexponential) quantified by individual-specific parameters, which may vary according to the value of individual-specific time-varying covariates. The variance of the individual PK observations is also modeled, and the parameters of this model are additional individual-specific PK parameters.
At the second stage of the hierarchy, the individual parameters are regarded as random variables and the probability distribution of these (often only the mean and variance) is modeled as a function of individual-specific covariates. These models and their parameter values are what we mean by Athe population kinetics@ of a given drug, while the use of study designs and data analysis methods designed to elucidate population PK models and their parameter values is what is meant by the population pharmacokinetic approach.
The population pharmacokinetic approach in drug development offers the possibility of gaining integrated information on pharmacokinetics not only from relatively sparse data, but also from dense data (or from a combination of dense and sparse data) obtained from subjects. The approach allows the analysis of data from a variety of unbalanced designs as well as from studies that are normally excluded because they do not lend themselves to the usual forms of pharmacokinetic analysis, such as concentration data obtained from pediatric and elderly patients, or from data obtained during the evaluation of the relationships between dose or concentration and efficacy or safety.
The subjects of pharmacokinetic studies are usually healthy volunteers or highly selected patients. Traditionally, the average behavior of a group (i.e., the mean plasma concentration-time profile) has been the main focus of interest. Interindividual variability in pharmacokinetics is viewed by many incorrectly as a nuisance factor that has to be overcome, often through complex study designs and control schemes, and reduced through restrictive inclusion criteria. Study design and selection of volunteers that are rigidly standardized so that they are as homogeneous as possible are typical features of pharmacokinetic investigations. These studies, therefore, are often performed under artificial conditions that do not represent the intended clinical use of the drug.
In contrast to traditional pharmacokinetic evaluation, the population pharmacokinetic approach encompasses some or all of the following features(2):
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It seeks to obtain relevant pharmacokinetic information in patients who are representative of the target population to be treated with the drug.
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It recognizes variability as an important feature that should be identified and measured during drug development or evaluation.
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It seeks to explain variability by identifying factors of demographic, pathophysiological, environmental, or drug-related origin that may influence the pharmacokinetic behavior of a drug.
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It seeks to quantitatively estimate the magnitude of the unexplained part of the variability in the patient population.
The magnitude of the unexplained (random) variability is important because the efficacy and safety of a drug may decrease as unexplainable variability increases. Drug levels outside the target range become more likely, the greater the uncompensated variability in the relationship of dosage to steady state drug concentration. In addition to interindividual variability, the degree to which steady state drug concentrations in individuals typically vary about their long-term average is also important. Concentrations appear to vary due to inexplicable day-to-day or week-to-week kinetic variability and due to errors in concentration measurement. Estimates of this kind of variability (residual intrasubject, interoccasion variability) are important for therapeutic drug monitoring using the empiric Bayes approach. The knowledge of the relationship between concentrations, response, and physiology is essential to design dosing strategies for rational therapeutics that may not necessarily require therapeutic drug monitoring.
A framework for defining optimum dosing strategies in a population, in a subgroup, or for the individual patient is provided by resolving the above issues. Recognizing the importance of resolving these issues in drug development has led to a surge in recent years in the application of population pharmacokinetics to new drug development and the regulatory process. In a recent survey of 206 new drug applications and supplements reviewed by the Office of Clinical Pharmacology and Biopharmaceutics of the FDA in fiscal years 1995 and 1996, it was found that over 23% (i.e., 47) of these submissions contained population pharmacokinetics and/or pharmacodynamic reports (3). The use of the population approach (population pharmacokinetics/pharmacodynamics) provided useful information for the drug label in 83% of the 47 submissions on safety, efficacy and dosage optimization (3). However, in 17% of the 47 applications, the use of the approach did not yield any positive impact because the population approach was not integrated into the original plan of the drug development program (3). Population pharmacokinetics should, therefore, be integrated into drug development.
III. POPULATION METHODS
This discussion of population methods focuses on methods that provide estimates of some or all of the components of variability. Therefore, the naive averaged data approach (see Glossary of Terms) will not be discussed.
A. The Two-Stage Approach
The usual method of pharmacokinetic data analysis is the two-stage approach. The first stage is the estimation of pharmacokinetic parameters through nonlinear regression using an individual=s experimental data (data rich situation). Individual estimates obtained in the first stage serve as input data for the second-stage calculation of descriptive summary statistics on the sample, typically mean vector and variance-covariance matrix. Analysis of dependencies between parameters and covariates using classical statistical approaches (linear stepwise regression, covariance analysis, cluster analysis) may be included in the second stage. The standard two-stage approach, when applicable, can yield adequate estimates of population characteristics. Mean estimates of parameters are usually unbiased, but the random effects (variance and covariance) are likely to be overestimated in all realistic situations (4 - 7). Refinements have been proposed to improve the standard two-stage approach by bias correction for the random effects covariance and differential "weighting" of individual data according to its quality and quantity (7 - 9).
B. The Population Approach
The population approach in the context of drug evaluation developed from a recognition that, if pharmacokinetics and pharmacodynamics were to be investigated in patients, pragmatic considerations dictated that data should be collected under less stringent and restrictive design conditions. Considering the complete sample, rather than the individual as a unit of analysis, the population method of analysis (i.e., analysis according to a hierarchical random effect model) aims to estimate the distribution of the parameters and their relationships with covariates. The approach uses individual pharmacokinetic data of the observational (experimental) type, which are unbalanced and fragmentary, in addition to or instead of conventional pharmacokinetic data from traditional pharmacokinetic studies characterized by rigid and extensive design. Analysis according to a hierarchical (non-linear) random effects model (10) provides estimates of population characteristics that define the population distribution of the pharmacokinetic (and/or pharmacodynamic) parameters. In the mixed-effects modeling context, the collection of population characteristics is composed of population typical values and population variability values (generally the variance-covariance matrix). In sparse data situations where estimates of individual parameters are, a priori, out of reach, an original one-stage or population estimation approach is required. A population analysis of pharmacokinetic data, therefore, consists of estimating directly the parameters of the population from the full set of individual concentration values. The individuality of each subject is maintained and accounted for, even when raw data are sparse.
IV. WHEN TO PERFORM A POPULATION PHARMACOKINETIC STUDY AND ANALYSIS
In drug development, the population approach can help increase knowledge of the quantitative relationships between drug input patterns, patient characteristics, drug disposition, and responses (11). The population approach may be used to estimate population parameters of a response surface model in phases 1 and 2B of clinical drug development, where information is gathered on how the drug will be used in subsequent stages of drug development and after release (11). The population approach may increase the efficiency and specificity of drug development by suggesting more informative designs and analyses of experiments. Application of the population approach to phase 1 and perhaps much of phase 2B, where patients are sampled extensively, does not necessarily involve complex methods of data analysis. The two-stage methods can be used to analyze the data, and standard regression methods can be used to model dependence of parameters on covariates. Alternatively, the data from individual studies can be pooled and analyzed using the nonlinear mixed-effects modeling approach.
The population approach can also be applied to phases 2A and 3 of drug development to gain information on drug safety (efficacy) and to gather additional information on drug pharmacokinetics (and pharmacodynamics) in special populations, such as the elderly (11, 12). It is also useful in postmarketing surveillance (phase 4) studies. Studies performed in phase 3 and 4 of clinical drug development lend themselves to the use of the full pharmacokinetic screen study design.
V. STUDY DESIGN AND EXECUTION
Certain preliminary pharmacokinetic information should be known before any population pharmacokinetics study is undertaken. The drug=s major elimination pathways in humans should be known. Preliminary studies should have established the basic model describing the pharmacokinetics of the drug. The latter is important because the sparse data collected during population pharmacokinetic studies may not provide adequate information for the deduction of a pharmacokinetic model. In addition, a sensitive and specific assay (see Assay section) capable of measuring all species (parent drug and metabolites) of clinical relevance should be available before a population pharmacokinetic study is undertaken. When properly performed, population pharmacokinetic studies in patients combined with suitable mathematical/statistical analysis (e.g., using nonlinear mixed-effects modeling) is a valid approach and, on some occasions, an alternative to extensive studies.
A. Study Design
In the population pharmacokinetics context, there are two broad approaches for obtaining information about pharmacokinetic variability: (a) trough screen (single or multiple) studies and (b) full pharmacokinetic screen (experimental population pharmacokinetic) studies. They yield an increasing amount of information.
1. Single-Trough Screen
A single blood sample is obtained from each patient at or close to the trough of drug concentrations, shortly before the next dose (13), and a frequency distribution of plasma or serum levels in the sample of patients is calculated. Provided that the sample size is large, that assay and sampling errors are small, and that the dosing regimen and sampling times are identical for all patients, a histogram of such a trough screen gives a fairly accurate picture of the variability in trough concentrations in a target population. If these conditions are not met, such histograms do not represent strict pharmacokinetic variability because the data include many other sources of random fluctuation with significant contribution to the observed spread (14). When related with therapeutic outcome and occurrence of side effects, such histograms can be useful to improve the knowledge of the optimal concentration range of a given drug.
The relationships of patient characteristics to the trough levels can be explored by simple statistical procedures such as multiple linear regression. Although simple, the trough (pharmacokinetic) screen will only yield information about oral clearance and no other parameters of interest (e.g., apparent volume of distribution, half-life). Only qualitative, not quantitative, information will be obtained. Components of variability C interindividual and residual variability C cannot be separated. This method will identify, qualitatively, pharmacokinetically relevant factors and their differences among subgroups (subpopulations). When implementing this sampling strategy, the difficulty of getting patients and physicians to adhere to the sampling strategy should be kept in mind. Compliance with at least the last two doses before trough level measurement is adequate for this type of study, but the drug should be dosed to steady state. Because of uncertainty in doses and samples, the method can only reasonably be applied to drugs dosed at intervals less than or equal to one elimination half-life unless timing of dose and of level can be assured, as in inpatient studies (15). Large numbers of subjects would be needed for this type of study because the data would be noisy.
With this design, it is not advisable to contemplate measuring peak observations unless the drug is given intravenously or is a certain type of sustained release formulation. The time for achieving maximum concentration depends on rates of all processes of drug disposition and may vary among subjects. Thus, the simple estimation of peak levels is subject to large uncertainty. Sampling peak levels also yields information on variability of largely irrelevant kinetic processes for drugs for which effects relate to steady-state mean concentrations, or the area under the concentration curve.
2. Multiple-Trough Screen
In this design, two or more blood samples are obtained near the trough of steady-state concentrations from most or all patients. In addition to relating blood concentrations to patient characteristics, it is possible now to separate interindividual and residual variabilities. Since patients are studied in greater detail, this design requires fewer subjects, and the relationships to patient characteristics can be evaluated with higher precision. To estimate interindividual variability of the oral clearance, nonlinear mixed-effects modeling should be used. When using pharmacokinetic models for parameter estimation, a sensitivity analysis (16) should be required to fix a parameter such as absorption rate constant to estimate other parameters and to determine the fixed parameter value that has the least effect on the estimation of the remaining parameters. The drawbacks of the single-trough screen design apply here. Although the estimates of intersubject and residual variability may or may not be biased, they may not be precise unless a large number of patients are studied.
3. Full Pharmacokinetic Screen
With this approach, blood samples are drawn from subjects at various times (typically 1 to 6 time points) following drug administration (6). The objective is to obtain, where feasible, multiple drug levels per patient at different times. This approach permits an estimation of pharmacokinetic parameters of the drug in the study population and an explanation of variability using the nonlinear mixed-effects modeling approach. The full pharmacokinetic screen (experimental population pharmacokinetic) study should be designed to explore the relationship between the pharmacokinetics of a drug and demographic/pathophysiological features of the target population (with its subgroups) for which the drug is being developed. A full pharmacokinetic screen study requires careful design considerations.
Population pharmacokinetic analysis is useful for looking at influences of pathophysiological conditions on parameters of a model with a well-established structure. The qualitative aspects of the model should be well known before embarking on a population study.
The objective for carrying out a population pharmacokinetic study should be clearly defined since this will determine the study design. When designing a population pharmacokinetic study, the practical limitations of sampling times, number of samples/subject, and number of subjects should be considered. Preliminary information on variability from pilot studies make it possible, through simulation, to anticipate certain fatal study designs as well as informative ones. Simulation studies can optimize design features for accurate and precise estimation of population pharmacokinetic parameters (17 - 22). Optimization of sampling design is critical to efficient experimental design when there are severe limitations on the number of subjects and/or samples/subject, as in pediatrics and the elderly (20). The use of informative study designs for population pharmacokinetic studies that yield informative data is encouraged (17, 19 - 22). The use of Bayesian designs for pediatric patients where adult data may serve as informative priors may be appropriate. Such a study should include enough patients in important subgroups to ensure accurate and precise parameter estimation and the detection of any subgroup differences.
B. Importance of Sampling Individuals on More Than One Occasion
The variance of an individual=s PK observations about the individual-specific PK model on a given occasion (i.e., the intra-individual variability; see Introduction) can conceptually be factored into two components: variability of PK observations due to variability of the PK model from occasion to occasion (inter-occasion variability), and variability of PK observations about the individual PK model appropriate for the particular occasion (noise; PK model misspecification). To be sure, some inter-occasion variability may be explained by inter-occasion variation in individual time-varying covariates, but to the extent that it is not, it represents, along with the noise, the irreducible uncertainty in predicting, and hence controlling drug concentrations. Drugs with narrow therapeutic indices and large inter-occasion variability, for example, will be very difficult to control. If a population PK study consists of PK observations solely from individuals each studied on only a single occasion, the inter-occasion variability will appear incorrectly in the inter-individual variability term and not in the intra-individual variability term. This may lead to inappropriate optimism about the ability to control individual therapy within the therapeutic range by using feedback (e.g., therapeutic drug monitoring, or simply adjusting dose according to observed drug effects), and also to a fruitless search for inter-individual covariates that might explain the spuriously inflated) inter-individual variability. It is of utmost importance to avoid this artifact by ensuring that at least a moderate subset of subjects contributing data to a population PK study contribute data from more than one occasion. Indeed if this is done, one may hope to separately estimate the components of intra-individual variability (23).
C. Simulation
Simulation of a planned study offers a powerful tool for evaluating and understanding the consequences of different study designs. Shortcomings in study design result in the collection of uninformative data. Simulation can reveal the effect of input variables and assumptions on the results of a planned population pharmacokinetic study. Simulation allows study designers to assess the consequences of the design factors chosen and the assumptions made. Thus, simulation enables the pharmacometrician to better predict the results of a population study and to choose the study design that will best meet the study objectives. It is important to simulate a population pharmacokinetic study using alternative study designs to determine the most informative design, given the study objectives, before initiating such studies. Simulation is a useful tool to provide convincing objective evidence of the merits of a proposed study design and analysis (24).
D. Study Protocol
Two types of protocol may be considered depending on the setting in which a population pharmacokinetic study is to be performed. If it is added on to a clinical trial (as can be envisaged in most situations), the population study should be carefully interwoven with the existing clinical protocol to ensure that it does not compromise the primary objectives of the study. Every effort should be made to convince investigators of the relevance of including a population pharmacokinetic study. Graphical displays of simulation results may help to achieve this objective. In addition, a population pharmacokinetic study protocol should be written since a population study can also be defined as evaluating data from existing data and/or data coming from more than one study. When a population study is a stand alone study, a comprehensive protocol should be prepared. The population pharmacokinetic study as part of the clinical protocol and the population pharmacokinetic study protocol are discussed briefly.
1. Clinical Protocol
The objectives of the population pharmacokinetic study should be clearly defined. These objectives, should be secondary to the primary clinical study objectives or primary when they would not compromise the study in question. The criteria for sampling subjects and methods for data analysis (described in the population pharmacokinetic study protocol) should be clearly stated. The data to be used for population analysis should be defined, including patients and subgroups to be used and covariates to be measured. The sampling design should be specified and any subgroup stratification should be defined (25). In a multicenter trial, it may sometimes be necessary to obtain extensive data from some centers and sparse data from others (2). This type of data collection can be useful for informative data analysis protecting against model misspecification and it should be specified in the protocol. The data analysis plan should be described in advance in the protocol as accurately as possible. Statements such as Aa pharmacokinetic screen will be performed@ or Adata will be analyzed using NONMEM@ are inappropriate because they do not convey information on the study objective or how the analysis will be carried out.
If possible, special case report forms that can be easily understood by investigators should be designed to meet the needs of the pharmacokinetic evaluation.
2. Population Pharmacokinetic Study Protocol
The practical details of the pharmacokinetic evaluation should be described in a population pharmacokinetic study protocol, although the principles may be specified in the clinical study protocol in a general way. The primary (same as that in the clinical protocol) and secondary objectives should be clearly stated. The secondary objectives should be those that enable the data analyst to search for the unexpected, after the primary objectives have been addressed. The sampling design, data assembly, data checking procedure, and procedures for handling missing data and data anomalies should be clearly spelled out in the protocol. The data to be used for population analysis should be defined, including patients and subgroups to be used and covariates to be measured. The sampling design should be specified and any subgroup stratification should be defined (25). Real-time data assembly (see Data Assembly) would permit population pharmacokinetic data analysis to be performed before the end of a clinical trial and would make it possible to include the results in the filing of the new drug application (NDA). If drug-drug interactions are to be characterized, the protocol should prespecify whether to determine (1) the effect of the presence or absence of a specific concomitant medication or (2) the total daily dose of the concomitant medication or (3) the plasma concentration of the potentially interacting medication. If food effect is to be evaluated, the time of sampling in relation to food intake, and the composition of food, should be specified in the protocol. Also, the procedure for analyzing the data (and validation when appropriate) should be specified (see Data Analysis).
Distinguishing between clinically relevant and statistically significant covariates is important. Time variant covariates represent particular problems. In this case, several measurements should be made during the course of the study and, if this information is found to be incomplete, model-based techniques may be used for imputation between available data (See Handling of Missing Data). This also applies to time invariant covariates. Sensible methods of dealing with missing data should be predefined in the data analysis plan of the protocol. The issue of interoccasion variability (23) should be recognized and addressed in long-term studies. It is understandable that population pharmacokinetic data analysis, as a modeling exercise, cannot be planned to the fullest detail. However, the protocol should include study objectives; patient inclusion/exclusion criteria and pharmacokinetic evaluability criteria; sampling design; data handling and checking procedures; initial assumptions for modeling; a list of possible covariates to be investigated and the rationale for choosing them; and whether a sensitivity analysis and a validation procedure is envisaged.
E. Study Execution
A population pharmacokinetic study should be conducted according to current good clinical practice and good laboratory practice standards. The sampling strategy and the recording of samples should be part of good clinical practice and the handling of samples part of good laboratory practice. Error in recording sampling times relative to dosing history could result in biased and imprecise parameter estimates, depending on the nature and degree of the error (22).
Every effort should be made to ensure that study subjects and clinical investigators comply with study protocol. To improve compliance, the protocol should not be overly complicated and blood sampling times should be convenient to both clinical staff and patients. The necessity of blood sampling should be carefully explained to patients and investigators. Instructions provided to the investigators should be clear and concise. These measures should be backed up by adequate monitoring by the sponsor while the study is ongoing. Adequate resources should be available for optimal sample preparation, storage at the investigator site, and transportation and storage of biological samples prior to analysis.
Noncompliance with drug intake can be a source of confounding and lead to inappropriate interpretation of study results (26). Special care should be taken to use methodologies that are as objective as possible to reconstruct dosage history. Communication between all parties involved is essential for the successful conduct of a population study, especially if the study is part of a large scale clinical trial.
VI. ASSAY
Correct evaluation of pharmacokinetic data depends on the accuracy of the analytic data obtained. Clinical investigators and their staff should be educated on the importance of sample timing, recording, proper labeling, and handling of samples.
The accuracy of analytical data depends on the criteria used to validate the method. Consequently, drug and/or metabolite(s) stability, assay sensitivity, selectivity, recovery, linearity, precision, and accuracy should be carefully scrutinized before samples are analyzed. The importance of using validated assay methods for analyzing pharmacokinetic data cannot be over emphasized.
VII. DATA HANDLING
A. Data Assembly and Editing
Real-time data assembly prevents the problems that generally arise when population pharmacokinetic data are stored until the end of a clinical trial. Real-time data assembly permits an ongoing evaluation of site compliance with the study protocol and provides the opportunity to correct violations of study procedures and policy. Evaluation of pharmcokinetic data can provide the data safety monitoring board with insights into drug exposure safety evaluations and drug-drug interactions. Adequate policies and procedures should be in place for study blind maintenance (27). Real-time data assembly creates the opportunity for editing the concentration-time data, drug dosing history, and covariate data necessary to meet the pharmacokinetic objectives of a clinical trial (28). Data assembly to create a population pharmacokinetic database after study completion may result in delays that are incompatible with the time course of the development program. It is important, therefore, to specify in the study protocol the use of real-time data analysis.
Data editing means using a set of procedures for detecting and correcting errors in the data. The procedures should be planned before study initiation and predefined in the study protocol. Criteria for declaring data usable or unusable (e.g., time of blood sampling missing, dosing information with no associated concentrations, concentrations with missing dosing information) should be spelled out in the study protocol.
B. Handling of Missing Data
After assembling data for population analysis, the issue of any missing covariate data should be addressed. Missing data represent a potential source of bias. Thus, every effort should be made to fulfill the protocol requirements concerning the collection and management of data. Deletion of subjects with missing covariates can yield biased and imprecise parameter estimates. Although caution should be taken when imputing missing values, it is usually better to estimate and impute a subject=s missing covariate data values than to delete that subject from the data set. Simple methods of imputation include the use of median, mean, or mode for missing values. These methods are biased and inefficient when predictors are correlated (29). Using maximum likelihood procedures (i.e., deriving regression models) for predicting each predictor from all other predictors is a better method. Alternatively, where imputation across a time series is possible, such a method should be used (30). Imputation procedures should be described, including a detailed explanation of how such imputations were done and of the underlying assumptions made. The sensitivity of the results of the analysis to the method of imputation of missing data should be tested, especially if the number of missing values is substantial. So-called multiple imputation, in which several imputed data sets are analyzed, can be used, where conclusions are of borderline significance, yet of clinical importance, to remove the optimistic bias from estimates of precision caused by imputing data and treating it as though it were actually observed (31).
C. Outliers
The statistical definition of an outlier is, to some extent, arbitrary. The reasons for declaring a data point to be an outlier should be statistically convincing and prespecified in the protocol. Any physiological or study-related event that renders the data unusable should be explained in the study report. Because of the exploratory nature of population analysis, it may be that the study protocol did not specify a procedure for dealing with outliers. In such a situation, model building should be performed on the reduced data set (i.e., data set without the outliers) as long as the conclusions are appropriately restricted to the limited population defined by the outlier-removal procedure. Including extreme outliers is not a good practice when using least-squares or normal-theory type estimation methods, as these inevitably have a disproportionate effect on estimates. Also, it is well known that for most biological phenomena, outlying observations are far more frequent than suggested by the normal distribution (i.e., biological distributions are heavy-tailed). Some robust methods of population analysis have recently been suggested, and these may allow outliers to be retained, without giving them undue weight (32-34).
D. Data Type
Two types of data can be used in population analysis: experimental data and observational (or population) pharmacokinetic data. Experimental data arise from traditional pharmacokinetic studies characterized by controlled conditions of drug dosing and extensive blood sampling. Population pharmacokinetic data are collected, most often, as a supplement in a study designed and carried out for another purpose. The data are characterized by minimal control and few design restrictions: the dosing history is subject specific, the amount of pharmacokinetic data collected from each subject varies, the timing of blood sampling in relation to drug administration differs, and the number of samples per patient, typically 1 to 6, is small.
E. Data Integrity and Computer Software
Data management activities should be based on established standard operating procedures. The validity of the data analysis results depends on the quality and validity of methods and software used for data management (data entry, storage, verification, correction, and retrieval), and pharmacostatistical processing. Documentation of testing procedures for the computer software used for data management should be available. It is crucial that the software used for population analysis be adequately supported and maintained.
VIII. DATA ANALYSIS
Population modeling can potentially be used in several phases of new drug development, including the planning, design, and analysis of studies in the exploratory and confirmatory stages of new drug development. Thus, the protocol should describe the pharmacokinetic models to be tested. Careful documentation of modeling efforts, data visualization, model validation (when appropriate), and data listing should be provided.
Population pharmacokinetic data analysis can be carried out in three interwoven steps: (a) exploratory data analysis, (b) population pharmacokinetic model development, and (c) model validation. The data analysis plan should be clearly defined in the study protocol.
A. Exploratory Data Analysis
Exploratory data analysis isolates and reveals patterns and features in the population data set using graphical and statistical techniques. It also serves to uncover unexpected departures from familiar models. An important element of the exploratory approach is its flexibility, both in tailoring the analysis to the structure of the data and in responding to patterns that successive analysis steps uncover.
Most population analysis procedures are based on explicit assumptions about the data, and the validity of the analyses depends upon the validity of assumptions. Exploratory data analysis techniques provide powerful diagnostic tools for confirming assumptions or, when the assumptions are not met, for suggesting corrective actions. Without such tools, confirmation of assumptions can be replaced only by hope. Exploratory data analysis should be coupled with more sophisticated population modeling techniques in the analysis of population pharmacokinetic data (35). Exploratory data analysis performed should be well described in the population report.
B. Population Pharmacokinetic Model Development
1. Objectives, Hypotheses, and Assumptions
The objectives of the analyses should be clearly stated. The hypotheses being investigated should be clearly articulated. It is recommended that all known assumptions inherent in the population analysis be explicitly expressed.
2. Population Model Development
The steps taken (i.e., sequence of models tested) to develop a population model (35-37) should be clearly outlined to permit the reproducibility of the analysis. The criteria and rationale for model building procedures dealing with confounding, covariate, and parameter redundancy should be clearly stated. The criteria and rationale for model reduction to arrive at the final population model should also be clearly explained.
3. Reliability of Results
The reliability of the analysis results should be checked using diagnostic plots; confidence intervals (standard errors) for key parameters should be checked using nonparametric techniques (such as the jackknife (35)) and the profile likelihood plot (mapping the objective function (38)). This is appropriate because the possibility of biased results is increased by the complexity of the population models and by the sparse individual data available. The nonlinearity of the statistical model and ill-conditioning of a given problem can produce numerical difficulties and force the estimation algorithm into a false minimum. Because the maximum likelihood procedure is sensitive to bizarre observations, it may be necessary to check the stability of the model (39). It is important to evaluate the quality of the results of a population study/analysis for robustness. Evaluation for robustness may be approached by sensitivity analysis (38); the use of case deletion diagnostics (35, 37) is also encouraged. Evidence of robustness renders the results reasonable and independent of the analyst.
C. Model Validation
Validation can be defined as the evaluation of the predictability of the model developed (i.e., the model form together with the model parameter estimates) with a learning or index data set on a validation data set not used for model building and estimation. A model may be valid for one purpose and not valid for another. The objective of validation is to examine whether the model is a good description of the validation data set in terms of its behavior and of the application proposed.
Validation depends on the objective of the analysis. Not all population models may need to be validated. Population models developed for explaining variability (which does not require dosage adjustment recommendation) and for providing descriptive information for labeling may be tested for stability only (39). Also, population pharmacokinetic models developed as part of a population pharmacokinetic /pharmacodynamic model may not need to be validated. However, the predictive performance of a population pharmacokinetic model developed for dosage recommendation as part of labeling should be tested. In such a situation, model validation procedure should be an integral part of the protocol.
1. Types of Validation
There are two types of validation: external and internal. External validation is the application of the developed model to a new data set (validation data set) from another study. Internal validation refers to the use of data-splitting and resampling techniques (cross-validation and bootstrapping) for validation purposes. External validation provides the most stringent method for testing a developed model.
For testing predictive performance, data-splitting is an effective method of model validation when it is not practical to collect a new set of data to test the model. The disadvantage of this method is that, in the area of linear regression, the predictive accuracy of the model is a function of the sample size resulting from the data-splitting (40). To maximize the predictive accuracy, it is recommended that the entire sample be used for model development and assessment (40). Data-splitting may not validate the final model if one desires to recombine the index and validation data sets to derive a refined model for predictive purposes. However, if data-splitting is to be used, a random subset of the data (two-thirds, i.e., the index data set) should be used for model building and the remaining data should be used for model validation. At the end of the exercise, the index and validation data sets should be pooled and the final population model fitted to the data to determine the appropriateness of each covariate retained in the final model.
Cross-validation is repeated data-splitting. The benefits of cross-validation over data-splitting are that (1) the size of the model development database can be much larger so that less data are discarded from the estimation process and (2) not relying on a single sample split reduces variability. Due to high variation of accuracy estimates, cross-validation is inefficient when the entire validation process is repeated (41).
Bootstrapping, an alternative method of internal validation, has the advantage of using the entire data set for model development. Sample size is critical in pediatric settings where ethical and medical concerns limit recruitment into studies. The bootstrap resampling procedure can be useful for evaluating the performance of a population model when there is no test data set (39).
2. Validation Methods
The issue of validation of population models remains unresolved. The advantages and disadvantages of methods addressed in the literature and of methods used in applications have been discussed above. The data analyst should justify the method he/she chooses. Although the science of validation of population models is still evolving, consideration will be given to well-described innovative methods of model validation.
This is calculated as the difference between observed and model-predicted concentrations. The mean prediction error is calculated and used as a measure of accuracy and the mean absolute error (or root mean square error) is used as a measure of precision.
This method can be used when only one sample per subject is obtained. When more than one observation is obtained per subject, the method is inadequate because prediction errors are not independent if several concentrations per subject are available (42). The method does not take into account the correlation of observations within subjects.
This method (43) takes into account variability and correlation of observations within an individual. The mean standardized prediction error and the variance are calculated, and a t-test (appropriately a z-test) performed to determine whether the mean is significantly different from zero and the standard deviation approximates 1. Confidence intervals about the standard deviation of the standardized prediction errors can be constructed. This test performed on the mean of the standardized prediction errors incorrectly assumes that the estimates for the population parameter values are given without error. The use of the approach is discouraged.
This method (44) avoids the problems encountered in prediction error of concentrations by performing validation with model parameters. Model parameters are predicted from the validation data set with or without covariates and bias and precision are calculated for the predictions.
A simple plot of residuals obtained by freezing the final model and predicting into a validation data set against covariates can yield information on the clinical significance of the model in terms of a covariate or subpopulation (45).
These methods are useful approaches for examining the predictive performance of population models. When there is no test data set, the bootstrap approach should be used: the mean parameter values obtained by repeatedly fitting the final population model to at least 200 bootstrap replicate data sets are compared to the final population model parameter estimates obtained without bootstrap replication (39).
A new technique, the so-called Posterior Predictive Check, may prove useful in determining whether important clinical features of present and future data sets are faithfully reproduced by the model (46)
IX. POPULATION ANALYSIS REPORT
The report should contain the following: (a) introduction, (b) objectives, hypotheses, and assumptions (c) assay, (d) data, (e) data analysis methods, (f) results, (g) discussion, (h) application, (I) appendix, and (j) electronic format files.
A. Introduction
The introduction should briefly state the general intent of the analysis. It should include enough background information to place the analysis in its proper context within the drug=s clinical development and to indicate any special features of a population pharmacokinetic study.
B. Objectives, Hypotheses, and Assumptions
The objectives of the analysis, and study where applicable, should be stated. In addition to the primary objective, any secondary objectives should be explicitly stated. If the analysis was performed as a result of the implementation of a study protocol, the report should note whether the objectives were preplanned or were formulated during or after study completion. This is not necessary for the analysis of pooled data. The assumptions made and the hypotheses tested should be clearly stated in the report (see section VIII B.1).
C. Assay
This section should contain a description of the assay method(s) used in quantitating drug concentrations. Assay performance (quality control samples) should also be included. The validity of the method(s) should also be described.
D. Data
Where data are pooled for analysis, the report should state the studies from which the data were pooled. The data set should be part of the appendix to the report. The report should contain the response variable and all covariate information and explain how they were obtained. The report should include a description of the sampling design used to collect the plasma samples and a description of the covariate, including their distributions and the accuracy and precision with which they were measured. An electronic copy of the data set should be submitted. Data quality control and editing procedures should be described in this section.
E. Data Analysis Methods
This section should contain a description of the treatment of outliers and missing data (where applicable), and a detailed description of the criteria and procedures for model building and reduction incorporating exploratory data analysis. A flow diagram(s) of the analysis performed and representative control/command files for each significant model building/reduction step should be provided.
F. Results
The key results of the analysis should be compiled into comprehensible tables and plots. To aid interpretation and application, a thorough description of the results should be provided. Complete output of results obtained for the final population model and key intermediate steps should be included.
G. Discussion
The report should include a comprehensive statement of the rationale for the model building and reduction procedures, interpretation of the results, protocol violations, and any other relevant information.
H. Application of Results
A discussion of how the results of the analysis will be used (e.g., to support labeling, individualize dosage, support safety, or define additional studies) should be provided.
In addition, the use of graphics to communicate the application of a population model (e.g., for dosage adjustment) is recommended.
I. Appendix
The appendix should contain the data set(s) used in population analysis. The output table from the final model should be in this section, as well as any additional plots that are deemed important. Where the analysis was performed as a result of a clinical study or a population pharmacokinetic study, the study protocol should be included in the appendix.
J. Electronic Format Files
Data set and representative command files used for population analyses may be submitted as ASCII files and/or PDF files with the filing of a new drug application. It is understood that data format may be software specific. The Agency may, on some occasions, request that the data be formatted in a manner that is compatible with another type of software. An electronic copy of the report may also be a part of the submission. However, the submission of these data and reports in electronic form does not eliminate the need to submit a paper copy.
X. LABEL
Where population model parameter estimates are included in the label, the total number of subjects used for the analysis and the precision with which the parameters were estimated should be included in the report. Where the results of the population analysis provide descriptive information for the label, it should be stated that the information was obtained from a population analysis. Information from population analyses used to characterize subpopulations should include the total sample size used for the analysis and the proportion of subjects belonging to the subpopulation.
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GLOSSARY OF TERMS
Accuracy: A state characterized by measurements or estimates clustering tightly about the true value.
Bias: The degree to which the typical prediction is either too high or too low.
Bootstrapping: A computer-based resampling method for estimating sampling variances, confidence intervals, stability of regression models, and other properties of statistics.
Covariates: A set of explanatory variables.
Cross-validation: A statistical method for estimating prediction error.
Data assembly: The merging of covariate information, dosing history, sample times relative to dosing history, and concentration measurements to form the population pharmacokinetic database.
Data editing: A set of procedures for detecting and correcting errors in the data.
Data-splitting: The act of partitioning available data into two portions C estimation or index data set and validation data set.
Exploratory data analysis: A method of data analysis that emphasizes the use of graphical and statistical techniques to isolate patterns and features in a data set, revealing these forcefully to the data analyst.
External validation: The application of the developed model to a new data set (validation data set) from another study.
Fixed effects: The population average values of pharmacokinetic parameters that may in turn be a function of various patient demographic or pathophysiological variables (Whiting B, Kelman AW, Grevel J. Population pharmacokinetics: theory and clinical application. Clin Pharmacokinet 1986; 11: 387 - 401).
Full pharmacokinetic screen: A sampling design in which blood samples are drawn from subjects at various times (typically 1 to 6 time points) following drug administration.
Imputation: The filling in of plausible and consistent values for missing data.
Interoccasion variability: Random variability in individual pharmacokinetic parameters between study occasions.
Intersubject variability: The variation of response (e.g., concentration) from one subject to another to a given treatment regimen; measures the magnitude of random individual variability in relation to fixed effects.
Internal validation: The use of data-splitting and resampling techniques (cross-validation and bootstrapping) for validation purposes.
Jackknife technique: A statistical method for reducing bias in parameter estimates and calculating realistic variances.
Model stability: The choice of variables included in the population model.
Model validation: The evaluation of the predictability of the model (i.e., the model form together with the model parameter estimates) developed with learning or index data set on a validation data set not used for model building and estimation.
Multiple-trough screen: A sampling design in which two or more blood samples are obtained near the trough of steady state concentrations, at least from most patients.
Nonlinear mixed-effects modeling: A nonlinear regression technique that accounts for both fixed and random effects, hence mixed effects.
Naive averaged data approach: A method of estimating mean (population) pharmacokinetic parameters by first averaging the concentration at each time point and fitting a model to the averaged data.
Outlier: Collective term used to refer to either a contaminant or a discordant observation (Beckman & Cook, 1983; Beckman RJ, Cook RD. OutlierY..s. Technometrics 1983; 25: 119 - 149 ). A discordant observation is any observation that appears surprising or discrepant to the investigator; a contaminant observation is any observation that is not realized from the target distribution (Beckman & Cook, 1983; Beckman RJ, Cook RD. Outlier..Y..s. Technometrics 1983; 25: 119 - 149).
Population: A group of subjects studied, usually 30 or more.
Population approach: A model-based approach to drug development.
Population pharmacokinetics: The study of variability in plasma drug concentration between individuals when standard dosagte regimens are administered.
Precision: A description of how sets of measurements or estimates cluster about some value.
Prediction error: The difference between an observed value and a model predicted value.
Random effects: The intersubject variability and residual intrasubject variability
Residual intrasubject variability: The variation in response (e.g., concentration) due to inexplicable day-to-day kinetic variability and response (concentration) measurement error.
Single-trough screen: A sampling design in which a single blood sample is obtained from each or some patients in a study at or close to the trough (steady-state minimum) of drug concentrations shortly before the next dose (13).
Simulation: A numerical technique for conducting experiments with certain types of mathematical models describing the behavior of the system under study.
Standard two-stage approach: A method of estimating population pharmacokinetic parameters in which a pharmacokinetic model is fitted to each subject's data in the first step, and in the second step estimates of population characteristics of each parameter is computed as the empirical mean (arithmetic or geometric) and variance of the individual parameter estimates.
Traditional pharmacokinetic study: A pharmacokinetic study in which subjects are sampled intensively.
Unbalanced design: A study design (in the context of this guidance) in which all subjects participating in a study do not supply the same number of observations.
Date created: September 11, 1997; last updated: July 5, 2005 |
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