Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis

pyDarwin: A Machine Learning Enhanced Automated Nonlinear Mixed-Effect Model Selection Toolbox

pyDarwin is an open-source Python package for nonlinear mixed-effect model selection. pyDarwin combines machine-learning algorithms and NONMEM to perform a global search for the optimal model in a user-defined model search space. Compared with traditional stepwise search, pyDarwin provides an efficient platform for conducting an objective, robust, less labor-intensive model selection process without compromising model interpretability. In this tutorial, we will begin by introducing the essential components and concepts within the package. Subsequently, we will provide an overview of the pyDarwin modeling workflow and the necessary files needed for model selection. To illustrate the entire process, we will conclude with an example utilizing quetiapine clinical data.

Alternative Pharmacokinetic Metrics in Single-Dose Studies to Ensure Bioequivalence of Prolonged-Release Products at Steady State-A Case Study

(1) Background: this article investigates which PK metrics in a single-dose study (concentration at the end of posology interval, C_τ, partial areas under the curve, pAUCs, or half-value duration, HVD) are more sensitive and less variable for predicting the failure of a prolonged-release product at steady-state that was the bioequivalent for C_max, AUC_0-t and AUC_0-inf, in the single-dose study; (2) Methods: a cross-over study was performed in 36 subjects receiving desvenlafaxine 100 mg prolonged-release tablets. Conventional (C_max, AUC_0-t and AUC_0-inf) and additional (C_τ, pAUCs and HVD) PK metrics were considered after single-dose conditions. Predicted PK metrics at steady state (AUC_0-τ, C_max,ss, and C_τ,ss) were derived using a population PK model approach; (3) Results: the existing differences in the shape of the concentration-time curves precluded to show equivalence for C_τ,ss in the simulated study at steady state. This failure to show equivalence at steady state was predicted by C_τ, pAUCs and HVD in the single-dose study. C_τ was the most sensitive metric for detecting the different shape, with a lower intra-subject variability than HVD; (4) Conclusions: conventional PK metrics for single-dose studies (C_max, AUC_0-t and AUC_0-inf) are not enough to guarantee bioequivalence at steady state for prolonged-release products.

Population Pharmacokinetic/Pharmacodynamic Modelling of Daptomycin for Schedule Optimization in Patients with Renal Impairment

The aims of this study are (i) to develop a population pharmacokinetic/pharmacodynamic model of daptomycin in patients with normal and impaired renal function, and (ii) to establish the optimal dose recommendation of daptomycin in clinical practice. Several structural PK models including linear and non-linear binding kinetics were evaluated. Monte Carlo simulations were conducted with a fixed combination of creatinine clearance (30–90 mL/min/1.73 m²) and body weight (50–100 kg). The final dataset included 46 patients and 157 daptomycin observations. A two-compartment model with first-order peripheral distribution and elimination kinetics assuming non-linear protein-binding kinetics was selected. The bactericidal effect for Gram+ strains with MIC ≤ 0.5 mg/L could be achieved with 5–12 mg/kg daily daptomycin based on body weight and renal function. The administration of 10–17 mg/kg q48 h daptomycin allows to achieve bactericidal effect for Gram+ strains with MIC ≤ 1 mg/L. Four PK samples were selected as the optimal sampling strategy for an accurate AUC estimation. A quantitative framework has served to characterize the non-linear binding kinetics of daptomycin in patients with normal and impaired renal function. The impact of different dosing regimens on the efficacy and safety outcomes of daptomycin treatment based on the unbound exposure of daptomycin and individual patient characteristics has been evaluated.

Parametric and Nonparametric Methods in Population Pharmacokinetics: Experts' Discussion on Use, Strengths, and Limitations

Population pharmacokinetics consists of analyzing pharmacokinetic (PK) data collected in groups of individuals. Population PK is widely used to guide drug development and to inform dose adjustment via therapeutic drug monitoring and model-informed precision dosing. There are 2 main types of population PK methods: parametric (P) and nonparametric (NP). The characteristics of P and NP population methods have been previously reviewed. The aim of this article is to answer some frequently asked questions that are often raised by scholars, clinicians, and researchers about P and NP population PK methods. The strengths and limitations of both approaches are explained, and the characteristics of the main software programs are presented. We also review the results of studies that compared the results of both approaches in the analysis of real data. This opinion article may be informative for potential users of population methods in PK and guide them in the selection and use of those tools. It also provides insights on future research in this area.

Development of a genetic algorithm and NONMEM workbench for automating and improving population pharmacokinetic/pharmacodynamic model selection

The current approach to selection of a population PK/PD model is inherently flawed as it fails to account for interactions between structural, covariate, and statistical parameters. Further, the current approach requires significant manual and redundant model modifications that heavily lend themselves to automation. Within the discipline of numerical optimization it falls into the "local search" category. Genetic algorithms are a class of algorithms inspired by the mathematics of evolution. GAs are general, powerful, robust algorithms and can be used to find global optimal solutions for difficult problems even in the presence of non-differentiable functions, as is the case in the discrete nature of including/excluding model components in search of the best performing mixed-effects PK/PD model. A genetic algorithm implemented in an R-based NONMEM workbench for identification of near optimal models is presented. In addition to the GA capabilities, the workbench supports modeling efforts by: (1) Organizing and displaying models in tabular format, allowing the user to sort, filter, edit, create, and delete models seamlessly, (2) displaying run results, parameter estimates and precisions, (3) integrating xpose4 and PsN to facilitate generation of model diagnostic plots and run PsN scripts, (4) running regression models between post-hoc parameter estimates and covariates. This approach will further facilitate the scientist to shift efforts to focus on model evaluation, hypotheses generation, and interpretation and applications of resulting models.

Concordance of Exposure Changes Because of Renal Impairment Between Results of Dedicated Renal Impairment Studies and Population Pharmacokinetic Predictions

This analysis compared the results from noncompartmental analysis and population pharmacokinetic (PopPK) predictions of exposure changes in patients with renal impairment (RI) for 27 new molecular entities (NMEs) approved between 2000 and 2015. Renal function was identified as a covariate in the final PopPK model for 17 NMEs. The final PopPK model was used to simulate (n  =  1000 replicates/individual) the results of a dedicated PK study in subjects with renal impairment. For the majority of NMEs, concordance between observed, and predicted area under the curve (AUC) geometric mean ratio (GMR) was observed (ie, in 17, 11, and 11 NMEs for mild, moderate, and severe renal impairment groups, respectively, the observed and predicted AUC GMR were within the same fold of change). Inclusion of colinear covariates in the PopPK model appeared to be the major driver for the NMEs for which there was discordance. PopPK, when done properly, is a valuable tool for supporting labeling recommendations for subjects with renal impairment.

Population pharmacokinetic modelling to quantify the magnitude of drug-drug interactions between amlodipine and antiretroviral drugs

PURPOSE

Drug-drug interactions (DDIs) with antiretroviral drugs (ARVs) represent an important issue in elderly people living with HIV (PLWH). Amlodipine is a commonly prescribed antihypertensive drug metabolized by CYP3A4, thus predisposed to a risk of DDIs. Guidance on the management of DDIs is mostly based on theoretical considerations derived from coadministration with other CYP3A4 inhibitors. This study aimed at characterizing the magnitude of DDIs between amlodipine and ARV drugs in order to establish dosing recommendations.

METHODS

A population pharmacokinetic analysis was developed using non-linear mixed effect modelling (NONMEM) and included 163 amlodipine concentrations from 55 PLWH. Various structural and error models were compared to characterize optimally the concentration-time profile of amlodipine. Demographic and clinical characteristics as well as comedications were tested as potential influential covariates. Model-based simulations were performed to compare amlodipine exposure (i.e. area under the curve, AUC) between coadministered ARV drugs.

RESULTS

Amlodipine concentration-time profile was best described using a one-compartment model with first-order absorption and a lag-time. Amlodipine apparent clearance was influenced by both CYP3A4 inhibitors and efavirenz (CYP3A4 inducer). Model-based simulations revealed that amlodipine AUC increased by 96% when coadministered with CYP3A4 inhibitors, while efavirenz decreased drug exposure by 59%.

CONCLUSION

Coadministered ARV drugs significantly impact amlodipine disposition in PLWH. Clinicians should adjust amlodipine dosage accordingly, by halving the dosage in PLWH receiving ARV with inhibitory properties (mainly ritonavir-boosted darunavir), whereas they should double amlodipine doses when coadministering it with efavirenz, under appropriate monitoring of clinical response and tolerance.

Impact of disease, drug and patient adherence on the effectiveness of antiviral therapy in pediatric HIV

INTRODUCTION

Maintaining effective antiretroviral treatment for life is a major problem in both resource-limited and resource-rich countries. Despite the progress observed in paediatric antiretroviral therapy, approximately 12% of children still experience treatment failure due to drug resistance, inadequate dosing and poor adherence. We explore the current status of antiretroviral therapy in children with focus on the interaction between disease, drug pharmacokinetics and patient behavior, all of which are strongly interconnected and determine treatment outcome. Areas covered: An overview is provided of the viral characteristics and available drug combinations aimed at the prevention of resistance. In this context, the role of patient adherence is scrutinized. A detailed assessment of factors affecting adherence is presented together with the main strategies to enhance treatment response in children. Expert opinion: Using modeling and simulation, a framework for characterizing the forgiveness of non-adherence for specific antiretroviral drugs in children is proposed in which information on pharmacokinetics, pharmacokinetic-pharmacodynamic relationships and viral dynamics is integrated. This approach represents an opportunity for the simplification of dosing regimens taking into account the interaction between these factors. Based on clinical trial simulation scenarios, we envisage the possibility of assessing the impact of variable adherence to antiretroviral drug combinations in HIV-infected children.

Children in clinical trials: towards evidence-based pediatric pharmacotherapy using pharmacokinetic-pharmacodynamic modeling

INTRODUCTION

In pediatric pharmacotherapy, many drugs are still used off-label, and their efficacy and safety is not well characterized. Different efficacy and safety profiles in children of varying ages may be anticipated, due to developmental changes occurring across pediatric life.

AREAS COVERED

Beside pharmacokinetic (PK) studies, pharmacodynamic (PD) studies are urgently needed. Validated PKPD models can be used to derive optimal dosing regimens for children of different ages, which can be evaluated in a prospective study before implementation in clinical practice. Strategies should be developed to ensure that formularies update their drug dosing guidelines regularly according to the most recent advances in research, allowing for clinicians to integrate these guidelines in daily practice. Expert commentary: We anticipate a trend towards a systems-level approach in pediatric modeling to optimally use the information gained in pediatric trials. For this approach, properly designed clinical PKPD studies will remain the backbone of pediatric research.

Pharmacology-based toxicity assessment: towards quantitative risk prediction in humans

Despite ongoing efforts to better understand the mechanisms underlying safety and toxicity, ~30% of the attrition in drug discovery and development is still due to safety concerns. Changes in current practice regarding the assessment of safety and toxicity are required to reduce late stage attrition and enable effective development of novel medicines. This review focuses on the implications of empirical evidence generation for the evaluation of safety and toxicity during drug development. A shift in paradigm is needed to (i) ensure that pharmacological concepts are incorporated into the evaluation of safety and toxicity; (ii) facilitate the integration of historical evidence and thereby the translation of findings across species as well as between in vitro and in vivo experiments and (iii) promote the use of experimental protocols tailored to address specific safety and toxicity questions. Based on historical examples, we highlight the challenges for the early characterisation of the safety profile of a new molecule and discuss how model-based methodologies can be applied for the design and analysis of experimental protocols. Issues relative to the scientific rationale are categorised and presented as a hierarchical tree describing the decision-making process. Focus is given to four different areas, namely, optimisation, translation, analytical construct and decision criteria. From a methodological perspective, the relevance of quantitative methods for estimation and extrapolation of risk from toxicology and safety pharmacology experimental protocols, such as points of departure and potency, is discussed in light of advancements in population and Bayesian modelling techniques (e.g. non-linear mixed effects modelling). Their use in the evaluation of pharmacokinetics (PK) and pharmacokinetic-pharmacodynamic relationships (PKPD) has enabled great insight into the dose rationale for medicines in humans, both in terms of efficacy and adverse events. Comparable benefits can be anticipated for the assessment of safety and toxicity profile of novel molecules.

A genetic algorithm based global search strategy for population pharmacokinetic/pharmacodynamic model selection

The current algorithm for selecting a population pharmacokinetic/pharmacodynamic model is based on the well-established forward addition/backward elimination method. A central strength of this approach is the opportunity for a modeller to continuously examine the data and postulate new hypotheses to explain observed biases. This algorithm has served the modelling community well, but the model selection process has essentially remained unchanged for the last 30 years. During this time, more robust approaches to model selection have been made feasible by new technology and dramatic increases in computation speed. We review these methods, with emphasis on genetic algorithm approaches and discuss the role these methods may play in population pharmacokinetic/pharmacodynamic model selection.

Covariate selection in pharmacometric analyses: a review of methods

Covariate selection is an activity routinely performed during pharmacometric analysis. Many are familiar with the stepwise procedures, but perhaps not as many are familiar with some of the issues associated with such methods. Recently, attention has focused on selection procedures that do not suffer from these issues and maintain good predictive properties. In this review, we endeavour to put the main variable selection procedures into a framework that facilitates comparison. We highlight some issues that are unique to pharmacometric analyses and provide some thoughts and strategies for pharmacometricians to consider when planning future analyses.

Genetic algorithm guided population pharmacokinetic model development for simvastatin, concurrently or non-concurrently co-administered with amlodipine

An automated model development was performed for simvastatin, co-administered with amlodipine concurrently or non-concurrently (i.e., 4 hours later) in 17 patients with coexisting hyperlipidemia and hypertension. The single objective hybrid genetic algorithm (SOHGA) was implemented in the NONMEM software by defining the search space for structural, statistical and covariate models. Candidate models obtained from the SOHGA runs were further assessed for biological plausibility and the precision of parameter estimates, followed by traditional backward elimination process for model refinement. The final population pharmacokinetic model shows that the elimination rate constant for simvastatin acid, the active form by hydrolysis of its lactone prodrug (i.e., simvastatin), is only 44% in the concurrent amlodipine administration group compared with the non-concurrent group. The application of SOHGA for automated model selection, combined with traditional model selection strategies, appears to save time for model development, which also can generate new hypotheses that are biologically more plausible.

Establishing best practices and guidance in population modeling: an experience with an internal population pharmacokinetic analysis guidance

This tutorial describes the development of a population pharmacokinetic (Pop PK) analysis guidance within Pfizer, which strives for improved consistency and efficiency, and a more systematic approach to model building. General recommendations from the Pfizer internal guidance and a suggested workflow for Pop PK model building are discussed. A description is also provided for mechanisms by which conflicting opinions were captured and resolved across the organization to arrive at the final guidance.

CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e51; doi:10.1038/psp.2013.26; advance online publication 3 July 2013

Pharmacodynamic modeling of cough responses to capsaicin inhalation calls into question the utility of the C5 end point

BACKGROUND

Inhaled capsaicin elicits cough reproducibly in human subjects and is widely used in the study of cough and antitussive therapies. However, the traditional end points C2 and C5 (the concentrations of capsaicin inducing at least 2 or 5 coughs, respectively) display extensive overlap between health and disease and therefore might not best reflect clinically relevant mechanisms.

OBJECTIVES

We sought to investigate capsaicin dose responses in different disease groups.

METHODS

Two novel capsaicin cough challenges were compared in patients with chronic cough (CC; n = 20), asthmatic patients (n = 18), and healthy volunteers (HVs; n = 20). Increasing doubling doses of capsaicin (0.48-1000 μmol/L, 4 inhalations per dose) were administered in challenge 1, whereas the order of the doses was randomized in challenge 2. A nonlinear mixed-effects model compared dose-response parameters by disease group and sex. Parameters were also correlated with objective cough frequency.

RESULTS

The model classified subjects based on maximum cough response evoked by any concentration of capsaicin (Emax) and the capsaicin dose inducing half-maximal response (ED50). HVs and asthmatic patients were not statistically different for either parameter and therefore combined for analysis (mean ED50, 38.6 μmol/L [relative SE, 28%]; mean Emax, 4.5 coughs [relative SE, 11%]). Compared with HVs/asthmatic patients, patients with CC had lower ED50 values (14.7 μmol/L [relative SE, 28%], P = .008) and higher Emax values (8.6 coughs [relative SE, 11%], P < .0001). Emax values highly correlated with 24-hour cough frequency (r = 0.71, P < .001) and were 37% higher in female compared with male subjects, regardless of disease group (P < .001).

CONCLUSIONS

Nonlinear mixed-effects modeling demonstrates that maximal capsaicin cough responses better discriminate health from disease and predict spontaneous cough frequency and therefore provide important insights into the mechanisms underlying CC.

Serum cystatin C is a major predictor of vancomycin clearance in a population pharmacokinetic analysis of patients with normal serum creatinine concentrations

We developed a population pharmacokinetic model of vancomycin by integrating the effects of cystatin C and other demographic factors in a large population of Korean patients with normal serum creatinine concentrations to elucidate the precise role of serum cystatin C concentrations in the prediction of vancomycin clearance. A population pharmacokinetic model of vancomycin was developed using NONMEM software from a total of 1,373 vancomycin concentration measurements in 678 patients whose serum creatinine concentrations were lower than 1.2 mg/dL. Covariate selection revealed that cystatin C was the most influential factor and had negative influence ((-0.78)) in the relationship. Total body weight, sex, age, and serum creatinine were also significantly correlated with the clearance. The estimated intersubject variabilities of clearance and volume of distribution were 24.7% and 25.1%, respectively. A 14-fold difference in predicted trough concentrations was observed according to only cystatin C concentrations in a population of simulated individuals with median demographic characteristics. The use of serum cystatin C as marker of vancomycin clearance for more accurate predictions of serum vancomycin concentrations could be useful, particularly among patients with normal serum creatinine concentrations.

Application of a single-objective, hybrid genetic algorithm approach to pharmacokinetic model building

A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q₁ = 4.9 % and q₃ = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data.

Integrated analysis of preclinical data to support the design of the first in man study of LY2181308, a second generation antisense oligonucleotide

AIMS

To predict the concentration and target inhibition profiles of the survivin inhibitor antisense oligonucleotide LY2181308 in humans.

METHODS

An indirect pharmacokinetic/pharmacodynamic (PK/PD) model was built to predict the inhibition of survivin mRNA and protein in humans following LY2181308 dosing. Plasma and tissue PK data from cynomolgus monkeys were analyzed by non-linear mixed effect modelling techniques. Human PK parameters were predicted using allometric scaling. Assumptions about the pharmacodynamic parameters were made based upon the target and tumour growth inhibition data from mouse xenograft models. This enabled the prediction of the clinical PK/PD profiles.

RESULTS

Following a 750 mg dose, LY2181308 tumour concentrations ranging from 18.8 to 54µgg(-1) were predicted to lead to 50 to 90% target inhibition. In humans, LY2181308 tumour concentrations fro 13.9 to 52.8µgg(-1) (n=4, LY2181308 750mg) were observed associated with a median survivin mRNA and protein inhibition of 20%±34 (SD) (n=9) and 23%±63 (SD) (n=10), respectively. The human PK parameters were adequately estimated: central V(d) , 4.09 l (90% CI, 3.6, 4.95), distribution clearances, 2.54 (2.36, 2.71), 0.0608 (0.033, 0.6) and 1.67 (1.07, 2.00)lh(-1) , peripheral V(d) s, 25 900 (19 070, 37 200), 0.936 (0.745, 2.07) and 2.51 (1.01, 2.922)l, mean elimination clearance 23.1lh(-1) (5.6, 33.4) and mean terminal half-life, 32.7 days (range 22-52 days).

CONCLUSION

The model reasonably predicted LY2181308 PK in humans. Overall, the integration of preclinical PK/PD data enabled to appropriately predict dose and dosing regimen of LY2181308 in humans with pharmacologically relevant survivin inhibition achieved at 750mg.

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.

Population pharmacokinetics of clofarabine and its metabolite 6-ketoclofarabine in adult and pediatric patients with cancer

Clofarabine for injection is a second-generation nucleoside analog approved in the United States (Clolar(®)) and Europe (Evoltra(®)) for the treatment of pediatric relapsed or refractory acute lymphoblastic leukemia. This report describes the population pharmacokinetics of clofarabine and its metabolite 6-ketoclofarabine in adult and pediatric patients with hematologic malignancies or solid tumors. Clofarabine pharmacokinetics were best described by a 2-compartment model with linear elimination and first-order absorption after oral administration. Clofarabine was rapidly absorbed following oral administration with a mean absorption time of less than 2 h and bioavailability of 57.5%. The important covariates affecting clofarabine pharmacokinetics were age, weight, and estimated creatinine clearance (eCrCL). No difference in pharmacokinetics was observed between sexes, races, or disease type. The elimination half-life was dependent on all the covariates but was generally less than 7 h in all cases. A difference in clofarabine pharmacokinetics was observed between adults and children. For a pediatric patient 3 years old weighing 16 kg with an eCrCL of 138 mL/min/1.73 m(2), the population estimates for total systemic clearance and volume of distribution at steady-state were 18.3 L/h (1.14 L/h/kg) and 92.9 L (5.81 L/kg), respectively. α- and β-half-life were 0.9 and 4.4 h, respectively. For an elderly patient 82 years old weighing 96 kg with an eCrCL of 46 mL/min/1.73 m(2), the population estimates for CL and Vdss were 21.5 L/h (0.22 L/h/kg) and 257.4 L (268 L/kg), respectively. α- and β-half-life were 0.5 and 10.6 h, respectively. Because of the difference in pharmacokinetics, adults have higher exposure than children given a similar dose standardized to body surface area. The exact mechanism of this difference is not understood. As eCrCL decreased, exposure increased due to reduced total systemic clearance. In the case of moderate (eCrCL 30 to 60 mL/min/1.73 m(2)) and severe (eCrCL <30 mL/min/1.73 m(2)) renal impairment, dose reduction may be needed to maintain similar exposure in an equivalent patient of the same age, weight, and normal renal function after both oral and intravenous administration. 6-Ketoclofarabine was a minor metabolite with peak plasma concentrations occurring about 1 h after the start of the infusion and having a metabolite ratio averaging less than 5% and not more than 8% for any particular individual. 6-Ketoclofarabine was rapidly cleared from plasma with an average apparent half-life of 4.9 h (range 3.9 to 6.2 h). No accumulation of 6-ketoclofarabine was observed with predose samples all below the limit of quantification on Days 8 and 15. Further monitoring of 6-ketoclofarabine is not required in future studies.

Pharmacokinetic-pharmacodynamic analysis of the static allodynia response to pregabalin and sildenafil in a rat model of neuropathic pain

The objective of this study was to develop a pharmacokinetic-pharmacodynamic (PK-PD) model of the static allodynia response to pregabalin with and without sildenafil in a chronic constriction injury model of neuropathic pain. Six treatment groups were evaluated every 30 min for 6 h. Rats were treated with either 1) a saline infusion; 2) a 2-h pregabalin infusion at 4 mgxkg(-1)xh(-1); 3) a 2-h pregabalin infusion at 10 mgxkg(-1)xh(-1); 4) a 2.2-mg loading dose + 12 mgxkg(-1)xmin(-1) infusion of sildenafil; 5) a 2-h pregabalin infusion at 1.6 mgxkg(-1)xh(-1) with sildenafil; and 6) a 2-h infusion of pregabalin at 4 mgxkg(-1)xh with sildenafil. The static allodynia endpoint was modeled by using three population PD approaches: 1) the behavior of the injured paw using a three-category ordinal logistic regression model; 2) paw withdrawal threshold (PWT) (g) between the injured and uninjured paw using the Hill equation with a baseline function; and 3) the baseline normalized difference in PWT between the injured and uninjured paw. The categorical model showed a significant shift in the concentration-response relationship of pregabalin to lower concentrations with concomitant sildenafil. Likewise, the continuous PK-PD models demonstrated a reduction in the EC(50) of pregabalin necessary for PD response in the presence of sildenafil. The difference-transformed PD model resulted in a 54.4% (42.3-66.9%) decrease in EC(50), whereas the percentage-transformed PD model demonstrated a 53.5% (42.7-64.3%) shift. It is concluded from these studies that there is a synergistic PD interaction between pregabalin and sildenafil.

Population pharmacokinetic model of the pregabalin-sildenafil interaction in rats: application of simulation to preclinical PK-PD study design

PURPOSE

Preliminary evidence has suggested a synergistic interaction between pregabalin and sildenafil for the treatment of neuropathic pain. The focus of this study was to determine the influence of sildenafil on the pharmacokinetics (PK) of pregabalin with the objective of informing the design of a quantitative pharmacodynamic (PD) study.

METHODS

The pharmacokinetics were determined in rats following 2-hr intravenous infusions of pregabalin at doses of 4 mg/kg/hr and 10 mg/kg/hr with and without a sildenafil bolus (2.2 mg) and steady state infusion (12 mg/kg/hr for 6 h). This PK model was utilized in a preclinical trial simulation with the aim of selecting the optimal sampling strategy to characterize the PK-PD profile in a future study. Eight logistically feasible PK sampling strategies were simulated in NONMEM and examined through trial simulation techniques.

RESULTS

A two-compartment population PK model best described pregabalin pharmacokinetics. Significant model covariates included either a binary effect of sildenafil administration (30.2% decrease in clearance) or a concentration-dependent effect due to sildenafil's active metabolite.

CONCLUSIONS

Analysis of simulations indicated that three post-PD samples had the best cost/benefit ratio by providing a significant increase in the precision (and minor improvement in bias) of both PK and PD parameters compared with no PK sampling.

Pharmacokinetics of sapropterin in patients with phenylketonuria

BACKGROUND AND OBJECTIVE

Untreated phenylketonuria is characterized by neurocognitive and neuromotor impairment, which result from elevated blood phenylalanine concentrations. To date, the recommended management of phenylketonuria has been the use of a protein-restricted diet and the inclusion of phenylalanine-free protein supplements; however, this approach is often associated with poor compliance and a suboptimal clinical outcome. Sapropterin dihydrochloride, herein referred to as sapropterin, a synthetic formulation of 6R-tetrahydrobiopterin (6R-BH4), has been shown to be effective in reducing blood phenylalanine concentrations in patients with phenylketonuria. The objective of the current study was to characterize the pharmacokinetics and pharmacokinetic variability of sapropterin and to identify the characteristics that influence this variability.

PATIENTS AND METHODS

This was a 12-week, fixed-dose phase of an open-label extension study. The study was conducted at 26 centres in North America and Europe.Patients with phenylketonuria were eligible to participate if they were > or =8 years of age and had received > or =80% of the scheduled doses in a previous 6-week, randomized, placebo-controlled study or had been withdrawn from that study after exceeding a plasma phenylalanine concentration of > or =1500 micromol/L to > or =1800 micromol/L, depending on the subject's age and baseline plasma phenylalanine concentration. A total of 78 patients participated. Patients received oral once-daily doses of sapropterin (Kuvan) 5, 10 or 20 mg/kg/day. Blood samples for the pharmacokinetic analysis were obtained during weeks 6, 10 and 12. A D-optimal sparse sampling strategy was used, and data were analysed by population-based, nonlinear, mixed-effects modelling methods.

MAIN OUTCOME MEASURE

In a prospectively planned analysis, the apparent clearance, apparent volume of distribution, absorption rate constant and associated interindividual variabilities of each parameter were estimated by modelling observed BH4 plasma concentration-time data.

RESULTS

The best structural model to describe the pharmacokinetics of sapropterin was a two-compartment model with first-order input, first-order elimination and a baseline endogenous BH4 concentration term. Total bodyweight was the only significant covariate identified, the inclusion of which on both the apparent clearance (mean = 2100 L/h/70 kg) and central volume of distribution (mean = 8350 L/70 kg) substantially improved the model's ability to describe the data. The mean (SD) terminal half-life of sapropterin was 6.69 (2.29) hours and there was little evidence of accumulation, even at the highest dose.

CONCLUSION

These findings, taken together with the observed therapeutic effect, support bodyweight-based, once-daily dosing of sapropterin 5-20 mg/kg/day.

The lasso--a novel method for predictive covariate model building in nonlinear mixed effects models

Covariate models for population pharmacokinetics and pharmacodynamics are often built with a stepwise covariate modelling procedure (SCM). When analysing a small dataset this method may produce a covariate model that suffers from selection bias and poor predictive performance. The lasso is a method suggested to remedy these problems. It may also be faster than SCM and provide a validation of the covariate model. The aim of this study was to implement the lasso for covariate selection within NONMEM and to compare this method to SCM. In the lasso all covariates must be standardised to have zero mean and standard deviation one. Subsequently, the model containing all potential covariate-parameter relations is fitted with a restriction: the sum of the absolute covariate coefficients must be smaller than a value, t. The restriction will force some coefficients towards zero while the others are estimated with shrinkage. This means in practice that when fitting the model the covariate relations are tested for inclusion at the same time as the included relations are estimated. For a given SCM analysis, the model size depends on the P-value required for selection. In the lasso the model size instead depends on the value of t which can be estimated using cross-validation. The lasso was implemented as an automated tool using PsN. The method was compared to SCM in 16 scenarios with different dataset sizes, number of investigated covariates and starting models for the covariate analysis. Hundred replicate datasets were created by resampling from a PK-dataset consisting of 721 stroke patients. The two methods were compared primarily on the ability to predict external data, estimate their own predictive performance (external validation), and on the computer run-time. In all 16 scenarios the lasso predicted external data better than SCM with any of the studied P-values (5%, 1% and 0.1%), but the benefit was negligible for large datasets. The lasso cross-validation provided a precise and nearly unbiased estimate of the actual prediction error. On a single processor, the lasso was faster than SCM. Further, the lasso could run completely in parallel whereas SCM must run in steps. In conclusion, the lasso is superior to SCM in obtaining a predictive covariate model on a small dataset or on small subgroups (e.g. rare genotype). Run in parallel the lasso could be much faster than SCM. Using cross-validation, the lasso provides a validation of the covariate model and does not require the user to specify a P-value for selection.

Modelling response time profiles in the absence of drug concentrations: definition and performance evaluation of the K-PD model

The plasma concentration-time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK(50) which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC(50), the pharmacodynamic potency, and clearance, the PK "potency" at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC(50) to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK-PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K-PD model should definitively not be substituted for the gold standard PK-PD model when correct full model can and should be identified.

Population pharmacokinetic modelling of gentamicin and vancomycin in patients with unstable renal function following cardiothoracic surgery

AIMS

To describe the population pharmacokinetics of gentamicin and vancomycin in cardiothoracic surgery patients with unstable renal function.

METHODS

Data collected during routine care were analyzed using NONMEM. Linear relationships between creatinine clearance (CL(Cr)) and drug clearance (CL) were identified, and two approaches to modelling changing CL(Cr) were examined. The first included baseline (BCOV) and difference from baseline (DCOV) effects and the second allowed the influence of CL(Cr) to vary between individuals. Final model predictive performance was evaluated using independent data. The data sets were then combined and parameters re-estimated.

RESULTS

Model building was performed using data from 96 (gentamicin) and 102 (vancomycin) patients, aged 17-87 years. CL(Cr) ranged from 9 to 172 ml min(-1) and changes varied from -76 to 58 ml min(-1) (gentamicin) and -86 to 93 ml min(-1) (vancomycin). Inclusion of BCOV and DCOV improved the fit of the gentamicin data but had little effect on that for vancomycin. Inclusion of interindividual variability (IIV) in the influence of CL(cr) resulted in a poorly characterized model for gentamicin and had no effect on vancomycin modelling. No bias was seen in population compared with individual CL estimates in independent data from 39 (gentamicin) and 37 (vancomycin) patients. Mean (95% CI) differences were 4% (-3, 11%) and 2% (-2, 6%), respectively. Final estimates were: CL(Gent) (l h(-1)) = 2.81 x (1 + 0.015 x (BCOV(CLCr)-BCOV(CLCr Median)) + 0.0174 x DCOV(CLCr)); CL(Vanc) (l h(-1)) = 2.97 x (1 + 0.0205 x (CL(Cr)-CL(Cr Median))). IIV in CL was 27% for both drugs.

CONCLUSIONS

A parameter describing individual changes in CL(cr) with time improves population pharmacokinetic modelling of gentamicin but not vancomycin in clinically unstable patients.

Population analysis of a 24-h paclitaxel infusion in advanced endometrial cancer: a gynaecological oncology group study

AIMS

To examine determinants of paclitaxel disposition and the association between paclitaxel exposure and toxicity or survival in patients with advanced stage or recurrent endometrial cancer treated with doxorubicin plus paclitaxel.

METHODS

A limited sampling scheme was used to examine the population pharmacokinetics of paclitaxel in 160 patients from one arm of a randomized Phase III trial of doxorubicin plus paclitaxel or cisplatin. Four plasma samples per patient were collected at approximately 0, 3, 22 and 27 h after the first 24-h infusion of paclitaxel and submitted to the Gynecological Oncology Group (GOG) Pharmacology Core Laboratory. Total paclitaxel concentrations were quantified by LC/MS and paclitaxel disposition was examined using NONMEM. Paclitaxel exposure was evaluated for associations with toxicity or survival.

RESULTS

Patient weight, age and serum glutamic-oxaloacetic transaminase level were determinants of paclitaxel clearance (clearance increased 0.437 l h-1 kg-1; decreased 0.223 l h-1 year-1 and 0.105 l h-1 IU-1). Bayesian shrinkage was minimal for this parameter. In different measures of paclitaxel exposure, AUC was most predictive of toxicity, with higher AUC associated with granulocytopenia [probability of 1% at AUC=1 to 22% at AUC=4 microg l-1 h-1 for performance status (PS)=0]. PS was more strongly associated with survival than disease stage and higher paclitaxel AUC was associated with worse survival irrespective of PS and stage.

CONCLUSIONS

Paclitaxel AUC is an independent predictor of granulocytopenia and survival in patients with advanced stage or recurrent endometrial cancer. Future studies are needed to validate the latter finding. This study confirms the appropriateness of evaluating pharmacokinetics and pharmacodynamics in multicentre oncology trials.

A genetic algorithm-based, hybrid machine learning approach to model selection

We describe a general and robust method for identification of an optimal non-linear mixed effects model. This includes structural, inter-individual random effects, covariate effects and residual error models using machine learning. This method is based on combinatorial optimization using genetic algorithm.

Recommended reading in population pharmacokinetic pharmacodynamics

Developing the skills or expertise to create useful population pharmacokinetic-pharmacodynamic models can be a daunting task-the level of mathematical and statistical complexity is such that newcomers to the field are frequently overwhelmed. A good place to start in learning the field is to read articles in the literature. However, the number of articles dealing with population pharmacokinetic pharmacodynamics is exponentially increasing on a yearly basis, so choosing which articles to read can be difficult. The purpose of this review is to provide a recommended reading list for newcomers to the field. The list was chosen based on perceived impact of the article in the field, the quality of the article, or to highlight some important detail contained within the article. After reading the articles in the list, it is believed that the reader will have a broad overview of the field and have a sound foundation for more-detailed reading of the literature.

Population pharmacokinetics of clofarabine, a second-generation nucleoside analog, in pediatric patients with acute leukemia

The population pharmacokinetics of plasma clofarabine and intracellular clofarabine triphosphate were characterized in pediatric patients with acute leukemias. Traditional model-building techniques with NONMEM were used. Covariates were entered into the base model using a forward selection significance level of .05 and a backwards deletion criterion of .005. Model performance, stability, and influence analysis were assessed using the nonparametric bootstrap and n-1 jackknife. Simulations were used to understand the relationship between important covariates and exposure. A 2-compartment model with weight (scaled to a 40-kg reference patient) modeled as a power function on all pharmacokinetic parameters (0.75 on clearance-related terms and 1.0 on volume-related terms) was fit to plasma clofarabine concentrations (n = 32). White blood cell (WBC) count, modeled as a power function (scaled to a WBC count of 10 x 10(3)/microL), was a significant predictor of central volume with power term 0.128 +/- 0.0314. A reference patient had a systemic clearance of 32.8 L/h (27% between-subject variability [BSV]), a central volume of 115 L (56% BSV), an intercompartmental clearance of 20.5 L/h (27% BSV), and a peripheral volume of 94.5 L (39% BSV). Intracellular clofarabine triphosphate concentrations were modeled using a random intercept model without any covariates. The average predicted concentration was 11.6 +/- 2.62 microM (80% BSV), and although clofarabine triphosphate half-life could not be definitively estimated, its value was taken to be longer than 24 hours. The results confirm that clofarabine should continue being dosed on a per-squaremeter or per-body-weight basis.

What is the best size descriptor to use for pharmacokinetic studies in the obese?

The prevalence of obesity in the western world is dramatically rising, with many of these individuals requiring therapeutic intervention for a variety of disease states. Despite the growing prevalence of obesity there is a paucity of information describing how doses should be adjusted, or indeed whether they need to be adjusted, in the clinical setting. This review is aimed at identifying which descriptors of body size provide the most information about the relationship between dose and concentration in the obese. The size descriptors, weight, lean body weight, ideal body weight, body surface area, body mass index, fat-free mass, percent ideal body weight, adjusted body weight and predicted normal body weight were considered as potential size descriptors. We conducted an extensive review of the literature to identify studies that have assessed the quantitative relationship between the parameters clearance (CL) and volume of distribution (V) and these descriptors of body size. Surprisingly few studies have addressed the relationship between obesity and CL or V in a quantitative manner. Despite the lack of studies there were consistent findings: (i) most studies found total body weight to be the best descriptor of V. A further analysis of the studies that have addressed V found that total body weight or another descriptor that incorporated fat mass was the preferred descriptor for drugs that have high lipophilicity; (ii) in contrast, CL was best described by lean body mass and no apparent relationship between lipophilicity or clearance mechanism and preference for body size descriptor was found. In conclusion, no single descriptor described the influence of body size on both CL and V equally well. For drugs that are dosed chronically, and therefore CL is of primary concern, dosing for obese patients should not be based on their total weight. If a weight-based dose individualization is required then we would suggest that chronic drug dosing in the obese subject should be based on lean body weight, at least until a more robust size descriptor becomes available.

Population pharmacokinetic model for daunorubicin and daunorubicinol coadministered with zosuquidar.3HCl (LY335979)

PURPOSE

The impact of zosuquidar.3HCl, an inhibitor of P-glycoprotein, on the pharmacokinetics of daunorubicin and daunorubicinol was examined in a phase I trial using a population approach. Pharmacokinetic and pharmacodynamic properties of zosuquidar.3HCl were also determined.

METHODS

The pharmacokinetics of daunorubicin and daunorubicinol were studied following daunorubicin administration on day 1 (50 mg/m2 i.v. infusion over 10 min) alone and on day 3 concomitantly with zosuquidar.3HCl (i.v. 200 or 300 mg/m2 over 6 h or 400 mg over 3 h). Of a total of 18 patients entered, 16 with acute leukemia completed the study.

RESULTS

A three-compartment pharmacokinetic model adequately described daunorubicin concentration-time profiles. Five- and four-compartment models adequately described the daunorubicin-daunorubicinol pharmacokinetics in the absence and presence of zosuquidar.3HCl, respectively. The impact of zosuquidar.3HCl on coadministered daunorubicin was minimal, with a 10% reduction in daunorubicin clearance. The model predicted a 50% decrease in daunorubicinol apparent clearance in the presence of zosuquidar.3HCl. A direct concentration-effect relationship between zosuquidar.3HCl concentrations and inhibition of rhodamine 123 (Rh123) efflux in CD56 lymphocytes was defined by a sigmoid E(max) model. The IC(50) was 31.7 microg/l. The zosuquidar.3HCl dosing regimen led to concentrations in excess of the IC(90) (169.6 microg/l) and provided maximal P-glycoprotein inhibition during the distribution phases of daunorubicin.

CONCLUSIONS

The decrease in daunorubicin and daunorubicinol clearance in the presence of zosuquidar.3HCl likely reflects inhibition of P-glycoprotein in the bile canaliculi impeding their biliary excretion. The results need to be interpreted carefully due to the sequential nature of daunorubicin administration and analysis.

A population pharmacokinetic model for paclitaxel in the presence of a novel P-gp modulator, Zosuquidar Trihydrochloride (LY335979)

AIMS

To develop a population pharmacokinetic model for paclitaxel in the presence of a MDR modulator, zosuquidar 3HCl.

METHODS

The population approach was used (implemented with NONMEM) to analyse paclitaxel pharmacokinetic data from 43 patients who received a 3-h intravenous infusion of paclitaxel (175 mg x m(-2) or 225 mg x m(-2)) alone in cycle 2 or concomitantly with the oral administration of zosuquidar 3HCl in cycle 1.

RESULTS

The structural pharmacokinetic model for paclitaxel, accounting for the Cremophor ELTM impact, was a three-compartment model with a nonlinear model for paclitaxel plasma clearance (CL), involving a linear decrease in this parameter during the infusion and a sigmoidal increase with time after the infusion. The final model described the effect of Zosuquidar 3HCl on paclitaxel CL by a categorical relationship. A 25% decrease in paclitaxel CL was observed, corresponding to an 1.3-fold increase in paclitaxel AUC (from 14829 microg x l(-1) x h to 19115 microg x l(-1) x h following paclitaxel 175 mg x m(-2)) when zosuquidar Cmax was greater than 350 microg x l(-1). This cut-off concentration closely corresponded to the IC50 of a sigmoidal Emax relationship (328 microg x l(-1)). A standard dose of 175 mg x m(-2) of paclitaxel could be safely combined with doses of zosuquidar 3HCl resulting in plasma concentrations known, from previous studies, to result in maximal P-gp inhibition.

CONCLUSIONS

This analysis provides a model which accurately characterized the increase in paclitaxel exposure, which is most likely to be due to P-gp inhibition in the bile canaliculi, in the presence of zosuquidar 3HCl (Cmax > 350 microg x l(-1)) and is predictive of paclitaxel pharmacokinetics following a 3 h infusion. Hence the model could be useful in guiding therapy for paclitaxel alone and also for paclitaxel administered concomitantly with a P-gp inhibitor, and in designing further clinical trials.

Use of prior information to stabilize a population data analysis

When modeling new data with a complex population pharmacokinetic/pharmacodynamic model, there may not be sufficient information to obtain estimates of all parameters. In this case information from previous studies can also be used to help stabilize estimation. Using simulated data, we explored three different ways to do this. (i) Some parameter values were fixed to estimates obtained from earlier data. (ii) The earlier data were combined with the current data. (iii) The objective function based on the current data was augmented by a penalty function expressing summary information obtained from the earlier data. This last method is similar to the use of a Bayesian prior. It may be particularly useful when either the combined data set of method (ii) is very large and leads to large computation times or when the early data are not readily available. With this method, two different types of penalty functions were used. With our examples, the three methods all resulted in stabilized estimation. Methods (ii) and (iii) gave similar results for parameter and standard error estimation, especially with respect to fixed effects parameters. For hypothesis testing, results obtained with method (i) are very problematic. There are also problems with the results obtained with method (iii), but they are much less severe, and when the design for the earlier data is known, they can be corrected by using a computer-intensive simulation test procedure.

A pharmacokinetic model for alpha interferon administered subcutaneously

AIMS

To model the pharmacokinetic profiles of alpha interferon (alphaIFN) after a single subcutaneous (s.c.) injection of 3 million units of alpha 2b interferon, to correlate the pharmacokinetic parameters with patient demographic covariates, and to develop a limiting sampling strategy for determining the alphaIFN plasma area under the curve of concentration vs time (AUC).

METHODS

The plasma alphaIFN pharmacokinetics were determined in 27 patients with chronic hepatitis C virus infection after the first s.c. injection of the drug. Ten patients had normal renal function and 17 were chronic haemodialysis patients. Plasma samples were assayed by an Elisa method. Concentration-time data was analysed by a population approach using NONMEM.

RESULTS

The pharmacokinetic model which better described the concentration vs time data was a one-compartment model with two processes of absorption: a zero-order followed by a first-order process. The mean clearance of dialysis patients represented 37% (with 95% confidence interval: 30% -44%) of the mean value of the patients with normal renal function. The volume of distribution was significantly correlated to the body surface area. Bayesian analysis using NONMEM allowed determination of the individual plasma AUC from three samples within the 24 h period post s.c. injection.

CONCLUSIONS

The present pharmacokinetic model will allow one to obtain individual parameters such as, the area under the curve of concentration vs time from a limited-sampling strategy, and to perform pharmacokinetic-pharmacodynamic analysis of combined alphaIFN plasma concentrations and viraemic data.

Phamacokinetic-pharmacodynamic modelling of behavioural responses

Drug concentrations at the site of action in studies on behavioural pharmacology, are seldom constant. Therefore, observed changes in behaviour can be due to the natural time course of behavioural processes, but equally to changes in drug concentration, and it is therefore crucial to separate the former from the latter. One solution is keeping drug concentrations constant. However, one can also exploit the variation in drug concentration caused by absorption, distribution and elimination of a drug. This is done by simultaneous measurement of drug effect and concentration, while the drug enters and leaves a biologically relevant compartment, such as blood or cerebrospinal fluid. The concept of determining concentration-effect curves in individual animals, by monitoring in parallel drug effect and changes in concentration in one single experiment, has not yet found wide application in behavioural studies. The fact that behavioural processes, like any other physiological process, change over time, may have contributed to the scarcity of pharmacokinetic-pharmacodynamic (PK/PD) studies in behavioural pharmacology. However, there are now mathematical techniques that allow PK/PD modelling even if the effect parameter changes over time or cannot be properly assessed in every instance. Here we use PK/PD modelling to characterize fear-induced ultrasonic vocalizations and the anxiolytic effect of buspirone. This approach reduces the number of animals required to assess concentration-effect relationships. More importantly, it allows the identification of differences in individual drug response over a wide range of concentrations. Consequently, we suggest that PK/PD modelling can be used as a tool to study drug-induced changes in behavioural response. An introduction in PK/PD modelling is presented.

Expanding clinical applications of population pharmacodynamic modelling

Population pharmacokinetics or pharmacodynamics is the study of the variability in drug concentration or pharmacological effect between individuals when standard dosage regimens are administered. We provide an overview of pharmacokinetic models, pharmacodynamic models, population models and residual error models. We outline how population modelling approaches seek to explain interpatient variability with covariate analysis, and, in some approaches, to characterize the unexplained interindividual variability. The interpretation of the results of population modelling approaches is facilitated by shifting the emphasis from the perspective of the modeller to the perspective of the clinician. Both the explained and unexplained interpatient variability should be presented in terms of their impact on the dose-response relationship. Clinically relevant questions relating to the explained and unexplained variability in the population can be posed to the model, and confidence intervals can be obtained for the fraction of the population that is estimated to fall within a specific therapeutic range given a certain dosing regimen. Such forecasting can be used to develop optimal initial dosing guidelines. The development of population models (with random effects) permits the application of Bayes's formula to obtain improved estimates of an individual's pharmacokinetic and pharmacodynamic parameters in the light of observed responses. An important challenge to clinical pharmacology is to identify the drugs that might benefit from such adaptive-control-with-feedback dosing strategies. Drugs used for life threatening diseases with a proven pharmacokinetic-pharmacodynamic relationship, a small therapeutic range, large interindividual variability, small interoccasion variability and severe adverse effects are likely to be good candidates. Rapidly evolving changes in health care economics and consumer expectations make it unlikely that traditional drug development approaches will succeed in the future. A shift away from the narrow focus on rejecting the null hypothesis towards a broader focus on seeking to understand the factors that influence the dose-response relationship--together with the development of the next generation of software based on population models--should permit a more efficient and rational drug development programme.

Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients

Deriving a population pharmacokinetic model from real data is always associated with numerous assumptions. Violations of these assumptions, especially if undetected, may lead to inappropriate conclusions being made from the analysis. Routinely, only a few of the assumptions are explicitly stated and justified in the reporting of a population model. Here, we attempt to be exhaustive in the presentation of the assumptions made in the course of an analysis of moxonidine pharmacokinetics. The different ways that assumptions were justified, through experience, graphical examination, or additional modeling, are outlined. Models for relaxing assumptions regarding the covariate and statistical submodels, not previously reported in the area of population pharmacokinetic modeling, are also described.

Bayesian population pharmacokinetic and pharmacodynamic analyses using mixture models

Population studies of the pharmacokinetics or pharmacodynamics of drugs help us, learn about the variability in drug disposition and effects, information that can be used to treat future patients at safe and effective doses. We present a new approach to population modeling based on a weighted mixture of normal distributions having random weights and means. This method allows estimation of underlying continuous population distributions without prespecifying the parametric form or shape of these probability distributions. Additionally, this method can carry out nonparametric regression of pharmacokinetic or dynamic parameters on patient covariates while estimating the underlying distributions. Two examples illustrate the method and its flexibility.

Nonlinear mixed effects modeling of single dose and multiple dose data for an immediate release (IR) and a controlled release (CR) dosage form of alprazolam

PURPOSE

NONMEM was applied to single dose and multiple dose bioavailability data for an immediate release (IR) and a controlled release (CR) dosage form of alprazolam to acquire additional information from the data which are not easily obtainable by traditional means.

METHODS

The objective function value (OBJ) and diagnostic plots were used as measures of goodness of fit of the model to the data. A change in the OBJ value of 7.9 was necessary to show statistical significance (p < 0.005) between two models when the two models differed by 1 parameter.

RESULTS

A two-compartment linear model with first-order absorption and elimination best describes the data. Including a lag time, two different rates of absorption (KAIR and KACR), and bioavailability for the CR relative to the IR dosage form significantly improved the fit of the model to the data. Cigarette smoking was associated with a 100% increase in clearance of alprazolam as compared to non-smokers. The higher residual variability observed in this study, where interoccasion variability (IOV) was not initially modeled, could be explained to a large extent by the presence of significant interoccasion variability (IOV).

CONCLUSIONS

Since alprazolam has been suggested to be mainly metabolized by the CYP3A4 isozyme in humans, it appears that tobacco could be an inducer of CYP3A4 and/or alprazolam may be metabolized by other isozyme(s) (specifically, CYP1A1/1A2) that are induced by cigarette smoke. The population pharmacokinetic model approach combined with exploratory graphical data analysis is capable of identifying important covariates from well-controlled "data rich" Phase I studies early in drug development.