Comparison of some practical sampling strategies for population pharmacokinetic studies

Predictors of valproic acid steady-state serum levels in adult and pediatric psychiatric inpatients: a comparative analysis

RATIONALE

Valproic acid (VPA) is commonly used as a second-line mood stabilizer or augmentative agent in severe mental illnesses. However, population pharmacokinetic studies specific to psychiatric populations are limited, and clinical predictors for the precision application of VPA remain undefined.

OBJECTIVES

To identify steady-state serum VPA level predictors in pediatric/adolescent and adult psychiatric inpatients.

METHODS

We analyzed data from 634 patients and 1,068 steady-state therapeutic drug monitoring (TDM) data points recorded from 2015 to 2021. Steady-state VPA levels were obtained after tapering during each hospitalization episode. Electronic patient records were screened for routine clinical parameters and co-medication. Generalized additive mixed models were employed to identify independent predictors.

RESULTS

Most TDM episodes involved patients with psychotic disorders, including schizophrenia (29.2%) and schizoaffective disorder (17.3%). Polypharmacy was common, with the most frequent combinations being VPA + quetiapine and VPA + promethazine. Age was significantly associated with VPA levels, with pediatric/adolescent patients (< 18 years) demonstrating higher dose-adjusted serum levels of VPA (β = 7.6±2.34, p < 0.001) after accounting for BMI. Women tended to have higher adjusted VPA serum levels than men (β = 5.08±1.62, p < 0.001). The formulation of VPA (Immediate-release vs. extended-release) showed no association with VPA levels. Co-administration of diazepam exhibited a dose-dependent decrease in VPA levels (F = 15.7, p < 0.001), suggesting a potential pharmacokinetic interaction.

CONCLUSIONS

This study highlights the utility of population-specific pharmacokinetic data for VPA in psychiatric populations. Age, gender, and co-administration of diazepam were identified as predictors of VPA levels. Further research is warranted to establish additional predictors and optimize the precision application of VPA in psychiatric patients.

Robust and Adaptive Two-stage Designs in Nonlinear Mixed Effect Models

To get informative studies for nonlinear mixed effect models (NLMEM), design optimization can be performed based on Fisher Information Matrix (FIM) using the D-criterion. Its computation requires knowledge about models and parameters, which are often prior guesses. Thus, adaptive designs composed of several stages may be used. Robust approach can also be used to account for various candidate models. In the estimation step of a given stage, model selection (MS) or model averaging (MA) can be performed. In this work we propose a new two-stage adaptive design strategy, based on the robust expected FIM and MA over several candidate models. The methodology is applied to a clinical trial simulation in ophthalmology to optimize doses and time measurements. A set of dose-response candidate models is defined, and one-stage designs are compared to two-stage 50/50 designs (i.e., each stage performed with half of the available subjects), using either local optimal design or robust design, and performing analysis with one model, MS or MA. Performing a two-stage design with MS at the interim analysis can correct the choice of a wrong model for designing the first stage. Overall, starting from a robust design (1- or 2-stage) is valuable and leads to reasonable bias and precision. The proposed robust adaptive design strategy is a new tool to design longitudinal studies that could be used in different therapeutic areas.

Population Pharmacokinetics of Danofloxacin in Yellow River Carp (Cyprinus carpio haematopterus) After One Single Oral Dose

This study aimed to determine the population pharmacokinetics of danofloxacin in healthy Yellow River carp (Cyprinus carpio Haematopterus) after single oral administration at 10 mg/kg body weight (BW). A sparse sampling was applied in this study and plasma samples were randomly collected from the tail veins of six carp at 0.25, 0.5, 1, 2, 4, 6, 8, 12, 16, 24, 36, 48, 72, 96, 120 and 144 h after administration. A maximum of four plasma samples was collected from each carp. Then the concentrations of danofloxacin in plasma samples were determined through an HPLC method. Danofloxacin could be quantified in plasma up to 144 h after administration. The corresponding population pharmacokinetic modeling was developed according to the non-linear mixed effect method, including covariate and covariance models to explain some variations from unknown sources and improve the prediction ability. On the premise of sparse sampling, the typical values of the population (fixed effect) and inter-individual variation (random effect) were described by the current population pharmacokinetic model. The estimated typical values and coefficient of variation between individuals (CV%) of absorption rate constant (tvKa), apparent distribution volume (tvV) and clearance (tvCL) were 2.48 h⁻¹ and 0.203%, 47.8 L/kg and 8.40%, 0.694 L/h/kg and 4.35%, respectively. The current danofloxacin oral dosing (10 mg/kg BW) can provide suitable plasma concentrations to inhibit those pathogens with MIC values below 0.016 μg/ml based on the calculated PK/PD indices of AUC/MIC or C_max/MIC. Further studies are still needed to determine the in vitro and in vivo antibacterial efficacy of danofloxacin against pathogens isolated from Yellow River carp and finally draw a reasonable dosing regimen.

Assessing the predictive performance of population pharmacokinetic models for intravenous polymyxin B in critically ill patients

Polymyxin B (PMB) has reemerged as a last‐line therapy for infections caused by multidrug‐resistant gram‐negative pathogens, but dosing is challenging because of its narrow therapeutic window and pharmacokinetic (PK) variability. Population PK (POPPK) models based on suitably powered clinical studies with appropriate sampling strategies that take variability into consideration can inform PMB dosing to maximize efficacy and minimize toxicity and resistance. Here we reviewed published PMB POPPK models and evaluated them using an external validation data set (EVD) of patients who are critically ill and enrolled in an ongoing clinical study to assess their utility. Seven published POPPK models were employed using the reported model equations, parameter values, covariate relationships, interpatient variability, parameter covariance, and unexplained residual variability in NONMEM (Version 7.4.3). The predictive ability of the models was assessed using prediction‐based and simulation‐based diagnostics. Patient characteristics and treatment information were comparable across studies and with the EVD (n = 40), but the sampling strategy was a main source of PK variability across studies. All models visually and statistically underpredicted EVD plasma concentrations, but the two‐compartment models more accurately described the external data set. As current POPPK models were inadequately predictive of the EVD, creation of a new POPPK model based on an appropriately powered clinical study with an informed PK sampling strategy would be expected to improve characterization of PMB PK and identify covariates to explain interpatient variability. Such a model would support model‐informed precision dosing frameworks, which are urgently needed to improve PMB treatment efficacy, limit resistance, and reduce toxicity in patients who are critically ill.

A pharmacokinetic simulation study to assess the performance of a sparse blood sampling approach to quantify early drug exposure

Estimating early exposure of drugs used for the treatment of emergent conditions is challenging because blood sampling to measure concentrations is difficult. The objective of this work was to evaluate predictive performance of two early concentrations and prior pharmacokinetic (PK) information for estimating early exposure. The performance of a modeling approach was compared with a noncompartmental analysis (NCA). A simulation study was performed using literature‐based models for phenytoin (PHT), levetiracetam (LEV), and valproic acid (VPA). These models were used to simulate rich concentration‐time profiles from 0 to 2 h. Profiles without residual unexplained variability (RUV) were used to obtain the true partial area under the curve (pAUC) until 2 h after the start of drug infusion. From the profiles with the RUV, two concentrations per patient were randomly selected. These concentrations were analyzed under a population model to obtain individual population PK (PopPK) pAUCs. The NCA pAUCs were calculated using a linear trapezoidal rule. Percent prediction errors (PPEs) for the PopPK pAUCs and NCA pAUCs were calculated. A PPE within ±20% of the true value was considered a success and the number of successes was obtained for 100 simulated datasets. For PHT, LEV, and VPA, respectively, the median value of the success statistics obtained using the PopPK approach of 81%, 92%, and 88% were significantly higher than the 72%, 80%, and 67% using the NCA approach (p < 0.05; Mann–Whitney U test). This study provides a means by which early exposure can be estimated with good precision from two concentrations and a PopPK approach. It can be applied to other settings in which early exposures are of interest.

Population Pharmacokinetics and Dose Optimization of Ceftazidime and Imipenem in Patients with Acute Exacerbations of Chronic Obstructive Pulmonary Disease

Background: Ceftazidime and imipenem have been increasingly used to treat Acute Exacerbations of Chronic Obstructive Pulmonary Disease (AECOPD) due to their extended-spectrum covering Pseudomonas aeruginosa. This study aims to describe the population pharmacokinetic (PK) and pharmacodynamic (PD) target attainment for ceftazidime and imipenem in patients with AECOPD. Methods: We conducted a prospective PK study at Bach Mai Hospital (Viet Nam). A total of 50 (ceftazidime) and 44 (imipenem) patients with AECOPD were enrolled. Population PK analysis was performed using Monolix 2019R1 and Monte Carlo simulations were conducted to determine the optimal dose regimen with respect to the attainment of 60% and 40% fT>MIC for ceftazidime and imipenem, respectively. A dosing algorithm was developed to identify optimal treatment doses. Results: Ceftazidime and imipenem PK was best described by a one-compartment population model with a volume of distribution and clearance of 23.7 L and 8.74 L/h for ceftazidime and 15.1 L and 7.88 L/h for imipenem, respectively. Cockcroft–Gault creatinine clearance represented a significant covariate affecting the clearance of both drugs. Increased doses with prolonged infusion were found to cover pathogens with reduced susceptibility. Conclusions: This study describes a novel and versatile three-level dosing algorithm based on patients’ renal function and characteristic of the infective pathogen to explore ceftazidime and imipenem optimal regimen for AECOPD.

Mathematical modeling and simulation in animal health. Part III: Using nonlinear mixed-effects to characterize and quantify variability in drug pharmacokinetics

A common feature of human and veterinary pharmacokinetics is the importance of identifying and quantifying the key determinants of between-patient variability in drug disposition and effects. Some of these attributes are already well known to the field of human pharmacology such as bodyweight, age, or sex, while others are more specific to veterinary medicine, such as species, breed, and social behavior. Identification of these attributes has the potential to allow a better and more tailored use of therapeutic drugs both in companion and food-producing animals. Nonlinear mixed effects (NLME) have been purposely designed to characterize the sources of variability in drug disposition and response. The NLME approach can be used to explore the impact of population-associated variables on the relationship between drug administration, systemic exposure, and the levels of drug residues in tissues. The latter, while different from the method used by the US Food and Drug Administration for setting official withdrawal times (WT) can also be beneficial for estimating WT of approved animal drug products when used in an extralabel manner. Finally, NLME can also prove useful to optimize dosing schedules, or to analyze sparse data collected in situations where intensive blood collection is technically challenging, as in small animal species presenting limited blood volume such as poultry and fish.

Reporting Guidelines for Clinical Pharmacokinetic Studies: The ClinPK Statement

BACKGROUND AND OBJECTIVE

Transparent reporting of all research is essential for assessing the validity of any study. Reporting guidelines are available and endorsed for many types of research but are lacking for clinical pharmacokinetic studies. Such tools promote the consistent reporting of a minimal set of information for end users, and facilitate knowledge translation of research. The objective of this study was to create a guideline to assist in the transparent and complete reporting of clinical pharmacokinetic studies.

METHODS

Preliminary content to be considered was identified from a systematic search of the literature and regulatory documents. Stakeholders were identified to participate in a modified Delphi exercise and a virtual meeting to generate consensus for items considered essential in the reporting of clinical pharmacokinetic studies. The proposed checklist was pilot tested on 100 recently published clinical pharmacokinetic studies. Overall and itemized compliance with the proposed guidance was determined for each study.

RESULTS

Sixty-eight stakeholders from nine countries consented to participate. Four rounds of a modified Delphi survey and a series of small virtual meetings were required to generate consensus for a 24-item checklist considered to be essential to the reporting of clinical pharmacokinetic studies. When applied to the 100 most recently published clinical pharmacokinetic studies, 45 were determined to be compliant with at least 80 % of the checklist items. Explanatory text was prepared using examples of compliant reporting from these and other relevant studies.

CONCLUSIONS

The reader's ability to judge the validity of pharmacokinetic research can be greatly compromised by the incomplete reporting of study information. Using consensus methods, we have developed a tool to guide transparent and accurate reporting of clinical pharmacokinetic studies. Endorsement and implementation of these guidelines by researchers, clinicians and journals would promote more consistent reporting of these studies and allow for better assessment of utility for clinical applications.

Simulation-Based Evaluation of PK/PD Indices for Meropenem Across Patient Groups and Experimental Designs

PURPOSE

Antibiotic dose predictions based on PK/PD indices rely on that the index type and magnitude is insensitive to the pharmacokinetics (PK), the dosing regimen, and bacterial susceptibility. In this work we perform simulations to challenge these assumptions for meropenem and Pseudomonas aeruginosa.

METHODS

A published murine dose fractionation study was replicated in silico. The sensitivity of the PK/PD index towards experimental design, drug susceptibility, uncertainty in MIC and different PK profiles was evaluated.

RESULTS

The previous murine study data were well replicated with fT > MIC selected as the best predictor. However, for increased dosing frequencies fAUC/MIC was found to be more predictive and the magnitude of the index was sensitive to drug susceptibility. With human PK fT > MIC and fAUC/MIC had similar predictive capacities with preference for fT > MIC when short t1/2 and fAUC/MIC when long t1/2.

CONCLUSIONS

A longitudinal PKPD model based on in vitro data successfully predicted a previous in vivo study of meropenem. The type and magnitude of the PK/PD index were sensitive to the experimental design, the MIC and the PK. Therefore, it may be preferable to perform simulations for dose selection based on an integrated PK-PKPD model rather than using a fixed PK/PD index target.

Inter occasion variability in individual optimal design

Inter occasion variability (IOV) is of importance to consider in the development of a design where individual pharmacokinetic or pharmacodynamic parameters are of interest. IOV may adversely affect the precision of maximum a posteriori (MAP) estimated individual parameters, yet the influence of inclusion of IOV in optimal design for estimation of individual parameters has not been investigated. In this work two methods of including IOV in the maximum a posteriori Fisher information matrix (FIM_MAP) are evaluated: (i) MAP_occ—the IOV is included as a fixed effect deviation per occasion and individual, and (ii) POP_occ—the IOV is included as an occasion random effect. Sparse sampling schedules were designed for two test models and compared to a scenario where IOV is ignored, either by omitting known IOV (Omit) or by mimicking a situation where unknown IOV has inflated the IIV (Inflate). Accounting for IOV in the FIM_MAP markedly affected the designs compared to ignoring IOV and, as evaluated by stochastic simulation and estimation, resulted in superior precision in the individual parameters. In addition MAP_occ and POP_occ accurately predicted precision and shrinkage. For the investigated designs, the MAP_occ method was on average slightly superior to POP_occ and was less computationally intensive.

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 sparse sampling for estimating ganciclovir/valganciclovir AUC in solid organ transplant patients using NONMEN

BACKGROUND

Ganciclovir and valganciclovir (GCV/VGCV) are used for the treatment and prophylaxis of cytomegalovirus in solid organ transplant (SOT) patients. An area under the time-concentration curve of 40-50 μg × h/mL is related to efficacy. Therapeutic drug monitoring could prevent suboptimal drug exposure and adverse events, but obtaining full concentration profiles is not feasible. Sampling optimization by developing a reliable and clinically applicable limited sampling strategy (LSS) may simplify dose adjustment.

METHODS

An LSS was developed using an original pharmacokinetic (PK) data set of 40 full profiles from 20 adult SOT patients. The LSS was developed based on population and Bayesian prediction approaches. Population PK parameters from a previous model were used for simulation or as priors (NONMEM version 7.2). Median percentage of prediction error and median of absolute percentage prediction error were calculated for plasma clearance (CL) and central compartment distribution volume (V(2)). Bias and precisions were compared using 1-way analysis of variance (SPSSv19.0).

RESULTS

Sampling windows were designed according to the PK profile previously observed with the entire set of data. The 4 windows selected were distributed from 0.5 to 1.5 hours, 2 to 3 hours, 4 to 5 hours, and 6 to 8 hours. Predose and concentrations beyond 8 hours were not considered in any case because simulated negative concentrations occurred in both cases. Predicted exposure using 3 sampling times (0.5-1.5, 4-5, and 6-8 hours) showed the best predictive performance, by either the population or Bayesian approaches. Bias and imprecision for CL and V(2) were 0 and 0.60%, and -0.78% and 0.78%, respectively.

CONCLUSIONS

GCV/VCG area under the time-concentration curve in SOT patients could be predicted with acceptable accuracy for clinical management and dose individualization using LSS. The estimator of GCV/VGC, using 3 concentrations measured at 0.5-1.5, 4-5, and 6-8 hours after drug intake, could be used for dose adjustment.

Methods and software tools for design evaluation in population pharmacokinetics-pharmacodynamics studies

Population pharmacokinetic (PK)-pharmacodynamic (PKPD) models are increasingly used in drug development and in academic research; hence, designing efficient studies is an important task. Following the first theoretical work on optimal design for nonlinear mixed-effects models, this research theme has grown rapidly. There are now several different software tools that implement an evaluation of the Fisher information matrix for population PKPD. We compared and evaluated the following five software tools: PFIM, PkStaMp, PopDes, PopED and POPT. The comparisons were performed using two models, a simple-one compartment warfarin PK model and a more complex PKPD model for pegylated interferon, with data on both concentration and response of viral load of hepatitis C virus. The results of the software were compared in terms of the standard error (SE) values of the parameters predicted from the software and the empirical SE values obtained via replicated clinical trial simulation and estimation. For the warfarin PK model and the pegylated interferon PKPD model, all software gave similar results. Interestingly, it was seen, for all software, that the simpler approximation to the Fisher information matrix, using the block diagonal matrix, provided predicted SE values that were closer to the empirical SE values than when the more complicated approximation was used (the full matrix). For most PKPD models, using any of the available software tools will provide meaningful results, avoiding cumbersome simulation and allowing design optimization.

Population-Based Assessments of Clinical Drug-Drug Interactions: Qualitative Indices or Quantitative Measures?

Population-based assessments of drug-drug interactions have become more common since the introduction and acceptance of the population pharmacokinetic approach. Unlike traditional methods, population-based studies provide clinically relevant results that can be applied directly to a target patient population. Furthermore, population-based studies do not demand the traditional requirements of intensive pharmacokinetic sampling, rigorous inpatient stays, or stringent assessment schedules. As such, the population-based approach can effectively be used to confirm known drug-drug interactions and further characterize anticipated interactions. A prospectively designed analysis can also reveal drug-drug interactions that might otherwise have gone undetected with traditional methods. Ultimately, these results could help to alleviate clinicians' concerns about using widely marketed drugs in combination therapies and also reduce patients' risk of experiencing unacceptable side effects. This article intends to provide a balanced overview of the population-based approach and its merits, drawbacks, and potential utility in the assessment of drug-drug interactions during clinical drug development.

Considerations in Analyzing Single-Trough Concentrations Using Mixed-Effects Modeling

The purpose of this study was to assess the effect of trial design and data analysis choices on the bias and precision of pharmacokinetic (PK) parameter estimation. NONMEM was used to simulate and analyze plasma concentrations collected according to a dense (five samples) or sparse (single-trough samples) sampling scheme for a one-compartment open model with intravenous administration. The results indicated that the bias on estimates of CL with only single-trough data was 17% compared to less than 1% for only dense data. The estimates of CL were improved by fixing all other parameters and estimating only mean and variance of CL (-11% to 1.4%, depending on the estimation method). Adding dense data led to further improvements (-2.3% to 0.3%, depending on further improvements). In these cases, first-order conditional estimation (FOCE) methods resulted in better estimates of CL than first-order (FO) methods. These steps also improved the Bayesian estimates of CL. These studies support the following recommendations: (1) avoid collecting single-trough concentrations unless there is reasonable knowledge about the PK of the drug; (2) if collecting single-trough concentrations is inevitable, avoid estimating all parameters when modeling single-trough concentration data; (3) use prior information by modeling the single-trough concentration data along with dense data from other studies; and (4) use Bayes estimates if the PK model and its parameters are known with reasonable certainty.

Influence of body weight, ethnicity, oral contraceptives, and pregnancy on the pharmacokinetics of azithromycin in women of childbearing age

Women of childbearing age commonly receive azithromycin for the treatment of community-acquired infections, including during pregnancy. This study determined azithromycin pharmacokinetics in pregnant and nonpregnant women and identified covariates contributing to pharmacokinetic variability. Plasma samples were collected by using a sparse-sampling strategy from pregnant women at a gestational age of 12 to 40 weeks and from nonpregnant women of childbearing age receiving oral azithromycin for the treatment of an infection. Pharmacokinetic data from extensive sampling conducted on 12 healthy women were also included. Plasma samples were assayed for azithromycin by high-performance liquid chromatography. Population data were analyzed by nonlinear mixed-effects modeling. The population analysis included 53 pregnant and 25 nonpregnant women. A three-compartment model with first-order absorption and a lag time provided the best fit of the data. Lean body weight, pregnancy, ethnicity, and the coadministration of oral contraceptives were covariates identified as significantly influencing the oral clearance of azithromycin and, except for oral contraceptive use, intercompartmental clearance between the central and second peripheral compartments. No other covariate relationships were identified. Compared to nonpregnant women not receiving oral contraceptives, a 21% to 42% higher dose-adjusted azithromycin area under the plasma concentration-time curve (AUC) occurred in non-African American women who were pregnant or receiving oral contraceptives. Conversely, azithromycin AUCs were similar between pregnant African American women and nonpregnant women not receiving oral contraceptives. Although higher levels of maternal and fetal azithromycin exposure suggest that lower doses be administered to non-African American women during pregnancy, the consideration of azithromycin pharmacodynamics during pregnancy should guide any dose adjustments.

Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models

Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or changing between periods. We use the expected standard errors of treatment effect to compute the power for the Wald test of comparison or equivalence and the number of subjects needed for a given power. We perform various simulations mimicking crossover two-period trials to show the relevance of these developments. We then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3.2 of the r function PFIM.

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.

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.

Population pharmacodynamic parameter estimation from sparse sampling: effect of sigmoidicity on parameter estimates

The objective of this stimulation study was to evaluate effect of simoidicity of the concentration-effect (C-E) relationship on the efficiency of population parameter estimation from sparse sampling and is a continuation of previous work that addressed the effect of sample size and number of samples on parameters estimation from sparse sampling for drugs with C-E relationship characterized by high sigmoidicity (gamma > 5). The findings are based on observed C-E relationships for two drugs, octreotide and remifentanil, characterized by simple E (max) and sigmoid E (max) models (gamma = ~2.5), respectively. For each model, C-E profiles (100 replicates of 100 subjects each) were simulated for several sampling designs, with four or five samples/individual randomly obtained from within sampling windows based on EC(50)-normalized plasma drug concentrations, PD parameters based on observed population mean values, and inter-individual and residual variability of 30% and 25%, respectively. The C-E profiles were fitted using non-linear mixed effect modeling with the first-order conditional estimation method; variability parameters were described by an exponential error model. The results showed that, for the sigmoid E (max) model, designs with four or five samples reliably estimated the PD parameters (EC(50), E (max), E (0), and gamma), whereas the five-sample design, with two samples in the 2-3 E (max) region, provided in addition more reliable estimates of inter-individual variability; increasing the information content of the EC(50) region was not critical as long as this region was covered by a single sample in the 0.5-1.5 EC(50) window. For the simple E (max) model, because of the shallower profile, enriching the EC(50) region was more important. The impact of enrichment of appropriate regions for the two models can be explained based on the shape (sigmoidicity) of the concentration-effect relationships, with shallower C-E profiles requiring data enrichment in the EC(50) region and steeper curves less so; in both cases, the E (max) region needs to be adequately delineated, however. The results provide a general framework for population parameter estimation from sparse sampling in clinical trials when the underlying C-E profiles have different degrees of sigmoidicity.

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.

Conditional Weighted Residuals (CWRES): A Model Diagnostic for the FOCE Method

PURPOSE

Population model analyses have shifted from using the first order (FO) to the first-order with conditional estimation (FOCE) approximation to the true model. However, the weighted residuals (WRES), a common diagnostic tool used to test for model misspecification, are calculated using the FO approximation. Utilizing WRES with the FOCE method may lead to misguided model development/evaluation. We present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated based on the FOCE approximation.

MATERIALS AND METHODS

CWRES are calculated as the FOCE approximated difference between an individual's data and the model prediction of that data divided by the root of the covariance of the data given the model.

RESULTS

Using real and simulated data the CWRES distributions behave as theoretically expected under the correct model. In contrast, in certain circumstances, the WRES have distributions that greatly deviate from the expected, falsely indicating model misspecification. CWRES/WRES comparisons can also indicate if the FOCE estimation method will improve the results of an FO model fit to data.

CONCLUSIONS

Utilization of CWRES could improve model development and evaluation and give a more accurate picture of if and when a model is misspecified when using the FO or FOCE methods.

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.

Phase I and pharmacologic study of sequential topotecan-carboplatin-etoposide in patients with extensive stage small cell lung cancer

The inhibition of topoisomerase I by topotecan results in a compensatory increase in topoisomerase II associated with increased in vitro sensitivity of tumors to etoposide. Maximal synergy has been observed for the sequence of topotecan followed by etoposide. Carboplatin has clinical activity when combined with either of these two agents. These interactions were the pharmacologic rationale for topotecan p.o. days 1-5, carboplatin i.v. day 6, and etoposide p.o. days 6-10. Three successive dose levels were explored: (1) topotecan 2mg/day, carboplatin AUC 5, etoposide 150 mg/day; (2) topotecan 3mg/day, carboplatin AUC 5, etoposide 150 mg/day; and (3) topotecan 3mg/day, carboplatin AUC 5, etoposide 200mg/day. Filgrastim 5 microg/kg/day was injected s.c. days 11-18. Up to 6 cycles were administered every 21 days. Eligible patients had measurable or evaluable, extensive disease, small lung cell lung cancer, no prior chemotherapy, ECOG performance status 0-2, and adequate hematologic, renal, and hepatic function. Follow-up was weekly for CBC. Tumor response was assessed after 2 and 6 cycles. Dose limiting toxicity (DLT) was defined as any of the following in cycle 1: grade 3 or 4 non-hematologic toxicity other than nausea and vomiting, grade 4 neutropenia lasting more than 3 days, neutropenic fever or sepsis, grade 4 thrombocytopenia, or failure to recover neutrophils >or=1500/microl or platelets >or=100,000/microl by day 28. Ten patients were enrolled: median age 62 (range, 50-79); female/male 4/6; and performance status 0/1/2 in 2/7/1. Three patients each were treated on dose levels 1 and 2 without DLT. The first 2 patients entered on dose level 3 had no DLT. The third patient on dose level 3 developed grade 4 neutropenia lasting more than 3 days, neutropenic fever, and grade 4 thrombocytopenia on day 15 of cycle 1. The fourth patient on dose level 3 developed grade 4 thrombocytopenia on day 18 of cycle 1. One patient received only 1 cycle and was not evaluable for response. Seven patients completed 6 cycles: 1 had a complete response and 6 achieved a partial response. The third patient on dose level 3 received 2 cycles and had stable disease, but had to be removed from protocol treatment because of grade 4 neutropenia despite dose reduction in cycle 2. The fourth patient on dose level 3 achieved a partial response, but had to be removed from protocol therapy after cycle 5 because of recurrent grade 4 thrombocytopenia. In conclusion, neutropenia and thrombocytopenia were dose-limiting. The maximum tolerated dose (MTD) is topotecan 3mg/day p.o. days 1-5, carboplatin AUC 5i.v. day 6, and etoposide 150 mg/day p.o. days 6-10 with filgrastim.

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.

Population pharmacokinetics of amphotericin B lipid complex in neonates

The pharmacokinetics of amphotericin B lipid complex (ABLC) were investigated in neonates with invasive candidiasis enrolled in a phase II multicenter trial. Sparse blood (153 samples; 1 to 9 per patient, 1 to 254 h after the dose) and random urine and cerebrospinal fluid (CSF) samples of 28 neonates (median weight [WT], 1.06 kg; range, 0.48 to 4.9 kg; median gestational age, 27 weeks; range, 24 to 41 weeks) were analyzed. Patients received intravenous ABLC at 2.5 (n = 15) or 5 (n = 13) mg/kg of body weight once a day over 1 or 2 h, respectively, for a median of 21 days (range, 4 to 47 days). Concentrations of amphotericin B were quantified as total drug by high-performance liquid chromatography. Blood data for time after dose (TAD) of <24 h fitted best to a one-compartment model with an additive-error model for residual variability, WT0.75 (where 0.75 is an exponent) as a covariate of clearance (CL), and WT as a covariate of volume of distribution (V). Prior amphotericin B, postnatal age, and gestational age did not further improve the model. The final model equations were CL (liters/h) = 0.399 x WT(0.75) (interindividual variability, 35%) and V (liters) = 10.5 x WT (interindividual variability, 43%). Noncompartmental analysis of pooled data with a TAD of >24 h revealed a terminal half-life of 395 h. Mean concentrations in the urine after 1, 2, and 3 weeks ranged from 0.082 to 0.430 microg/ml, and those in CSF ranged from undetectable to 0.074 microg/ml. The disposition of ABLC in neonates was similar to that observed in other age groups: weight was the only factor that influenced clearance. Based on these results and previously published safety and efficacy data, we recommend a daily dosage between 2.5 and 5.0 mg/kg for treatment of invasive Candida infections in neonates.

Optimum blood sampling time windows for parameter estimation in population pharmacokinetic experiments

Clinical trials requiring the collection of pharmacokinetic information often specify blood samples to be taken at fixed times. This may be feasible when trial participants are in a controlled environment such as in early phase clinical trials, however it becomes problematic in trials where patients are in an out-patient clinic setting such as in late phase drug development. In such a situation it is common to take blood samples when it is convenient for all involved and may result in data that are uninformative. This paper proposes an approach to pharmacokinetic study design that allows greater flexibility as to when blood samples can be taken and still result in data that allows satisfactory parameter estimation. The sampling window approach proposed in this paper is based on determining time intervals around the D-optimum pharmacokinetic sampling times. These intervals are determined by allowing the sampling window design to result in a specified level of efficiency when compared to the fixed times D-optimum design. Several approaches are suggested for dealing with this design problem.

Optimal Blood Sampling Time Windows for Parameter Estimation Using a Population Approach: Design of a Phase II Clinical Trial

The objective of this paper is to determine optimal blood sampling time windows for the estimation of pharmacokinetic (PK) parameters by a population approach within the clinical constraints. A population PK model was developed to describe a reference phase II PK dataset. Using this model and the parameter estimates, D-optimal sampling times were determined by optimising the determinant of the population Fisher information matrix (PFIM) using PFIM_ _M 1.2 and the modified Fedorov exchange algorithm. Optimal sampling time windows were then determined by allowing the D-optimal windows design to result in a specified level of efficiency when compared to the fixed-times D-optimal design. The best results were obtained when K(a) and IIV on K(a) were fixed. Windows were determined using this approach assuming 90% level of efficiency and uniform sample distribution. Four optimal sampling time windows were determined as follow: at trough between 22 h and new drug administration; between 2 and 4 h after dose for all patients; and for 1/3 of the patients only 2 sampling time windows between 4 and 10 h after dose, equal to [4 h-5 h 05] and [9 h 10-10 h]. This work permitted the determination of an optimal design, with suitable sampling time windows which was then evaluated by simulations. The sampling time windows will be used to define the sampling schedule in a prospective phase II study.

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.

Pharmacodynamic parameter estimation: population size versus number of samples

The purpose of this study was to evaluate the effects of population size, number of samples per individual, and level of interindividual variability (IIV) on the accuracy and precision of pharmacodynamic (PD) parameter estimates. Response data were simulated from concentration input data for an inhibitory sigmoid drug efficacy (E(max)) model using Nonlinear Mixed Effect Modeling, version 5 (NONMEM). Seven designs were investigated using different concentration sampling windows ranging from 0 to 3 EC(50) (EC(50) is the drug concentration at 50% of the E(max)) units. The response data were used to estimate the PD and variability parameters in NONMEM. The accuracy and precision of parameter estimates after 100 replications were assessed using the mean and SD of percent prediction error, respectively. Four samples per individual were sufficient to provide accurate and precise estimate of almost all of the PD and variability parameters, with 100 individuals and IIV of 30%. Reduction of sample size resulted in imprecise estimates of the variability parameters; however, the PD parameter estimates were still precise. At 45% IIV, designs with 5 samples per individual behaved better than those designs with 4 samples per individual. For a moderately variable drug with a high Hill coefficient, sampling from the 0.1 to 1, 1 to 2, 2 to 2.5, and 2.5 to 3 EC(50) window is sufficient to estimate the parameters reliably in a PD study.

Population pharmacokinetics III: design, analysis, and application of population pharmacokinetic Studies

OBJECTIVE

To present a framework within which population pharmacokinetic (PPK) studies should be designed and analyzed and discuss the application of developed PPK models.

METHODS

Information on PPK was retrieved from a MEDLINE search (1979-December 2003) of the literature and a bibliographic evaluation of review articles and books. This information is used in conjunction with experience to explain the design and analysis of PPK studies. Also, examples are included to demonstrate the usefulness of PPK.

SYNTHESIS

A great deal of thought must be given to the design and analysis of PPK studies (ie, development of PPK models). Models are of 2 primary types--descriptive and predictive--and the process applied to these models is necessarily different. An approach that ensures model applicability is presented.

CONCLUSIONS

PPK models have great utility, and the applications are many. They are very different from single-subject pharmacokinetic models and therefore require different approaches to model estimation.

Optimization of individual and population designs using Splus

We address the problem of design optimization for individual and population pharmacokinetic studies. We develop Splus generic functions for pharmacokinetic design optimization: IFIM, a function for individual design optimization similar to the ADAPT II software, and PFIM_OPT, a function for population design optimization which is an extension of the Splus function PFIM for population design evaluation. Both evaluate and optimise designs using the Simplex algorithm. IFIM optimizes the sampling times in continuous intervals of times; PFIM_OPT optimizes either, for a given group structure of the population design, only the sampling times taken in some given continuous intervals or, both the sampling times and the group structure, performing then statistical optimization. A combined variance error model can be supplied with the possibility to include parameters of the error model as parameters to be estimated. The performance of the optimization with the Simplex algorithm is demonstrated with two pharmacokinetic examples: by comparison of the optimized designs to those of the ADAPT II software for IFIM, and to those obtained using a grid search or the Fedorov-Wynn algorithm for PFIM_OPT. The influence of the variance error model on design optimization was investigated. For a given total number of samples, different group structures of a population design are compared, showing their influence on the population design efficiency. The functions IFIM and PFIM_OPT offer new efficient solutions for the increasingly important task of optimization of individual or population pharmacokinetic designs.

POPED, a software for optimal experiment design in population kinetics

Population kinetic analysis is the methodology used to quantify inter-subject variability in kinetic studies. It entails the collection of (possibly sparse) data from dynamic experiments in a group of subjects and their quantitative interpretation by means of a mathematical model. This methodology is widely used in the pharmaceutical industry (where it is termed "pharmacokinetic population analysis") and recently it is becoming increasingly used in other areas of biomedical research. Unlike traditional kinetic studies, where the number of subjects can be quite small, population kinetic studies require large numbers of subjects. It is, therefore, of great interest to design these studies in the most efficient manner possible, to maximize the information content provided by the data. In this paper we propose an algorithm and a computer program, POPED, for the optimal design of a population kinetic experiment. In particular, the number of samples for each subject and the design of the individual sampling strategies, i.e. the number and location of the time points at which the output variable is sampled, will be considered. Among the various criteria proposed in the literature, D and ED optimality are the ones implemented in our software program, since they are the most widely used. A brief description of the techniques employed to perform design optimization is given, together with some details on their actual implementation. Some examples are then presented to show the program usage and the results provided.

Impact of model misspecification at design (and/or) estimation step in population pharmacokinetic studies

The aim of this work is to quantitatively assess the impact of structural model misspecifications on the estimates of mean and interindividual variability of clearance in the context of population approaches. This assessment is conducted from simulated datasets. Our results show that impact magnitude of model misspecification on the estimates depends on the step at which it occurs (design optimization and/or estimation), on the hyperparameter of interest, and on the estimation method. Bias and precision might be affected differently as well as powers of model discrimination tests. Some practical guidelines for reducing impact of model misspecifications are also suggested.

Statistical Evaluation of Clinical Trial Design for a Population Pharmacokinetic Study —A Case Study—

A population pharmacokinetic substudy design of a new chemical entity was evaluated based on the bias in parameter estimates and the power of detecting a specific subpopulation showing different clearance using a clinical trial simulation approach. The effect of analysis algorithms on type I error was also assessed. The design factors included the number of patients (n=100-300) and the number of sampling points per patient (n=2-6). Simulation data were generated from a model developed based on a Phase I study. The power was evaluated for a percentile of test statistics obtained by the simulation study. The clearance (CL) related parameters were estimated with sufficient accuracy in all study designs and all analysis algorithms: the first order (FO), first order conditional estimation (FOCE) and first order conditional estimation with interaction (FOCE-INTER) methods. With the FO and FOCE methods, the type I error rate increased as the frequency of sampling from each patient became higher, but such increase was hardly observed with the FOCE-INTER method. The power tended to depend on the size of the subpopulation. A large difference was found in the power of detecting a specific subpopulation showing a clearance decrease of 30% or 50%. Therefore, the most dominant factors controlling power would be the size of the subpopulation and the decreasing ratio of CL in the subpopulation. These findings obtained by the clinical trial simulation approach are useful for optimization of study design and determination of the limits of evaluation.

Further developments of the Fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics

We extend the development of the expression of the Fisher information matrix in nonlinear mixed effects models for designs evaluation. We consider the dependence of the marginal variance of the observations with the mean parameters and assume an heteroscedastic variance error model. Complex models with interoccasions variability and parameters quantifying the influence of covariates are introduced. Two methods using a Taylor expansion of the model around the expectation of the random effects or a simulated value, using then Monte Carlo integration, are proposed and compared. Relevance of the resulting standard errors is investigated in a simulation study with NONMEM.

Population pharmacokinetics of digoxin in Egyptian pediatric patients: impact of one data point utilization

A population pharmacokinetic (PK) study was designed to estimate the PK parameters of digoxin among a selected group of Egyptian pediatric patients (n = 30) with mean age +/- SD and body weight +/- SD of 8.88 +/- 3.01 years and 23.9 +/- 5.8 kg, respectively. All patients had heart failure and were maintained on digoxin given orally. Nonlinear mixed effect modeling software version 5 (NONMEM Project Group, San Francisco, CA) and one-compartment modeling were used for fitting the data. A one-trough steady-state plasma concentration level of digoxin was used in the analysis. The population mean estimates for clearance (CL/f) and volume of distribution (V/f), in which f represents oral bioavailability, were 8.61 L/h and 450 L, respectively. Because of the limited number of samples per patient, regression analysis could not detect a correlation between patient covariates and estimated PK parameters. The analysis did not converge to obtain good parameter estimates. At least two samples per patient should be used to improve the PK estimation and allow better analysis of the relation between the potential covariates and estimated PK parameters.

Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics

We address the problem of the choice and the evaluation of designs in population pharmacokinetic studies that use non-linear mixed-effects models. Criteria, based on the Fisher information matrix, have been developed to optimize designs and adapted to such models. We optimize designs under different constraints and evaluate them for a population pharmacokinetics study, within a new phase III trial of enoxaparin, a low molecular weight heparin. To do this, we approximate the expression of the Fisher information matrix for non-linear mixed-effects models including the residual error variance as a parameter to be estimated. We use the Fedorov-Wynn algorithm to minimize the inverse of the determinant of this matrix as required by the D-optimality criterion. Two optimal designs, as well as a design defined by pharmacologists, are evaluated by the simulation of 30 replicated data sets with NONMEM; all designs involve 220 patients with four measurements per patient. We also evaluate the relevance of the standard errors of estimation given from the Fisher information matrix by comparison with those given by NONMEM. The three designs provide more precise population parameter estimates; the optimal design gives the best precision and offers a simple clinical implementation. The expected standard errors given by the information matrix are close to those obtained by NONMEM on the simulation. Moreover, the proposed criterion of D-optimality appears to be a good measure to compare designs for population studies.