Optimization of individual and population designs using Splus

Scipion PKPD: an Open-Source Platform for Biopharmaceutics, Pharmacokinetics and Pharmacodynamics Data Analysis

PURPOSE

Biopharmaceutics examines the interrelationship of the drug's physical/chemical properties, the dosage form (drug product) in which the drug is given, and the administration route on the rate and extent of sys- temic drug absorption. Pharmacokinetics is the study of the movement of drugs in the body. It uses mathematical models to evaluate the movement of absorption, distribution, metabolism, and excretion (ADME) within an organism. Finally, Pharmacodynamics is the analysis of how these drugs af- fect that organism. Pharmacokinetics data normally comes in samples over time of the drug concentration either in plasma or in some specific tissue. Similarly, pharmacodynamics data comes normally in samples over time of some quantity of interest (biophysical quantity like temperature, blood pres- sure, etc.). The data is submitted to a non-parametric analysis, in which a description of the observed data is reported (e.g., the Area Under the Curve), or to a parametric analysis by fitting a model (normally based on differential equations) so that prediction about future events can be made. This paper aims to introduce Scipion PKPD, an open-source platform for data analysis of this kind in the three domains (Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics). The platform implements the most popular models and is open to new ones. The platform provides almost 100 different high-level operations that we call protocols.

METHODS

We have developed a Python module integrated into the work- flow engine Scipion. The plugin implements the numerical analysis and meta- data handling tools to address multiple problems (see Suppl. Material for a detailed list of the tasks solved).

RESULTS

We illustrate the use of this package with an integrative exam- ple that involves all these areas.

CONCLUSIONS

We show that the package successfully addresses these kinds of analyses. Scipion PKPD is freely available at https://github. com/cossorzano/scipion-pkpd .

Safety and tolerability of adjunctive lacosamide in a pediatric population with focal seizures - An open-label trial

PURPOSE

To evaluate safety and tolerability of adjunctive lacosamide in children with focal seizures.

METHODS

Patients were eligible for this open-label, fixed-titration trial (SP0847; NCT00938431) if aged 1 month-17 years with focal seizures taking 1-3 antiepileptic drugs. Findings from Cohort 1, aged 5-11 years, who received lacosamide ≤8 mg/kg/day, informed dosing for age-based cohorts 2-5, who then received ≤12 mg/kg/day (≤600 mg/day). Oral lacosamide was initiated at 2 mg/kg/day (1 mg/kg bid) and uptitrated by 2 mg/kg/day/week to the maximum cohort-defined dose (maximum trial duration: 13 weeks). Patients who did not achieve the maximum cohort-defined dose were discontinued.

RESULTS

Forty-seven patients (aged 6 months-≤17 years) enrolled (≥1 month-<4 years: n = 15; ≥4-<12 years: n = 23; ≥12-≤17 years: n = 9). 24/47 (51.1%) patients completed the trial at the maximum cohort-defined dose and 40/47 (85.1%) continued lacosamide in the extension trial. Treatment-emergent adverse events (TEAEs) were reported by 42/47 (89.4%) patients. The most common TEAEs (≥10% of patients) were vomiting (21.3%), diarrhea (14.9%), somnolence (12.8%), irritability, dizziness, and pyrexia (10.6% each). Twenty (42.6%) patients discontinued due to TEAEs, most commonly vomiting (8.5%), gait disturbance, dizziness, and somnolence (6.4% each). Six (12.8%) patients reported serious TEAEs, most commonly status epilepticus (3/47; 6.4%).

CONCLUSION

This fixed-titration trial supports the safety of adjunctive lacosamide in children (aged 6 months-≤17 years) with focal seizures. The TEAE profile was generally consistent with that observed in trials in adults, and no new safety concerns were identified.

Advanced Methods for Dose and Regimen Finding During Drug Development: Summary of the EMA/EFPIA Workshop on Dose Finding (London 4-5 December 2014)

Inadequate dose selection for confirmatory trials is currently still one of the most challenging issues in drug development, as illustrated by high rates of late‐stage attritions in clinical development and postmarketing commitments required by regulatory institutions. In an effort to shift the current paradigm in dose and regimen selection and highlight the availability and usefulness of well‐established and regulatory‐acceptable methods, the European Medicines Agency (EMA) in collaboration with the European Federation of Pharmaceutical Industries Association (EFPIA) hosted a multistakeholder workshop on dose finding (London 4–5 December 2014). Some methodologies that could constitute a toolkit for drug developers and regulators were presented. These methods are described in the present report: they include five advanced methods for data analysis (empirical regression models, pharmacometrics models, quantitative systems pharmacology models, MCP‐Mod, and model averaging) and three methods for study design optimization (Fisher information matrix (FIM)‐based methods, clinical trial simulations, and adaptive studies). Pairwise comparisons were also discussed during the workshop; however, mostly for historical reasons. This paper discusses the added value and limitations of these methods as well as challenges for their implementation. Some applications in different therapeutic areas are also summarized, in line with the discussions at the workshop. There was agreement at the workshop on the fact that selection of dose for phase III is an estimation problem and should not be addressed via hypothesis testing. Dose selection for phase III trials should be informed by well‐designed dose‐finding studies; however, the specific choice of method(s) will depend on several aspects and it is not possible to recommend a generalized decision tree. There are many valuable methods available, the methods are not mutually exclusive, and they should be used in conjunction to ensure a scientifically rigorous understanding of the dosing rationale.

Safety, dosing, and pharmaceutical quality for studies that evaluate medicinal products (including biological products) in neonates

The study of medications among pediatric patients has increased worldwide since 1997 in response to new legislation and regulations, but these studies have not yet adequately addressed the therapeutic needs of neonates. Additionally, extant guidance developed by regulatory agencies worldwide does not fully address the specificities of neonatal drug development, especially among extremely premature newborns who currently survive. Consequently, an international consortium from Canada, Europe, Japan, and the United States was organized by the Critical Path Institute to address the content of guidance. This group included neonatologists, neonatal nurses, parents, regulators, ethicists, clinical pharmacologists, specialists in pharmacokinetics, specialists in clinical trials and pediatricians working in the pharmaceutical industry. This group has developed a comprehensive, referenced White Paper to guide neonatal clinical trials of medicines - particularly early phase studies. Key points include: the need to base product development on neonatal physiology and pharmacology while making the most of knowledge acquired in other settings; the central role of families in research; and the value of the whole neonatal team in the design, implementation and interpretation of studies. This White Paper should facilitate successful clinical trials of medicines in neonates by informing regulators, sponsors, and the neonatal community of existing good practice.

The present and future of withdrawal period calculations for milk in the European Union: focus on heterogeneous, nonmonotonic data

Harmonization of the method for calculating the withdrawal period for milk dates from the 1990s. European harmonization has led to guidance with three accepted methods for determining the withdrawal period for milk that are currently applicable. These three methods can be used by marketing authorization holders, but, in some cases, their diversity can lead to very different withdrawal periods. This is particularly the case when concentrations in milk are nonmonotonic and heterogeneous, meaning that concentrations strictly increase and then strictly decrease with significant interindividual variability in the time to reach the maximal concentration. Here, we first describe the concepts associated with the different methods used in the harmonized approach currently applicable for the determination of milk withdrawal periods, and then, we propose the application of a modern pharmacometric tool. Finally, with a nonmonotonic heterogeneous dataset, we illustrate the usefulness of this tool in comparison with the three currently applicable methods and discuss the limitations and advantages of each method.

PopED lite: An optimal design software for preclinical pharmacokinetic and pharmacodynamic studies

BACKGROUND AND OBJECTIVE

Optimal experimental design approaches are seldom used in preclinical drug discovery. The objective is to develop an optimal design software tool specifically designed for preclinical applications in order to increase the efficiency of drug discovery in vivo studies.

METHODS

Several realistic experimental design case studies were collected and many preclinical experimental teams were consulted to determine the design goal of the software tool. The tool obtains an optimized experimental design by solving a constrained optimization problem, where each experimental design is evaluated using some function of the Fisher Information Matrix. The software was implemented in C++ using the Qt framework to assure a responsive user-software interaction through a rich graphical user interface, and at the same time, achieving the desired computational speed. In addition, a discrete global optimization algorithm was developed and implemented.

RESULTS

The software design goals were simplicity, speed and intuition. Based on these design goals, we have developed the publicly available software PopED lite (http://www.bluetree.me/PopED_lite). Optimization computation was on average, over 14 test problems, 30 times faster in PopED lite compared to an already existing optimal design software tool. PopED lite is now used in real drug discovery projects and a few of these case studies are presented in this paper.

CONCLUSIONS

PopED lite is designed to be simple, fast and intuitive. Simple, to give many users access to basic optimal design calculations. Fast, to fit a short design-execution cycle and allow interactive experimental design (test one design, discuss proposed design, test another design, etc). Intuitive, so that the input to and output from the software tool can easily be understood by users without knowledge of the theory of optimal design. In this way, PopED lite is highly useful in practice and complements existing tools.

Optimal sampling of antipsychotic medicines: a pharmacometric approach for clinical practice

AIM

To determine optimal sampling strategies to allow the calculation of clinical pharmacokinetic parameters for selected antipsychotic medicines using a pharmacometric approach.

METHODS

This study utilized previous population pharmacokinetic parameters of the antipsychotic medicines aripiprazole, clozapine, olanzapine, perphenazine, quetiapine, risperidone (including 9-OH risperidone) and ziprasidone. d-optimality was utilized to identify time points which accurately predicted the pharmacokinetic parameters (and expected error) of each drug at steady-state. A standard two stage population approach (STS) with MAP-Bayesian estimation was used to compare area under the concentration-time curves (AUC) generated from sparse optimal time points and rich extensive data. Monte Carlo Simulation (MCS) was used to simulate 1000 patients with population variability in pharmacokinetic parameters. Forward stepwise regression analysis was used to determine the most predictive time points of the AUC for each drug at steady-state.

RESULTS

Three optimal sampling times were identified for each antipsychotic medicine. For aripiprazole, clozapine, olanzapine, perphenazine, risperidone, 9-OH risperidone, quetiapine and ziprasidone the CV% of the apparent clearance using optimal sampling strategies were 19.5, 8.6, 9.5, 13.5, 12.9, 10.0, 16.0 and 10.7, respectively. Using the MCS and linear regression approach to predict AUC, the recommended sampling windows were 16.5-17.5 h, 10-11 h, 23-24 h, 19-20 h, 16.5-17.5 h, 22.5-23.5 h, 5-6 h and 5.5-6.5 h, respectively.

CONCLUSION

This analysis provides important sampling information for future population pharmacokinetic studies and clinical studies investigating the pharmacokinetics of antipsychotic medicines.

Optimal design in pediatric pharmacokinetic and pharmacodynamic clinical studies

It is not trivial to conduct clinical trials with pediatric participants. Ethical, logistical, and financial considerations add to the complexity of pediatric studies. Optimal design theory allows investigators the opportunity to apply mathematical optimization algorithms to define how to structure their data collection to answer focused research questions. These techniques can be used to determine an optimal sample size, optimal sample times, and the number of samples required for pharmacokinetic and pharmacodynamic studies. The aim of this review is to demonstrate how to determine optimal sample size, optimal sample times, and the number of samples required from each patient by presenting specific examples using optimal design tools. Additionally, this review aims to discuss the relative usefulness of sparse vs rich data. This review is intended to educate the clinician, as well as the basic research scientist, whom plan on conducting a pharmacokinetic/pharmacodynamic clinical trial in pediatric patients.

Impact of adherence and anthropometric characteristics on nevirapine pharmacokinetics and exposure among HIV-infected Kenyan children

BACKGROUND

There are insufficient data on pediatric antiretroviral therapy (ART) pharmacokinetics (PK), particularly for children in low- and middle-income countries.

METHODS

We conducted a prospective nevirapine (NVP) PK study among HIV-infected Kenyan children aged 3-13 years initiating an NVP-based ART regimen. NVP dose timing was measured through medication event monitors. Participants underwent 2 inpatient assessments: 1 at 4-8 weeks after ART initiation and 1 at 3-4 months after ART initiation. Allometric scaling of oral clearance (CL)/bioavailability (F) and volume of distribution (Vd)/F values were computed. Nonlinear mixed-effects modeling using the first-order conditional estimation with interaction method was performed with covariates. The impact of adherence on time below minimum effective concentration was assessed in the final PK model using medication event monitors data and model-estimated individual parameters.

RESULTS

Among 21 children enrolled, mean age was 5.4 years and 57% were female. CL/F was 1.67 L/h and Vd/F was 3.8 L for a median child weighing 15 kg. Participants' age had a significant impact on CL/F (P < 0.05), with an estimated decrease in CL of 6.2% for each 1-year increase in age. Total body water percentage was significantly associated with Vd/F (P < 0.001). No children had >10% of time below minimum effective concentration when the PK model assumed perfect adherence compared with 10 children when adherence data were used.

CONCLUSIONS

Age and body composition were significantly associated with children's NVP PK parameters. ART adherence significantly impacted drug exposure over time, revealing subtherapeutic windows that may lead to viral resistance.

Utilization of optimal study design for maternal and fetal sheep propofol pharmacokinetics study: a preliminary study

Multiple blood samples are generally required for measurement of pharmacokinetic (PK) parameters. D-optimal design is a popular and frequently used approach for determination of sampling time points in order to minimize the number of samples, while optimizing the estimation of PK parameters. Optimal design utilizing ADAPT (v5, BSR, University of Southern California, Los Angeles) developed a sparse sampling strategy to determine measurement of propofol in pregnant sheep. Propofal was administered as supplemental anesthetic agent to inhalation anesthesia to mimic anesthesia for open fetal surgery. In our preliminary study, propofol 3 mg/kg was given as a bolus to the ewe, followed by propofol infusion at rate 450 mcg/kg/min for 60 minutes, then decreased to 75 mcg/kg/min for 90 more minutes and then ceased. A three compartment model described the PK parameters with the fetus assumed as the third compartment. Initially, sampling times were chosen from thirteen time points as previously stated in the literature. Using priori propofol PK estimates, the final 9 sample time points were proposed in an optimal design with a change in infusion rate occurring between 65 and 75 minutes and sampling proposed at 5, 15, 25, 65, 75, 100, 110, 150, and 180 minutes. D-optimal design optimized the number and timing of samplings, which led to a reduction of cost and man power in the study protocol while preserving the ability to estimate propofol PK parameters in the maternal and fetal sheep model. Initial evaluation of samples collected from three sheep using the optimal design strategy confirmed the performance of the design in obtaining effective PK parameter estimates.

Statistical power calculations for mixed pharmacokinetic study designs using a population approach

Simultaneous modelling of dense and sparse pharmacokinetic data is possible with a population approach. To determine the number of individuals required to detect the effect of a covariate, simulation-based power calculation methodologies can be employed. The Monte Carlo Mapped Power method (a simulation-based power calculation methodology using the likelihood ratio test) was extended in the current study to perform sample size calculations for mixed pharmacokinetic studies (i.e. both sparse and dense data collection). A workflow guiding an easy and straightforward pharmacokinetic study design, considering also the cost-effectiveness of alternative study designs, was used in this analysis. Initially, data were simulated for a hypothetical drug and then for the anti-malarial drug, dihydroartemisinin. Two datasets (sampling design A: dense; sampling design B: sparse) were simulated using a pharmacokinetic model that included a binary covariate effect and subsequently re-estimated using (1) the same model and (2) a model not including the covariate effect in NONMEM 7.2. Power calculations were performed for varying numbers of patients with sampling designs A and B. Study designs with statistical power >80% were selected and further evaluated for cost-effectiveness. The simulation studies of the hypothetical drug and the anti-malarial drug dihydroartemisinin demonstrated that the simulation-based power calculation methodology, based on the Monte Carlo Mapped Power method, can be utilised to evaluate and determine the sample size of mixed (part sparsely and part densely sampled) study designs. The developed method can contribute to the design of robust and efficient pharmacokinetic studies.

Prediction of shrinkage of individual parameters using the bayesian information matrix in non-linear mixed effect models with evaluation in pharmacokinetics

PURPOSE

When information is sparse, individual parameters derived from a non-linear mixed effects model analysis can shrink to the mean. The objective of this work was to predict individual parameter shrinkage from the Bayesian information matrix (M BF ). We 1) Propose and evaluate an approximation of M BF by First-Order linearization (FO), 2) Explore by simulations the relationship between shrinkage and precision of estimates and 3) Evaluate prediction of shrinkage and individual parameter precision.

METHODS

We approximated M BF using FO. From the shrinkage formula in linear mixed effects models, we derived the predicted shrinkage from M BF . Shrinkage values were generated for parameters of two pharmacokinetic models by varying the structure and the magnitude of the random effect and residual error models as well as the design. We then evaluated the approximation of M BF FO and compared it to Monte-Carlo (MC) simulations. We finally compared expected and observed shrinkage as well as the predicted and estimated Standard Errors (SE) of individual parameters.

RESULTS

M BF FO was similar to M BF MC. Predicted and observed shrinkages were close . Predicted and estimated SE were similar.

CONCLUSIONS

M BF FO enables prediction of shrinkage and SE of individual parameters. It can be used for design optimization.

Clinical trial simulation to evaluate power to compare the antiviral effectiveness of two hepatitis C protease inhibitors using nonlinear mixed effect models: a viral kinetic approach

BACKGROUND

Models of hepatitis C virus (HCV) kinetics are increasingly used to estimate and to compare in vivo drug's antiviral effectiveness of new potent anti-HCV agents. Viral kinetic parameters can be estimated using non-linear mixed effect models (NLMEM). Here we aimed to evaluate the performance of this approach to precisely estimate the parameters and to evaluate the type I errors and the power of the Wald test to compare the antiviral effectiveness between two treatment groups when data are sparse and/or a large proportion of viral load (VL) are below the limit of detection (BLD).

METHODS

We performed a clinical trial simulation assuming two treatment groups with different levels of antiviral effectiveness. We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data. Next we evaluated the type I error and the power of the Wald test to assess a difference of antiviral effectiveness between the two groups. Standard error of the parameters and Wald test property were evaluated according to the number of patients, the number of samples per patient and the expected difference in antiviral effectiveness.

RESULTS

NLMEM provided precise and accurate estimates for both the fixed effects and the inter-individual variance parameters even with sparse data and large proportion of BLD data. However Wald test with small number of patients and lack of information due to BLD resulted in an inflation of the type I error as compared to the results obtained when no limit of detection of VL was considered. The corrected power of the test was very high and largely outperformed what can be obtained with empirical comparison of the mean VL decline using Wilcoxon test.

CONCLUSION

This simulation study shows the benefit of viral kinetic models analyzed with NLMEM over empirical approaches used in most clinical studies. When designing a viral kinetic study, our results indicate that the enrollment of a large number of patients is to be preferred to small population sample with frequent assessments of VL.

Basic concepts in population modeling, simulation, and model-based drug development

Modeling is an important tool in drug development; population modeling is a complex process requiring robust underlying procedures for ensuring clean data, appropriate computing platforms, adequate resources, and effective communication. Although requiring an investment in resources, it can save time and money by providing a platform for integrating all information gathered on new therapeutic agents. This article provides a brief overview of aspects of modeling and simulation as applied to many areas in drug development.

A simultaneous d-optimal designed study for population pharmacokinetic analyses of mycophenolic Acid and tacrolimus early after renal transplantation

Mycophenolic acid (MPA) and tacrolimus (TAC) are immunosuppressive agents used in combination with corticosteroids for the prevention of acute rejection after solid organ transplantation. Their pharmacokinetics (PK) show considerable unexplained intraindividual and interindividual variability, particularly in the early period after transplantation. The main objective of the present work was to design a study based on D-optimality to describe the PK of the 2 drugs with good precision and accuracy and to explain their variability by means of patients' demographics, biochemical test results, and physiological characteristics. Pharmacokinetic profiles of MPA and TAC were obtained from 65 stable adult renal allograft recipients on a single occasion (ie, day 15 after transplantation). A sampling schedule was estimated based on the D-optimality criterion with the POPED software, using parameter values from previously published studies on MPA and TAC modeling early after transplantation. Subsequently, a population PK model describing MPA and TAC concentrations was developed using nonlinear mixed-effects modeling. Optimal blood-sampling times for determination of MPA and TAC concentrations were estimated to be at 0 (predose) and at 0.24, 0.64, 0.98, 1.37, 2.38, and 11 hours after oral intake of mycophenolate and TAC. The PK of MPA and TAC were best described by a 2-compartment model with first-order elimination. For MPA, the absorption was best described by a transit compartment model, whereas first-order absorption with a lag time best described TAC transfer from the gastrointestinal tract. Parameters were estimated with good precision and accuracy. While hematocrit levels and CYP3A5 genetic polymorphism significantly influenced TAC clearance, the pharmaceutical formulation and MRP2 genetic polymorphism were retained as significant covariates on MPA absorption and elimination, respectively. The prospective use of the simultaneous D-optimal design approach for MPA and TAC has allowed good estimation of MPA and TAC PK parameters in the early period after transplantation characterized by a very high unexplained variability. The influence of some relevant covariates could be shown.

The role of population PK-PD modelling in paediatric clinical research

Children differ from adults in their response to drugs. While this may be the result of changes in dose exposure (pharmacokinetics [PK]) and/or exposure response (pharmacodynamics [PD]) relationships, the magnitude of these changes may not be solely reflected by differences in body weight. As a consequence, dosing recommendations empirically derived from adults dosing regimens using linear extrapolations based on body weight, can result in therapeutic failure, occurrence of adverse effect or even fatalities. In order to define rational, patient-tailored dosing schemes, population PK-PD studies in children are needed. For the analysis of the data, population modelling using non-linear mixed effect modelling is the preferred tool since this approach allows for the analysis of sparse and unbalanced datasets. Additionally, it permits the exploration of the influence of different covariates such as body weight and age to explain the variability in drug response. Finally, using this approach, these PK-PD studies can be designed in the most efficient manner in order to obtain the maximum information on the PK-PD parameters with the highest precision. Once a population PK-PD model is developed, internal and external validations should be performed. If the model performs well in these validation procedures, model simulations can be used to define a dosing regimen, which in turn needs to be tested and challenged in a prospective clinical trial. This methodology will improve the efficacy/safety balance of dosing guidelines, which will be of benefit to the individual child.

Pharmacokinetic design optimization in children and estimation of maturation parameters: example of cytochrome P450 3A4

The aim of this work was to determine whether optimizing the study design in terms of ages and sampling times for a drug eliminated solely via cytochrome P450 3A4 (CYP3A4) would allow us to accurately estimate the pharmacokinetic parameters throughout the entire childhood timespan, while taking into account age- and weight-related changes. A linear monocompartmental model with first-order absorption was used successively with three different residual error models and previously published pharmacokinetic parameters ("true values"). The optimal ages were established by D-optimization using the CYP3A4 maturation function to create "optimized demographic databases." The post-dose times for each previously selected age were determined by D-optimization using the pharmacokinetic model to create "optimized sparse sampling databases." We simulated concentrations by applying the population pharmacokinetic model to the optimized sparse sampling databases to create optimized concentration databases. The latter were modeled to estimate population pharmacokinetic parameters. We then compared true and estimated parameter values. The established optimal design comprised four age ranges: 0.008 years old (i.e., around 3 days), 0.192 years old (i.e., around 2 months), 1.325 years old, and adults, with the same number of subjects per group and three or four samples per subject, in accordance with the error model. The population pharmacokinetic parameters that we estimated with this design were precise and unbiased (root mean square error [RMSE] and mean prediction error [MPE] less than 11% for clearance and distribution volume and less than 18% for k(a)), whereas the maturation parameters were unbiased but less precise (MPE < 6% and RMSE < 37%). Based on our results, taking growth and maturation into account a priori in a pediatric pharmacokinetic study is theoretically feasible. However, it requires that very early ages be included in studies, which may present an obstacle to the use of this approach. First-pass effects, alternative elimination routes, and combined elimination pathways should also be investigated.

Application of optimal design methodologies in clinical pharmacology experiments

Pharmacokinetics and pharmacodynamics data are often analysed by mixed-effects modelling techniques (also known as population analysis), which has become a standard tool in the pharmaceutical industries for drug development. The last 10 years has witnessed considerable interest in the application of experimental design theories to population pharmacokinetic and pharmacodynamic experiments. Design of population pharmacokinetic experiments involves selection and a careful balance of a number of design factors. Optimal design theory uses prior information about the model and parameter estimates to optimize a function of the Fisher information matrix to obtain the best combination of the design factors. This paper provides a review of the different approaches that have been described in the literature for optimal design of population pharmacokinetic and pharmacodynamic experiments. It describes options that are available and highlights some of the issues that could be of concern as regards practical application. It also discusses areas of application of optimal design theories in clinical pharmacology experiments. It is expected that as the awareness about the benefits of this approach increases, more people will embrace it and ultimately will lead to more efficient population pharmacokinetic and pharmacodynamic experiments and can also help to reduce both cost and time during drug development.

A survey of the way pharmacokinetics are reported in published phase I clinical trials, with an emphasis on oncology

BACKGROUND AND OBJECTIVE

During the drug development process, phase I trials are the first occasion to study the pharmacokinetics of a drug. They are performed in healthy subjects, or in patients in oncology, and are designed to determine a safe and acceptable dose for the later phases of clinical trials. We performed a bibliographic survey to investigate the way pharmacokinetics are described and reported in phase I clinical trials.

METHODS

We performed a MEDLINE search to retrieve the list of papers published between 2005 and 2006 and reporting phase I clinical trials with a pharmacokinetic study. We used a spreadsheet to record general information concerning the study and specific information regarding the pharmacokinetics, such as the sampling times, number of subjects and method of analysis.

RESULTS

The search yielded 349 papers, of which 37 were excluded for various reasons. Nearly all of the papers in our review concerned cancer studies, although this was not a requirement in the search. Consistent with the selection process, 84% papers explicitly stated pharmacokinetics as an objective of the study. The methods section usually included a description of the pharmacokinetics (88%), but 10% of the papers provided no information concerning the methods used for the pharmacokinetics and in 2% the description was only partial. The analytical method was usually basic, with non-compartmental or purely descriptive methods. Observed concentrations and areas under the concentration-time curves were the pharmacokinetic variables most often reported. The results of the pharmacokinetic study were frequently reported in a separate paragraph of the results section, and only 22% of the studies related the pharmacokinetic findings to other results from the study, such as toxicity or efficacy. In addition, important information such as the number of subjects included in the pharmacokinetic study or the pharmacokinetic sampling scheme was sometimes not reported explicitly.

CONCLUSION

Concerns about the decreasing cost-effectiveness of the drug development process prompted the regulatory authorities to recently recommend better integration of all available information - including, in particular, pharmacokinetics - in this process. In our review, we found that this information was often either missing or incomplete, which hinders that objective. We suggest several improvements in the design and the reporting of the methods and results of these studies, to ensure that all relevant information has been included. Pharmacokinetic findings should also be integrated into the broader perspective of drug development, through the study of their relationship with toxicity and/or efficacy, even in the early phase I stages.

Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0

Nonlinear mixed effect models (NLMEM) with multiple responses are increasingly used in pharmacometrics, one of the main examples being the joint analysis of the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug. Efficient tools for design evaluation and optimisation in NLMEM are necessary. The R functions PFIM 1.2 and PFIMOPT 1.0 were proposed for these purposes, but accommodate only single response models. The methodology used is based on the Fisher information matrix, developed using a linearisation of the model. In this paper, we present an extended version, PFIM 3.0, dedicated to both design evaluation and optimisation for multiple response models, using a similar method as for single response models. In addition to handling multiple response models, several features have been integrated into PFIM 3.0 for model specification and optimisation. The extension includes a library of classical analytical pharmacokinetics models and allows the user to describe more complex models using differential equations. Regarding the optimisation algorithm, an alternative to the Simplex algorithm has been implemented, the Fedorov-Wynn algorithm to optimise more practical D-optimal design. Indeed, this algorithm optimises design among a set of sampling times specified by the user. This R function is freely available at http://www.pfim.biostat.fr. The efficiency of this approach and the simplicity of use of PFIM 3.0 are illustrated with a real example of the joint PKPD analysis of warfarin, an oral anticoagulant, with a model defined by ordinary differential equations.

Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic-pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation-maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first-order linearization estimation methods implemented in the NONMEM software (first-order (FO), first-order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

Towards optimal design of anti-malarial pharmacokinetic studies

Background

Characterization of anti-malarial drug concentration profiles is necessary to optimize dosing, and thereby optimize cure rates and reduce both toxicity and the emergence of resistance. Population pharmacokinetic studies determine the drug concentration time profiles in the target patient populations, including children who have limited sampling options. Currently, population pharmacokinetic studies of anti-malarial drugs are designed based on logistical, financial and ethical constraints, and prior knowledge of the drug concentration time profile. Although these factors are important, the proposed design may be unable to determine the desired pharmacokinetic profile because there was no formal consideration of the complex statistical models used to analyse the drug concentration data.

Methods

Optimal design methods incorporate prior knowledge of the pharmacokinetic profile of the drug, the statistical methods used to analyse data from population pharmacokinetic studies, and also the practical constraints of sampling the patient population. The methods determine the statistical efficiency of the design by evaluating the information of the candidate study design prior to the pharmacokinetic study being conducted.

Results

In a hypothetical population pharmacokinetic study of intravenous artesunate, where the number of patients and blood samples to be assayed was constrained to be 50 and 200 respectively, an evaluation of varying elementary designs using optimal design methods found that the designs with more patients and less samples per patient improved the precision of the pharmacokinetic parameters and inter-patient variability, and the overall statistical efficiency by at least 50%.

Conclusion

Optimal design methods ensure that the proposed study designs for population pharmacokinetic studies are robust and efficient. It is unethical to continue conducting population pharmacokinetic studies when the sampling schedule may be insufficient to estimate precisely the pharmacokinetic profile.

Comparison of model-based tests and selection strategies to detect genetic polymorphisms influencing pharmacokinetic parameters

We evaluate by simulation three model-based methods to test the influence of a single nucleotide polymorphism on a pharmacokinetic parameter of a drug: analysis of variance (ANOVA) on the empirical Bayes estimates of the individual parameters, likelihood ratio test between models with and without genetic covariate, and Wald tests on the parameters of the model with covariate. Analyses are performed using the FO and FOCE method implemented in the NONMEM software. We compare several approaches for model selection based on tests and global criteria. We illustrate the results with pharmacokinetic data on indinavir from HIV-positive patients included in COPHAR 2-ANRS 111 to study the gene effect prospectively. Only the tests based on the EBE obtain an empirical type I error close to the expected 5%. The approximation made with the FO algorithm results in a significant inflation of the type I error of the LRT and Wald tests.

Optimisation of sampling windows design for population pharmacokinetic experiments

This paper describes an approach for optimising sampling windows for population pharmacokinetic experiments. Sampling windows designs are more practical in late phase drug development where patients are enrolled in many centres and in out-patient clinic settings. Collection of samples under the uncontrolled environment at these centres at fixed times may be problematic and can result in uninformative data. Population pharmacokinetic sampling windows design provides an opportunity to control when samples are collected by allowing some flexibility and yet provide satisfactory parameter estimation. This approach uses information obtained from previous experiments about the model and parameter estimates to optimise sampling windows for population pharmacokinetic experiments within a space of admissible sampling windows sequences. The optimisation is based on a continuous design and in addition to sampling windows the structure of the population design in terms of the proportion of subjects in elementary designs, number of elementary designs in the population design and number of sampling windows per elementary design is also optimised. The results obtained showed that optimal sampling windows designs obtained using this approach are very efficient for estimating population PK parameters and provide greater flexibility in terms of when samples are collected. The results obtained also showed that the generalized equivalence theorem holds for this approach.

Computing normalised prediction distribution errors to evaluate nonlinear mixed-effect models: the npde add-on package for R

Pharmacokinetic/pharmacodynamic data are often analysed using nonlinear mixed-effect models, and model evaluation should be an important part of the analysis. Recently, normalised prediction distribution errors (npde) have been proposed as a model evaluation tool. In this paper, we describe an add-on package for the open source statistical package R, designed to compute npde. npde take into account the full predictive distribution of each individual observation and handle multiple observations within subjects. Under the null hypothesis that the model under scrutiny describes the validation dataset, npde should follow the standard normal distribution. Simulations need to be performed before hand, using for example the software used for model estimation. We illustrate the use of the package with two simulated datasets, one under the true model and one with different parameter values, to show how npde can be used to evaluate models. Model estimation and data simulation were performed using NONMEM version 5.1.

Bayesian Optimal Designs for Pharmacokinetic Models: Sensitivity to Uncertainty

We studied the sensitivity of the number of unique design points and their placement, in Bayesian optimal designs for pharmacokinetic models, with respect to the magnitude of prior uncertainty. We used two and three-parameter pharmacokinetic models with fixed and mixed effects and two Bayesian optimal design criteria, namely ED and API, using different error weighting schemes. We found that by increasing the magnitude of the uncertainty, in most cases, additional design points appear, compared to the corresponding local design, and this happens gradually, forming bifurcation patterns. These bifurcation patterns were interpreted as high sensitivity of the design from the magnitude of the uncertainty.

Overview of model-building strategies in population PK/PD analyses: 2002-2004 literature survey

AIMS

A descriptive survey of published population pharmacokinetic and/or pharmacodynamic (PK/PD) analyses from 2002 to 2004 was conducted and an evaluation made of how model building was performed and reported.

METHODS

We selected 324 articles in Pubmed using defined keywords. A data abstraction form (DAF) was then built comprising two parts: general characteristics including article identification, context of the analysis, description of clinical studies from which the data arose, and model building, including description of the processes of modelling. The papers were examined by two readers, who extracted the relevant information and transmitted it directly to a MySQL database, from which descriptive statistical analysis was performed.

RESULTS

Most published papers concerned patients with severe pathology and therapeutic classes suffering from narrow therapeutic index and/or high PK/PD variability. Most of the time, modelling was performed for descriptive purposes, with rich rather than sparse data and using NONMEM software. PK and PD models were rarely complex (one or two compartments for PK; E(max) for PD models). Covariate testing was frequently performed and essentially based on the likelihood ratio test. Based on a minimal list of items that should systematically be found in a population PK-PD analysis, it was found that only 39% and 8.5% of the PK and PD analyses, respectively, published from 2002 to 2004 provided sufficient detail to support the model-building methodology.

CONCLUSIONS

This survey allowed an efficient description of recent published population analyses, but also revealed deficiencies in reporting information on model building.

Optimal design for multiresponse pharmacokinetic-pharmacodynamic models - dealing with unbalanced designs

This paper addresses the problem of determining D-optimal designs for multiresponse pharmacokinetic-pharmacodynamic (PKPD) experiments where data on each response variable can be collected at different times. Most previous multiresponse model optimal design applications have considered the case where all response variables are measured at the same time points. However in practice it may not be possible to have all responses measured at the same sampling times. We propose an optimal design method to take into account the unbalanced nature of the problem. The method developed was applied to a PKPD problem that involved describing the time course of drug plasma concentrations, heart rate and mean arterial blood pressure for both a fixed effects and mixed effects regression model. Additionally a simulation study was carried out in NONMEM for one such population optimal design problem.

Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the MONOLIX software

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.

Design in nonlinear mixed effects models: Optimization using the Fedorov–Wynn algorithm and power of the Wald test for binary covariates

We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation.

Population clinical pharmacology of children: general principles

INTRODUCTION

Population modelling using mixed-effects models provides a means to study variability in drug responses among individuals representative of those for whom the drug will be used clinically.

DISCUSSION

The advantages of these models in paediatric studies are that they can be used to analyse sparse data, sampling times are not crucial and can be fitted around clinical procedures and individuals with missing data may still be included in the analysis. The introduction of explanatory covariates explains the predictable part of the between-individual variability. Simulations using parameter estimates and their variability can be used to investigate large numbers of children--many more than is possible in studies dealing with real children--for a fraction of the cost, which is an advantage when developing clinical trials. Paediatric population modelling has expanded greatly in the past decade and is now a routine procedure during the development and investigation of drugs. Children have benefitted and will continue to benefit from this approach.

Sample size calculations based on generalized estimating equations for population pharmacokinetic experiments

We present a method for calculating the sample size of a pharmacokinetic study analyzed using a mixed effects model within a hypothesis testing framework. A sample size calculation method for repeated measurement data analyzed using generalized estimating equations has been modified for nonlinear models. The Wald test is used for hypothesis testing of pharmacokinetic parameters. A marginal model for the population pharmacokinetic is obtained by linearizing the structural model around the subject specific random effects. The proposed method is general in that it allows unequal allocation of subjects to the groups and accounts for situations where different blood sampling schedules are required in different groups of patients. The proposed method has been assessed using Monte Carlo simulations under a range of scenarios. NONMEM was used for simulations and data analysis and the results showed good agreement.

Some considerations on the design of population pharmacokinetic studies

The goal of this manuscript is to introduce a framework for consideration of designs for population pharmacokinetic orpharmacokinetic-pharmacodynamic studies. A standard one compartment pharmacokinetic model with first-order input and elimination is considered. A series of theoretical designs are considered that explore the influence of optimizing the allocation of sampling times, allocating patients to elementary designs, consideration of sparse sampling and unbalanced designs and also the influence of single vs. multiple dose designs. It was found that what appears to be relatively sparse sampling (less blood samples per patient than the number of fixed effects parameters to estimate) can also be highly informative. Overall, it is evident that exploring the population design space can yield many parsimonious designs that are efficient for parameter estimation and that may not otherwise have been considered without the aid of optimal design theory.

Sample size computations for PK/PD population models

We describe an accurate, yet simple and fast sample size computation method for hypothesis testing in population PK/PD studies. We use a first order approximation to the nonlinear mixed effects model and chi-square distributed Wald statistic to compute the minimum sample size to achieve given degree of power in rejecting a null hypothesis in population PK/PD studies. The method is an extension of Rochon's sample size computation method for repeated measurement experiments. We compute sample sizes for PK and PK/PD models with different conditions, and use Monte Carlo simulation to show that the computed sample size retrieves the required power. We also show the effect of different sampling strategies, such as minimal, i.e., as many observations per individual as parameters in the model, and intensive on sample size. The proposed sample size computation method can produce estimates of minimum sample size to achieve the desired power in hypothesis testing in a greatly reduced time than currently available simulation-based methods. The method is rapid and efficient for sample size computation in population PK/PD study using nonlinear mixed effect models. The method is general and can accommodate any type of hierarchical models. Simulation results suggest that intensive sampling allows the reduction of the number of patients enrolled in a clinical study.

Pharmacokinetics/Pharmacodynamics and the stages of drug development: role of modeling and simulation

Pharmacokinetic (PK) and pharmacodynamic (PD) modeling and simulation (M&S) are well-recognized powerful tools that enable effective implementation of the learn-and-confirm paradigm in drug development. The impact of PK/PD M&S on decision making and drug development risk management is dependent on the question being asked and on the availability and quality of data accessible at a particular stage of drug development. For instance, M&S methodologies can be used to capture uncertainty and use the expected variability in PK/PD data generated in preclinical species for projection of the plausible range of clinical dose; clinical trial simulation can be used to forecast the probability of achieving a target response in patients based on information obtained in early phases of development. Framing the right question and capturing the key assumptions are critical components of the "learn-and-confirm" paradigm in the drug development process and are essential to delivering high-value PK/PD M&S results. Selected works of PK/PD modeling and simulation from preclinical to phase III are presented as case examples in this article.

A pragmatic approach to the design of population pharmacokinetic studies

The publication of a seminal article on nonlinear mixed-effect modeling led to a revolution in pharmacokinetics (PKs) with the introduction of the population approach. Since then, interest in obtaining accurate and precise estimates of population PK parameters has led to work on population PK study design that extended previous work on optimal sampling designs for individual PK parameter estimation. The issues and developments in the design of population PK studies are reviewed as a prelude to investigating, via simulation, the performance of 2 approaches (population Fisher information matrix D-optimal design and informative block [profile] randomized [IBR] design) for designing population PK studies. The results of our simulation study indicate that the designs based on the 2 approaches yielded efficient parameter estimates. The designs based on the 2 approaches performed similarly, and in some cases designs based on the IBR approach were slightly better. The ease with which the IBR designs can be generated makes them preferable in drug development, where pragmatism and time are of great consideration. We, therefore, refer to the IBR designs as pragmatic designs. Pragmatic designs that achieve high efficiency in the estimation parameters should be used in the design of population PK studies, and simulation should be used to determine the efficiency of the designs.

On some "disadvantages" of the population approach

In a seminal article on population pharmacokinetic modeling, researchers demonstrated how means and variances of pharmacokinetic parameters for a patient population could be inferred from sparse data collected under conditions of routine patient care. But they also identified 4 potential concerns about their methodology: unobserved confounding variables may bias the inferences; conditions under which data are collected may lead to inaccuracies of reporting or recording; correlations among important predictor variables may reduce statistical efficiency; and costs cannot be controlled by principles of study design. Experiences are reviewed that relate to these potential disadvantages. A method is presented for diagnosing the possible presence of confounding. A model is constructed and applied that captures the influences of data inaccuracies. An example of selecting from among correlated covariates is summarized. Finally, a methodology for optimal study design is reviewed and applied to an example.

Evaluation by simulation of tests based on non-linear mixed-effects models in pharmacokinetic interaction and bioequivalence cross-over trials

We propose tests based on non-linear mixed effects models (NLMEM) in pharmacokinetic interaction and bioequivalence cross-over trials comparing two treatments or two formulations. To compare the logarithm of the area under the curve (AUC) using these models, two approaches are studied: in the first one, concentration data are analysed globally, with and without the estimation of a treatment effect; and in the second one, they are analysed separately in each treatment group with the estimation of the individual parameters. Four tests for comparison of the logarithm AUC between two treatment arms are studied: a likelihood-ratio test (LRT), a Wald test and two tests, parametric and non-parametric, comparing the individual Empirical Bayes (EB) estimates. These tests are adapted to the case of equivalence, except the LRT which does not have any simple extension. We evaluate by simulation of the type I error and the power for both comparison and equivalence tests. They are compared to the standard tests recommended by the FDA and the EMEA, based on non-compartmental (NC) AUC. Trials for a usual PK model are simulated under H(0) and several H(1) using S-plus software and analysed with the nlme function. Different configurations of the number of subjects (n=12, 24 and 40) and of the number of samples per subject (J=10, 5 and 3) are studied. The type I error alpha of LRT and Wald comparison test in the 5000 replications of interaction cross-over trials is found to be 20.9 per cent and 21.7 per cent, respectively, in the original design (n=12, J=10), which is far superior to 5 per cent, and decreases when n increases. When n is fixed, alpha is found to increase with J. Power is satisfactory for both tests, after correction of the significance threshold. Results of EB and NC tests are similar with satisfactory powers and a type I error close to 5 per cent, except when J=3 for EB tests. Similar results are obtained for equivalence tests, except for EB and NC Student tests, which are not of a great interest. NC tests keep their place when the number of samples per subject J is large, but NLMEM seem useful for cross-over studies performed in special populations where J limited; the evaluation by Monte-Carlo simulations of empirical threshold seems however necessary because of the inflation of the type I error.

Evaluation of Bayesian Estimation of Pharmacokinetic Parameters

The validity of pharmacokinetic parameters estimated by the maximum a posteriori probability (MAP) Bayesian method was investigated by simulation studies. A 1-compartment model with bolus intravenous administration was used as a pharmacokinetic model, and the coefficients of variation for the parameters and residual error were set at 30% and 10%, respectively. The accuracy of the posterior modes of pharmacokinetic parameters estimated by the MAP Bayesian method was assessed by the difference between the true value and the estimated value. The results showed that the accuracy of the Bayesian estimation depended on sampling times and on the differences between the prior means and individual true parameter values. For assessing the reliability and accuracy of the Bayesian estimation, the authors suggest using the whole posterior distribution of the pharmacokinetic parameters to describe the 95th percentile range for predicted blood concentration profiles. The authors believe that the proposed procedures provide helpful information for evaluating the Bayesian estimation of pharmacokinetic profiles.