Incorporating measures of variability and uncertainty into the prediction of in vivo hepatic clearance from in vitro data.

The existing procedures for quantitative in vitro-in vivo clearance prediction can be significantly biased either by totally neglecting the existing variability and uncertainty by using mean parameter values or by implementing Monte Carlo simulation with statistical distribution of the parameters reconstructed from very small sets of data. The aim of the present study is to develop a methodology for the prediction of in vivo hepatic clearance in the presence of semiquantitative or qualitative data and accounting for the existing uncertainty and variability. The method consists of two steps: 1) transformation of the information available into fuzzy sets (fuzzification); and 2) computation of the in vivo clearance using arithmetic operations with fuzzy sets. To illustrate the approach, rat hepatocyte and microsomal data for eight benzodiazepine compounds are used. A comparison with a standard Monte Carlo procedure is made. The methodology proposed can be used when Monte Carlo simulation may be biased or cannot be implemented. The obtained fuzzy in vivo clearance can be used subsequently in fuzzy simulations of pharmacokinetic models.     

Fuzzy Simulation of Pharmacokinetic Models: Case Study of Whole Body Physiologically Based Model of Diazepam

The aim of the present study is to develop and implement a methodology that accounts for parameter variability and uncertainty in the presence of qualitative and semi-quantitative information (fuzzy simulations) as well as when some parameters are better quantitatively defined than others (fuzzy-probabilistic approach). The fuzzy simulations method consists of (i) representing parameter uncertainty and variability by fuzzy numbers and (ii) simulating predictions by solving the pharmacokinetic model. The fuzzy-probabilistic approach includes an additional transformation between fuzzy numbers and probability density functions. To illustrate the proposed method a diazepam WBPBPK model was used where the information for hepatic intrinsic clearance determined by in vitro-in vivo scaling was semi-quantitative. The predicted concentration time profiles were compared with those resulting from a Monte Carlo simulation. Fuzzy simulations can be used as an alternative to Monte Carlo simulation.     

Handling uncertainty in cost-effectiveness models

The use of modelling in economic evaluation is widespread, and it most often involves synthesising data from a number of sources. However, even when economic evaluations are conducted alongside clinical trials, some form of modelling is usually essential. The aim of this article is to review the handling of uncertainty in the cost-effectiveness results that are generated by the use of decision-analytic-type modelling. The modelling process is split into a number of stages: (i) a set of methods to be employed in a study are defined, which should include a 'reference case' of agreed methods to enhance the comparability of results; (ii) the clinical and demographic characteristics of the patients the model relates to should be specified as carefully as in any experimental study; and (iii) the data requirements of the model should be estimated using the principles of Bayesian statistics, such that prior distributions are specified for unknown model parameters. Monte Carlo simulation can then be employed to sample from these prior distributions to obtain a distribution of the cost effectiveness of the intervention. Such probabilistic analyses are related to parameter uncertainty. In addition, modelling uncertainty is likely to add a further layer of uncertainty to the results of particular analyses.     

Diazepam Pharamacokinetics from Preclinical to Phase I Using a Bayesian Population Physiologically Based Pharmacokinetic Model with Informative Prior Distributions in Winbugs

Modelling is an important applied tool in drug discovery and development for the prediction and interpretation of drug pharmacokinetics. Preclinical information is used to decide whether a compound will be taken forwards and its pharmacokinetics investigated in human. After proceeding to human little to no use is made of these often very rich data. We suggest a method where the preclinical data are integrated into a whole body physiologically based pharmacokinetic (WBPBPK) model and this model is then used for estimating population PK parameters in human. This approach offers a continuous flow of information from preclinical to clinical studies without the need for different models or model reduction. Additionally, predictions are based upon single parameter values, but making realistic predictions involves incorporating the various sources of variability and uncertainty. Currently, WBPBPK modelling is undertaken as a two-stage process: (i) estimation (optimisation) of drug-dependent parameters by either least squares regression or maximum likelihood and (ii) accounting for the existing parameter variability and uncertainty by stochastic simulation. To address these issues a general Bayesian approach using WinBUGS for estimation of drug-dependent parameters in WBPBPK models is described. Initially applied to data in rat, this approach is further adopted for extrapolation to human, which allows retention of some parameters and updating others with the available human data. While the issues surrounding the incorporation of uncertainty and variability within prediction have been explored within WBPBPK modeling methodology they have equal application to other areas of pharmacokinetics, as well as to pharmacodynamics.     

Handling of contamination variability in exposure assessment: a case study with ochratoxin A.

The contamination of foods dedicated to human consumption varies over space and time. In exposure assessment, this is usually addressed through probabilistic modelling. The present work explores how the variability and uncertainty of exposures estimated at the population level are affected by: (a) the (non-)parametric nature of input contamination distributions; (b) the time-window used to sample contamination values within those distributions. Focusing on exposure of the French population to food mycotoxin ochratoxin A, we implement a range of second-order Monte-Carlo simulations that allow distinguishing variability of exposures from uncertainty of distributional parameters estimates. A simulation runs 10,000 iterations. Overall estimates of parameters are given by the median across iterations and 95%CI by 2.5th and 97.5th percentiles. Our results show that: (a) parametric (log-normal) input distributions may lead to over-estimation of variability and greater uncertainty as compared to non-parametric ones (P97.5 [95%CI] of 7.1 [6.6;7.7] for Parametric-Occasion, 4.6 [4.3;5.0] for Non-Parametric-Occasion), and that (b) the 'Occasion' time-window combines better estimate of variability and lower uncertainty when exposure modelling is applied to populations living in developed countries with complex agri-food systems (P97.5 [95%CI]: 7.3 [6.2;8.9] for Non-Parametric-Week, 4.6 [4.3;5.0] for Non-Parametric-Occasion). A deterministic approach is nevertheless preferred to probabilistic modelling every time input data quality is questionable.     

Propagation of Population PK and PD Information Using a Bayesian Approach: Dealing with Non-Exchangeability

The aim of this work is to implement a conservative prior that safeguards against population non-exchangeability of prior and data likelihood, in the framework of population pharmacokinetic/pharmacodynamic analysis, incorporating multi-level hierarchical modelling. Three different exercises were performed: (i) we investigated the use of parametric priors in the multilevel hierarchical modelling framework; (ii) we assessed the average performance of the multilevel hierarchical model compared to the standard mixed effect model, considering also some interesting extreme cases and (iii) we implemented an application with a small Proof of Principle (PoP) study, which demonstrates the propagation of information across PD studies using multilevel modelling. Fitting with the 4-level model and informative parametric priors performed similar to a meta-analysis of the test datasets combined with the datasets that the priors came from, demonstrating that parametric priors can be used alternatively to meta-analysis. Further, the 4-level model gave posterior distributions which had larger uncertainty but at the same time were unbiased, compared to the 3-level model, and therefore implements a more conservative prior in a formal way, which is appropriate when the prior and the test populations are not exchangeable. For the application with the PoP study, the statistical power of detecting the difference in potency between two drugs, when inter-study variability was present, was greater when an extra level in the hierarchical model to account for it, was used. In conclusion, by applying the prior one hierarchical level above the level of the parameters of interest, we implemented a more conservative prior, compared to applying the prior directly on the parameters of interest. The approach is equivalent to Bayesian individualization, offers a safeguard against bias from the prior and also avoids the danger of the data being overwhelmed by a strong prior.     

Fundamentals of population pharmacokinetic modelling: validation methods

Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition; and population pharmacokinetic modelling provides an estimation of drug pharmacokinetic parameters. This method's defined outcome aims to understand how participants in population pharmacokinetic studies are representative of the population as opposed to the healthy volunteers or highly selected patients in traditional pharmacokinetic studies. This review focuses on the fundamentals of population pharmacokinetic modelling and how the results are evaluated and validated. This review defines the common aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. The concept of validation, as applied to population pharmacokinetic models, is explored focusing on the lack of consensus regarding both terminology and the concept of validation itself. Population pharmacokinetic modelling is a powerful approach where pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. Given the lack of consensus on the best approaches in model building and validation, sound fundamentals are required to ensure the selected methodology is suitable for the particular data type and/or patient population. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and the results relied upon.     

A probabilistic effect assessment model for hazardous substances at the workplace

A major problem in risk assessment is the quantification of uncertainties. A probabilistic model was developed to consider uncertainties in the effect assessment of hazardous substances at the workplace. Distributions for extrapolation factors (time extrapolation, inter- and intraspecies extrapolation) were determined on the basis of appropriate empirical data. Together with the distribution for the benchmark dose obtained from substance-specific dose-response modelling for the exemplary substances 2,4,4-trimethylpentene (TMP) and aniline, they represent the input distributions for probabilistic modelling. These distributions were combined by Monte Carlo simulation. The resulting target distribution describes the probability that an aspired protection level for workers is achieved at a certain dose and the uncertainty associated with the assessment. In the case of aniline, substance-specific data on differences in susceptibility (between species; among humans due to genetic polymorphisms of N-acetyltransferase) were integrated in the model. Medians of the obtained target distributions of the basic models for TMP and aniline, but not of the specific aniline model are similar to deterministically derived reference values. Differences of more than one order of magnitude between the medians and the 5th percentile of the target distributions indicate substantial uncertainty associated with the effect assessment of these substances. The probabilistic effect assessment model proves to be a practical tool to integrate quantitative information on uncertainty and variability in hazard characterisation.     

Influence of covariate distribution on the predictive performance of pharmacokinetic models in paediatric research

Aims

The accuracy of model-based predictions often reported in paediatric research has not been thoroughly characterized. The aim of this exercise is therefore to evaluate the role of covariate distributions when a pharmacokinetic model is used for simulation purposes.

Methods

Plasma concentrations of a hypothetical drug were simulated in a paediatric population using a pharmacokinetic model in which body weight was correlated with clearance and volume of distribution. Two subgroups of children were then selected from the overall population according to a typical study design, in which pre-specified body weight ranges (10–15 kg and 30–40 kg) were used as inclusion criteria. The simulated data sets were then analyzed using non-linear mixed effects modelling. Model performance was assessed by comparing the accuracy of AUC predictions obtained for each subgroup, based on the model derived from the overall population and by extrapolation of the model parameters across subgroups.

Results

Our findings show that systemic exposure as well as pharmacokinetic parameters cannot be accurately predicted from the pharmacokinetic model obtained from a population with a different covariate range from the one explored during model building. Predictions were accurate only when a model was used for prediction in a subgroup of the initial population.

Conclusions

In contrast to current practice, the use of pharmacokinetic modelling in children should be limited to interpolations within the range of values observed during model building. Furthermore, the covariate point estimate must be kept in the model even when predictions refer to a subset different from the original population.     

Fundamentals of population pharmacokinetic modelling: modelling and software

Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition. This review focuses on the fundamentals of population pharmacokinetic modelling and provides an overview of the commonly available software programs that perform these functions. This review attempts to define the common, fundamental aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. An overview of the most commonly available software programs is also provided. Population pharmacokinetic modelling is a powerful approach where sources and correlates of pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and the results relied upon. Various nonlinear mixed-effects modelling methods, packaged in a variety of software programs, are available today. When selecting population pharmacokinetic software programs, the consumer needs to consider several factors, including usability (e.g. user interface, native platform, price, input and output specificity, as well as intuitiveness), content (e.g. algorithms and data output) and support (e.g. technical and clinical).     

Simulating pharmacokinetic and pharmacodynamic fuzzy-parameterized models: a comparison of numerical methods

Statistical techniques have been traditionally used to deal with parametric variation in pharmacokinetic and pharmacodynamic models, but these require substantial data for estimates of probability distributions. In the presence of limited, inaccurate or imprecise information, simulation with fuzzy numbers represents an alternative tool to handle parametric uncertainty. Existing methods for implementing fuzzy arithmetic may, however, have significant shortcomings in overestimating (e.g., conventional fuzzy arithmetic) and underestimating (e.g., vertex method) the output uncertainty. The purpose of the present study is to apply and compare the applicability of conventional fuzzy arithmetic, vertex method and two recently proposed numerical schemes, namely transformation and optimization methods, for uncertainty modeling in pharmacokinetic and pharmacodynamic fuzzy-parameterized systems. A series of test problems were examined, including empirical pharmacokinetic and pharmacodynamic models, a function non-monotonic in its parameters, and a whole body physiologically based pharmacokinetic model. Our results verified that conventional fuzzy arithmetic can lead to overestimation of response uncertainty and should be avoided. For the monotonic pharmacokinetic and pharmacodynamic models, the vertex method accurately predicted fuzzy-valued output while incurring the least computational cost. It turned out that the choice of a suitable method for fuzzy simulation of the non-monotonic function depended on the required accuracy of the results: the vertex method was capable of eliciting an initial approximate solution with few function evaluations; for more accurate results, the transformation method was the most superior approach in terms of accuracy per unit CPU time.     

Population pharmacokinetics. A regulatory perspective.

The application of population approaches to drug development is recommended in several US Food and Drug Administration (FDA) guidance documents. Population pharmacokinetic (and pharmacodynamic) techniques enable identification of the sources of inter- and intra-individual variability that impinge upon drug safety and efficacy. This article briefly discusses the 2-stage approach to the estimation of population pharmacokinetic parameters, which requires serial multiple measurements on each participant, and comprehensively reviews the nonlinear mixed-effects modelling approach, which can be applied in situations where extensive sampling is not done on all or any of the participants. Certain preliminary information, such as the compartment model used in describing the pharmacokinetics of the drug, is required for a population pharmacokinetic study. The practical design considerations of the location of sampling times, number of samples/participants and the need to sample an individual more than once should be borne in mind. Simulation may be useful for choosing the study design that will best meet study objectives. The objectives of the population pharmacokinetic study can be secondary to the objectives of the primary clinical study (in which case an add-on population pharmacokinetic protocol may be needed) or primary (when a stand-alone protocol is required). Having protocols for population pharmacokinetic studies is an integral part of 'good pharmacometric practice'. Real-time data assembly and analysis permit an ongoing evaluation of site compliance with the study protocol and provide the opportunity to correct violations of study procedures. Adequate policies and procedures should be in place for study blind maintenance. Real-time data assembly creates the opportunity for detecting and correcting errors in concentration-time data, drug administration history and covariate data. Population pharmacokinetic analyses may be undertaken in 3 interwoven steps: exploratory data analysis, model development and model validation (i.e. predictive performance). Documentation for regulatory purposes should include a complete inventory of key runs in the analyses undertaken (with flow diagrams if possible), accompanied by articulation of objectives, assumptions and hypotheses. Use of diagnostic analyses of goodness of fit as evidence of reliability of results is advised. Finally, the use of stability testing or model validation may be warranted to support label claims. The opinions expressed in this article were revised by incorporating comments from various sources and published by the FDA as 'Guidance for Industry: Population Pharmacokinetics' (see the FDA home page http:/(/)www.fda.gov for further information).     

Development of a Physiology-Based Whole-Body Population Model for Assessing the Influence of Individual Variability on the Pharmacokinetics of Drugs

In clinical development stages, an a priori assessment of the sensitivity of the pharmacokinetic behavior with respect to physiological and anthropometric properties of human (sub-) populations is desirable. A physiology-based pharmacokinetic (PBPK) population model was developed that makes use of known distributions of physiological and anthropometric properties obtained from the literature for realistic populations. As input parameters, the simulation model requires race, gender, age, and two parameters out of body weight, height and body mass index. From this data, the parameters relevant for PBPK modeling such as organ volumes and blood flows are determined for each virtual individual. The resulting parameters were compared to those derived using a previously published model (P³M). Mean organ weights and blood flows were highly correlated between the two models, despite the different methods used to generate these parameters. The inter-individual variability differed greatly especially for organs with a log-normal weight distribution (such as fat and spleen). Two exemplary population pharmacokinetic simulations using ciprofloxacin and paclitaxel as model drugs showed good correlation to observed variability. A sensitivity analysis demonstrated that the physiological differences in the virtual individuals and intrinsic clearance variability were equally influential to the pharmacokinetic variability but were not additive. In conclusion, the new population model is well suited to assess the influence of individual physiological variability on the pharmacokinetics of drugs. It is expected that this new tool can be beneficially applied in the planning of clinical studies.     

The evolution of population pharmacokinetic models to describe the enterohepatic recycling of mycophenolic acid in solid organ transplantation and autoimmune disease

With the increasing use of mycophenolic acid (MPA) as an immunosuppressant in solid organ transplantation and in treating autoimmune diseases such as systemic lupus erythematosus, the need for strategies to optimize therapy with this agent has become increasingly apparent. This need is largely based on MPA's significant between-subject and between-occasion (within-subject) pharmacokinetic variability. While there is a strong relationship between MPA exposure and effect, the relationship between drug dose, plasma concentration and exposure (area under the concentration-time curve [AUC]) is very complex and remains to be completely defined. Population pharmacokinetic models using various approaches have been proposed over the past 10 years to further evaluate the pharmacokinetic and pharmacodynamic behaviour of MPA. These models have evolved from simple one-compartment linear iterations to complex multi-compartment versions that try to include various factors, which may influence MPA's pharmacokinetic variability, such as enterohepatic recycling and pharmacogenetic polymorphisms. There have been major advances in the understanding of the roles transport mechanisms, metabolizing and other enzymes, drug-drug interactions and pharmacogenetic polymorphisms play in MPA's pharmacokinetic variability. Given these advances, the usefulness of empirical-based models and the limitations of nonlinear mixed-effects modelling in developing mechanism-based models need to be considered and discussed. If the goal is to individualize MPA dosing, it needs to be determined whether factors which may contribute significantly to variability can be utilized in the population pharmacokinetic models. Some pharmacokinetic models developed to date show promise in being able to describe the impact of physiological processes such as enterohepatic recycling. Most studies have historically been based on retrospective data or poorly designed studies which do not take these factors into consideration. Modelling typically has been undertaken using non-controlled therapeutic drug monitoring data, which do not have the information content to support the development of complex mechanistic models. Only a few recent modelling approaches have moved away from empiricism and have included mechanisms considered important, such as enterohepatic recycling. It is recognized that well thought-out sampling schedules allow for better evaluation of the pharmacokinetic data. It is not possible to undertake complex absorption modelling with very few samples being obtained during the absorption phase (which has often been the case). It is important to utilize robust AUC monitoring which is now being propagated in the latest consensus guideline on MPA therapeutic drug monitoring. This review aims to explore the biological factors that contribute to the clinical pharmacokinetics of MPA and how these have been introduced in the development of population pharmacokinetic models. An overview of the processes involved in the enterohepatic recycling of MPA will be provided. This will summarize the components that complicate absorption and recycling to influence MPA exposure such as biotransformation, transport, bile physiology and gut flora. Already published population pharmacokinetic models will be examined, and the evolution of these models away from empirical approaches to more mechanism-based models will be discussed.     

Controversy I: Patients or healthy volunteers for pharmacokinetic studies?

Many factors should be considered when choosing an appropriate population for a pharmacokinetic trial. Although there are some generalities that apply to most studies, each investigation must be judged separately, since the relevant considerations will vary depending on the particular study, the nature of the drug, and the population that will receive it for therapeutic benefit. Some of the most important information that is generated from pharmacokinetic studies concerns the pharmacokinetic variability among patients and the factors that can influence this variability under the conditions that the drug will be used. This information can best be obtained from a combination of baseline studies to define the variability within the patient population(s) and comparative studies to determine the impact of specific variables on the disposition of the drug and its pharmacokinetic variability. These data can provide valuable information to the clinician that can be used to individualize drug dosage and optimize therapy as well as to identify populations who may be at high risk of therapeutic failure or drug toxicity. It is our feeling that baseline studies in patients are necessary for understanding the pharmacokinetics of a drug, whereas the objectives of most comparative studies can be achieved using healthy volunteers. For most comparative studies, the data obtained from healthy volunteers will reflect what will occur in patients, especially if the variable of interest is drug absorption. This is particularly important when practical and ethical considerations preclude the use of patients. When considering studies in the elderly, one must decide whether the variable of interest may be influenced by age.(ABSTRACT TRUNCATED AT 250 WORDS)     

Combining the ‘bottom up’ and ‘top down’ approaches in pharmacokinetic modelling: fitting PBPK models to observed clinical data

Pharmacokinetic models range from being entirely exploratory and empirical, to semi-mechanistic and ultimately complex physiologically based pharmacokinetic (PBPK) models. This choice is conditional on the modelling purpose as well as the amount and quality of the available data. The main advantage of PBPK models is that they can be used to extrapolate outside the studied population and experimental conditions. The trade-off for this advantage is a complex system of differential equations with a considerable number of model parameters. When these parameters cannot be informed from in vitro or in silico experiments they are usually optimized with respect to observed clinical data. Parameter estimation in complex models is a challenging task associated with many methodological issues which are discussed here with specific recommendations. Concepts such as structural and practical identifiability are described with regards to PBPK modelling and the value of experimental design and sensitivity analyses is sketched out. Parameter estimation approaches are discussed, while we also highlight the importance of not neglecting the covariance structure between model parameters and the uncertainty and population variability that is associated with them. Finally the possibility of using model order reduction techniques and minimal semi-mechanistic models that retain the physiological-mechanistic nature only in the parts of the model which are relevant to the desired modelling purpose is emphasized. Careful attention to all the above issues allows us to integrate successfully information from in vitro or in silico experiments together with information deriving from observed clinical data and develop mechanistically sound models with clinical relevance.     

Mixture Models and Subpopulation Classification: A Pharmacokinetic Simulation Study and Application to Metoprolol CYP2D6 Phenotype

Mixture models are applied in population pharmacometrics to characterize underlying population distributions that are not adequately approximated by a single normal or lognormal distribution. In addition to obtaining individualized maximum a posteriori Bayesian post hoc parameter estimates, the subpopulation to which an individual was classified can be determined. However, the accuracy of the classification of subjects to subpopulations is not well studied. We investigated the impact of several factors on the accuracy of classification in mixture models applied to pharmacokinetics using a simulation strategy. The availability of actual subject data allowed us to evaluate mixture model classification in a potentially common application, namely, the classification of clearance into poor metabolizer (PM) or extensive metabolizer (EM) subgroups with the known phenotype status in subjects receiving metoprolol. The factors explored in the simulation study were the magnitude of difference between the clearances in two subpopulations, the between subject variability in clearance, the mixing-fraction, and the population sample size. Populations were simulated at various levels of the above factors and analyzed with a mixture model using NONMEM. The population pharmacokinetics of metoprolol were modeled with the EM/PM phenotype as a known covariate, and without the phenotype covariate using a mixture model. Within the range of scenarios studied, the proportion of subjects classified into the correct subpopulation was high. The simulation-estimation study suggests that a greater separation between two subpopulations, a smaller variability in the parameter distribution, a larger sample size, and a smaller size subpopulation tend to be associated with a greater accuracy of subpopulation classification when a mixture model is applied to pharmacokinetic data. In a population pharmacokinetic analysis of metoprolol, a drug that undergoes polymorphic metabolism, it was possible to correctly identify phenotype status using a mixture model.