PopED: an extended, parallelized, nonlinear mixed effects models optimal design tool

Pharmacokinetic-pharmacodynamic modelling and simulation of methotrexate dosing in patients with rheumatoid arthritis

AIMS

To develop a non-linear mixed-effects population pharmacokinetic and pharmacodynamic (PK-PD) model describing the change in the concentration of methotrexate polyglutamates in erythrocytes (ery-MTX-PGn with "n" number of glutamate, representing PK component) and how this relates to modified 28-joint Disease Activity Score incorporating erythrocyte sedimentation rate (DAS-28-3) for rheumatoid arthritis (RA), representing PD component.

METHODS

An existing PK model was fitted to data from a study consisting of 117 RA patients. The estimation of population PK-PD parameters was performed using stochastic approximation expectation maximisation algorithm in Monolix 2021R2. The model was used to perform Monte Carlo simulations of a loading dose regimen (50mg subcutaneous methotrexate as loading doses, then 20mg weekly oral methotrexate) compared to a standard dosing regimen (10mg weekly oral methotrexate for 2 weeks, then 20mg weekly oral methotrexate).

RESULTS

Every 40 nmol/L increase in ery-MTX-PG3-5 total concentration correlated with 1-unit reduction in DAS-28-3. Significant covariate effects on the therapeutic response of methotrexate included the use of prednisolone in the first 4 weeks (positive use correlated with 25% reduction in DAS-28-3 when other variables were constant) and patient age (every 10-year increase in age correlated with 3.4% increase in DAS-28-3 when other variables were constant). 4 methotrexate loading doses led to a higher percentage of patients achieving a good/moderate response compared to the standard regimen (Week 4: 87.6% vs. 39.8%; Week 10: 64.7% vs. 57.0%).

CONCLUSIONS

A loading dose regimen was more likely to achieve higher ery-MTX-PG concentration and better therapeutic response after 4 weeks of methotrexate treatment.

Innovative research methodologies in the EU regulatory framework: an analysis of EMA qualification procedures from a pediatric perspective

Introduction

The European Medicines Agency (EMA) offers scientific advice to support the qualification procedure of novel methodologies, such as preclinical and in vitro models, biomarkers, and pharmacometric methods, thereby endorsing their acceptability in medicine research and development (R&D). This aspect is particularly relevant to overcome the scarcity of data and the lack of validated endpoints and biomarkers in research fields characterized by small samples, such as pediatrics.

Aim

This study aimed to analyze the potential pediatric interest in methodologies qualified as "novel methodologies for medicine development" by the EMA.

Methods

The positive qualification opinions of novel methodologies for medicine development published on the EMA website between 2008 and 2023 were identified. Multi-level analyses were conducted to investigate data with a hierarchical structure and the effects of cluster-level variables and cluster-level variances and to evaluate their potential pediatric interest, defined as the possibility of using the novel methodology in pediatric R&D and the availability of pediatric data. The duration of the procedure, the type of methodology, the specific disease or disease area addressed, the type of applicant, and the availability of pediatric data at the time of the opinion release were also investigated.

Results

Most of the 27 qualifications for novel methodologies issued by the EMA (70%) were potentially of interest to pediatric patients, but only six of them reported pediatric data. The overall duration of qualification procedures with pediatric interest was longer than that of procedures without any pediatric interest (median time: 7 months vs. 3.5 months, respectively; p = 0.082). In parallel, qualification procedures that included pediatric data lasted for a longer period (median time: 8 months vs. 6 months, respectively; p = 0.150). Nephrology and neurology represented the main disease areas (21% and 16%, respectively), while endpoints, biomarkers, and registries represented the main types of innovative methodologies (32%, 26%, and 16%, respectively).

Discussion

Our results underscore the importance of implementing innovative methodologies in regulatory-compliant pediatric research activities. Pediatric-dedicated research infrastructures providing regulatory support and strategic advice during research activities could be crucial to the design of ad hoc pediatric methodologies or to extend and validate them for pediatrics.

Model-Informed Precision Dosing to Reduce Vincristine-Induced Peripheral Neuropathy in Pediatric Patients: A Pharmacokinetic and Pharmacodynamic Modeling and Simulation Analysis

BACKGROUND

Vincristine-induced peripheral neuropathy (VIPN) is a common adverse effect of vincristine, a drug often used in pediatric oncology. Previous studies demonstrated large inter- and intrapatient variability in vincristine pharmacokinetics (PK). Model-informed precision dosing (MIPD) can be applied to calculate patient exposure and individualize dosing using therapeutic drug monitoring (TDM) measurements. This study set out to investigate the PK/pharmacodynamic (PKPD) relationship of VIPN and determine the utility of MIPD to support clinical decisions regarding dose selection and individualization.

METHODS

Data from 35 pediatric patients were utilized to quantify the relationship between vincristine dose, exposure and the development of VIPN. Measurements of vincristine exposure and VIPN (Common Terminology Criteria for Adverse Events [CTCAE]) were available at baseline and for each subsequent dosing occasions (1-5). A PK and PKPD analysis was performed to assess the inter- and intraindividual variability in vincristine exposure and VIPN over time. In silico trials were performed to portray the utility of vincristine MIPD in pediatric subpopulations with a certain age, weight and cytochrome P450 (CYP) 3A5 genotype distribution.

RESULTS

A two-compartmental model with linear PK provided a good description of the vincristine exposure data. Clearance and distribution parameters were related to bodyweight through allometric scaling. A proportional odds model with Markovian elements described the incidence of Grades 0, 1 and ≥ 2 VIPN overdosing occasions. Vincristine area under the curve (AUC) was the most significant exposure metric related to the development of VIPN, where an AUC of 50 ng⋅h/mL was estimated to be related to an average VIPN probability of 40% over five dosing occasions. The incidence of Grade ≥ 2 VIPN reduced from 62.1 to 53.9% for MIPD-based dosing compared with body surface area (BSA)-based dosing in patients. Dose decreases occurred in 81.4% of patients with MIPD (vs. 86.4% for standard dosing) and dose increments were performed in 33.4% of patients (no dose increments allowed for standard dosing).

CONCLUSIONS

The PK and PKPD analysis supports the use of MIPD to guide clinical dose decisions and reduce the incidence of VIPN. The current work can be used to support decisions with respect to dose selection and dose individualization in children receiving vincristine.

Dose rationale for gabapentin and tramadol in pediatric patients with chronic pain

Despite off-label use, the efficacy and safety of gabapentin and tramadol in pediatric patients (3 months to <18 years old) diagnosed with chronic pain has not been characterized. However, generating evidence based on randomized clinical trials in this population has been extremely challenging. The current investigation illustrates the use of clinical trial simulations (CTSs) as a tool for optimizing doses and protocol design for a prospective investigation in pediatric patients with chronic pain. Pharmacokinetic (PK) modeling and CTSs were used to describe the PKs of gabapentin and tramadol in the target population. In the absence of biomarkers of analgesia, systemic exposure (AUC, Css) was used to guide dose selection under the assumption of a comparable exposure-response (PKPD) relationship for either compound between adults and children. Two weight bands were identified for gabapentin, with doses titrated from 5 to 63 mg/kg. This yields gabapentin exposures (AUC0-8 ) of approximately 35 mg/L*h (1200 mg/day adult dose equivalent). For tramadol, median steady state concentrations between 200 and 300 ng/mL were achieved after doses of 2-5 mg/kg, but concentrations showed high interindividual variability. Simulation scenarios showed that titration steps are required to explore therapeutically relevant dose ranges taking into account the safety profile of both drugs. Gabapentin can be used t.i.d. at doses between 7-63 and 5-45 mg/kg for patients receiving gabapentin weighing <15 and ≥15 kg, respectively, whereas a t.i.d. regimen with doses between 1 and 5 mg/kg can be used for tramadol in patients who are not fast metabolisers.

The effect of cold storage and cooking on the viability of Clostridioides difficile spores in consumer foods

The increased detection of clinical cases of Clostridioides difficile coupled with the persistence of clostridial spores at various stages along the food chain suggest that this pathogen may be foodborne. This study examined C. difficile (ribotypes 078 and 126) spore viability in chicken breast, beef steak, spinach leaves and cottage cheese during refrigerated (4 °C) and frozen (-20 °C) storage with and without a subsequent sous vide mild cooking (60 °C, 1 h). Spore inactivation at 80 °C in phosphate buffer solution, beef and chicken were also investigated to provide D_80°C values and determine if PBS was a suitable model system for real food matrices. There was no decrease in spore concentration after chilled or frozen storage and/or sous vide cooking at 60 °C. Non-log-linear thermal inactivation was observed for both C. difficile ribotypes at 80 °C in phosphate buffer solution (PBS), beef and chicken. The predicted PBS D_80°C values of 5.72±[2.90, 8.55] min and 7.50±[6.61, 8.39] min for RT078 and RT126, respectively, were in agreement with the food matrices D_80°C values of 5.65 min (95% CI range from 4.29 to 8.89 min) for RT078 and 7.35 min (95% CI range from 6.81 to 7.01 min) for RT126. It was concluded that C. difficile spores survive chilled and frozen storage and mild cooking at 60 °C but may be inactivated at 80 °C. Moreover thermal inactivation in PBS was representative of that observed in real food matrices (beef and chicken).

Computational aspects of experimental designs in multiple-group mixed models

We extend the equivariance and invariance conditions for construction of optimal designs to multiple-group mixed models and, hence, derive the support of optimal designs for first- and second-order models on a symmetric square. Moreover, we provide a tool for computation of D- and L-efficient exact designs in multiple-group mixed models by adapting the algorithm of Harman et al. (Appl Stoch Models Bus Ind, 32:3–17, 2016). We show that this algorithm can be used both for size-constrained problems and also in settings that require multiple resource constraints on the design, such as cost constraints or marginal constraints.

NLoed: A Python Package for Nonlinear Optimal Experimental Design in Systems Biology

Modeling in systems and synthetic biology relies on accurate parameter estimates and predictions. Accurate model calibration relies, in turn, on data and on how well suited the available data are to a particular modeling task. Optimal experimental design (OED) techniques can be used to identify experiments and data collection procedures that will most efficiently contribute to a given modeling objective. However, implementation of OED is limited by currently available software tools that are not well suited for the diversity of nonlinear models and non-normal data commonly encountered in biological research. Moreover, existing OED tools do not make use of the state-of-the-art numerical tools, resulting in inefficient computation. Here, we present the NLoed software package and demonstrate its use with in vivo data from an optogenetic system in Escherichia coli. NLoed is an open-source Python library providing convenient access to OED methods, with particular emphasis on experimental design for systems biology research. NLoed supports a wide variety of nonlinear, multi-input/output, and dynamic models and facilitates modeling and design of experiments over a wide variety of data types. To support OED investigations, the NLoed package implements maximum likelihood fitting and diagnostic tools, providing a comprehensive modeling workflow. NLoed offers an accessible, modular, and flexible OED tool set suited to the wide variety of experimental scenarios encountered in systems biology research. We demonstrate NLoed's capabilities by applying it to experimental design for characterization of a bacterial optogenetic system.

Population Pharmacokinetics of Oral Migalastat in Adolescents and Adults With and Without Renal Impairment

Migalastat is approved for the treatment of Fabry disease (FD) with amenable variants. Objectives were to characterize effects of estimated glomerular filtration rate (eGFR) on oral clearance (CL), predict doses in mild to moderate renal impairment and in pediatric patients with FD, and to improve designs of FD studies. A 2-compartment model was fit to data from 260 subjects with/without FD and iteratively refined with evolving data. FD, eGFR, and weight affected CL, while weight and FD affected volume. Optimal sampling theory was used to choose pharmacokinetic sampling times for pediatric studies. Doses in patients with renal impairment and in pediatrics were determined by targeting exposure in adults receiving migalastat 123 mg every other day. A clinical study was conducted in 20 adolescent patients with FD ≥45 kg. eGFR had the largest effect on CL. Simulations showed that exposures in moderate renal impairment were within phase 2-3 exposures; patients aged 2-17 years require weight-based dosing; and predicted exposures in adolescent patients ≥45 kg receiving migalastat 123 mg every other day were similar to adults (data confirmed in a clinical study). Model-informed drug development optimized dosing and design of clinical studies and supported that no dose adjustments were needed in patients with mild to moderate renal impairment or in adolescent patients ≥45 kg.

Optimizing study design in LPS challenge studies for quantifying drug induced inhibition of TNFα response: Did we miss the prime time?

In this work we evaluate the study design of LPS challenge experiments used for quantification of drug induced inhibition of TNFα response and provide general guidelines of how to improve the study design. Analysis of model simulated data, using a recently published TNFα turnover model, as well as the optimal design tool PopED have been used to find the optimal values of three key study design variables - time delay between drug and LPS administration, LPS dose, and sampling time points - that in turn could make the resulting TNFα response data more informative. Our findings suggest that the current rule of thumb for choosing the time delay should be reconsidered, and that the placement of the measurements after maximal TNFα response are crucial for the quality of the experiment. Furthermore, a literature study summarizing a wide range of published LPS challenge studies is provided, giving a broader perspective of how LPS challenge studies are usually conducted both in a preclinical and clinical setting.

Estimation of Mycophenolic Acid Exposure in Heart Transplant Recipients by Population Pharmacokinetic and Limited Sampling Strategies

Purpose: The aim of this study is i) to establish a strategy to estimate the area under the curve of the dosing interval (AUC0-12h) of mycophenolic acid (MPA) in the heart transplant recipients and ii) to find the covariates that significantly affect the pharmacokinetics of MPA exposure. Methods: This single-center, prospective, open-label, observational study was conducted in 91 adult heart transplant recipients orally taking mycophenolate mofetil dispersible tablets. Samples collected intensively and sparsely were analyzed by the enzyme-multiplied immunoassay technique, and all the data were used in PPK modeling. Potential covariates were tested stepwise. The goodness-of-fit plots, the normalized prediction distribution error, and prediction-corrected visual predictive check were used for model evaluation. Optimal sampling times by ED-optimal strategy and multilinear regression (MLR) were analyzed based on the simulated data by the final PPK model. Moreover, using intensive data from 14 patients, the accuracy of AUC0-12h estimation was evaluated by Passing-Bablok regression analysis and Bland-Alman plots for both the PPK model and MLR equation. Results: A two-compartment model with first-order absorption and elimination with a lag time was chosen as the structure model. Co-medication of proton pump inhibitors (PPIs), estimated glomerular filtration rate (eGFR), and albumin (ALB) were found to significantly affect bioavailability (F), clearance of central compartment (CL/F), and the distribution volume of the central compartment (V2/F), respectively. Co-medication of PPIs decreased F by 27.6%. When eGFR decreased by 30 ml/min/1.73 m2, CL/F decreased by 23.7%. However, the impact of ALB on V2/F was limited to MPA exposure. The final model showed an adequate fitness of the data. The optimal sampling design was pre-dose and 1 and 4 h post-dose for pharmacokinetic estimation. The best-fit linear equation was finally established as follows: AUC0-12h = 3.539 × C0 + 0.288 × C0.5 + 1.349 × C1 + 6.773 × C4.5. Conclusion: A PPK model was established with three covariates in heart transplant patients. Co-medication of PPIs and eGFR had a remarkable impact on AUC0-12h of MPA. A linear equation was also concluded with four time points as an alternative way to estimate AUC0-12h for MPA.

Metaheuristics for pharmacometrics

Metaheuristics is a powerful optimization tool that is increasingly used across disciplines to tackle general purpose optimization problems. Nature-inspired metaheuristic algorithms is a subclass of metaheuristic algorithms and have been shown to be particularly flexible and useful in solving complicated optimization problems in computer science and engineering. A common practice with metaheuristics is to hybridize it with another suitably chosen algorithm for enhanced performance. This paper reviews metaheuristic algorithms and demonstrates some of its utility in tackling pharmacometric problems. Specifically, we provide three applications using one of its most celebrated members, particle swarm optimization (PSO), and show that PSO can effectively estimate parameters in complicated nonlinear mixed-effects models and to gain insights into statistical identifiability issues in a complex compartment model. In the third application, we demonstrate how to hybridize PSO with sparse grid, which is an often-used technique to evaluate high dimensional integrals, to search for D -efficient designs for estimating parameters in nonlinear mixed-effects models with a count outcome. We also show the proposed hybrid algorithm outperforms its competitors when sparse grid is replaced by its competitor, adaptive gaussian quadrature to approximate the integral, or when PSO is replaced by three notable nature-inspired metaheuristic algorithms.

Tutorial for $DESIGN in NONMEM: Clinical trial evaluation and optimization

This NONMEM tutorial shows how to evaluate and optimize clinical trial designs, using algorithms developed in design software, such as PopED and PFIM 4.0. Parameter precision and model parameter estimability is obtained by assessing the Fisher Information Matrix (FIM), providing expected model parameter uncertainty. Model parameter identifiability may be uncovered by very large standard errors or inability to invert an FIM. Because evaluation of FIM is more efficient than clinical trial simulation, more designs can be investigated, and the design of a clinical trial can be optimized. This tutorial provides simple and complex pharmacokinetic/pharmacodynamic examples on obtaining optimal sample times, doses, or best division of subjects among design groups. Robust design techniques accounting for likely variability among subjects are also shown. A design evaluator and optimizer within NONMEM allows any control stream first developed for trial design exploration to be subsequently used for estimation of parameters of simulated or clinical data, without transferring the model to another software. Conversely, a model developed in NONMEM could be used for design optimization. In addition, the $DESIGN feature can be used on any model file and dataset combination to retrospectively evaluate the model parameter uncertainty one would expect given that the model generated the data, particularly if outliers of the actual data prevent a reasonable assessment of the variance‐covariance. The NONMEM trial design feature is suitable for standard continuous data, whereas more elaborate trial designs or with noncontinuous data‐types can still be accomplished in optimal design dedicated software like PopED and PFIM.

Population pharmacokinetics and pharmacodynamics of investigational regimens' drugs in the TB-PRACTECAL clinical trial (the PRACTECAL-PKPD study): a prospective nested study protocol in a randomised controlled trial

INTRODUCTION

Drug-resistant tuberculosis (TB) remains a global health threat, with little over 50% of patients successfully treated. Novel regimens like the ones being studied in the TB-PRACTECAL trial are urgently needed. Understanding anti-TB drug exposures could explain the success or failure of these trial regimens. We aim to study the relationship between the patients' exposure to anti-TB drugs in TB-PRACTECAL investigational regimens and their treatment outcomes.

METHODS AND ANALYSIS

Adults with multidrug-resistant TB randomised to investigational regimens in TB-PRACTECAL will be recruited to a nested pharmacokinetic-pharmacodynamic (PKPD) study. Venous blood samples will be collected at 0, 2 and 23 hours postdose on day 1 and 0, 6.5 and 23 hours postdose during week 8 to quantify drug concentrations in plasma. Trough samples will be collected during week 12, 16, 20 and 24 visits. Opportunistic samples will be collected during weeks 32 and 72. Drug concentrations will be quantified using liquid chromatography-tandem mass spectrometry. Sputum samples will be collected at baseline, monthly to week 24 and then every 2 months to week 108 for MICs and bacillary load quantification. Full blood count, urea and electrolytes, liver function tests, lipase, ECGs and ophthalmology examinations will be conducted at least monthly during treatment.PK and PKPD models will be developed for each drug with nonlinear mixed effects methods. Optimal dosing will be investigated using Monte-Carlo simulations.

ETHICS AND DISSEMINATION

The study has been approved by the Médecins sans Frontières (MSF) Ethics Review Board, the LSHTM Ethics Committee, the Belarus RSPCPT ethics committee and PharmaEthics and the University of Witwatersrand Human Research ethics committee in South Africa. Written informed consent will be obtained from all participants. The study results will be shared with public health authorities, presented at scientific conferences and published in a peer-reviewed journal.

TRIAL REGISTRATION NUMBER

NCT04081077; Pre-results.

Easy and reliable maximum a posteriori Bayesian estimation of pharmacokinetic parameters with the open-source R package mapbayr

Pharmacokinetic (PK) parameter estimation is a critical and complex step in the model‐informed precision dosing (MIPD) approach. The mapbayr package was developed to perform maximum a posteriori Bayesian estimation (MAP‐BE) in R from any population PK model coded in mrgsolve. The performances of mapbayr were assessed using two approaches. First, “test” models with different features were coded, for example, first‐order and zero‐order absorption, lag time, time‐varying covariates, Michaelis–Menten elimination, combined and exponential residual error, parent drug and metabolite, and small or large inter‐individual variability (IIV). A total of 4000 PK profiles (combining single/multiple dosing and rich/sparse sampling) were simulated from each test model, and MAP‐BE of parameters was performed in both mapbayr and NONMEM. Second, a similar procedure was conducted with seven “real” previously published models to compare mapbayr and NONMEM on a PK outcome used in MIPD. For the test models, 98% of mapbayr estimations were identical to those given by NONMEM. Some discordances could be observed when dose‐related parameters were estimated or when models with large IIV were used. The exploration of objective function values suggested that mapbayr might outdo NONMEM in specific cases. For the real models, a concordance close to 100% on PK outcomes was observed. The mapbayr package provides a reliable solution to perform MAP‐BE of PK parameters in R. It also includes functions dedicated to data formatting and reporting and enables the creation of standalone Shiny web applications dedicated to MIPD, whatever the model or the clinical protocol and without additional software other than R.

Clinical Pharmacokinetics of Oral Sodium Selenite and Dosing Implications in the Treatment of Patients with Metastatic Cancer

Background

Selenite is a radiosensitizer and inhibitor of androgen receptor expression and function. In a phase I study (NCT02184533) in 15 subjects with metastatic cancer receiving daily oral sodium selenite with palliative radiation therapy, disease stabilization was observed, as evidenced by tumor regression, marked reduction in pain symptoms, and decreased prostate-specific antigen levels (only patients with castrate-resistant prostate cancer).

Objective

The aim of this work was to characterize the pharmacokinetics of selenite to suggest dosing strategies and to propose a study design for further investigation.

Methods

With selenium plasma concentrations obtained from five dosing cohorts (5.5, 11, 16.5, 33, and 49.5 mg), a population pharmacokinetic model was constructed using NONMEM. The model described externally administered selenite (inorganic) with a baseline component for endogenous selenium levels. Using the pharmacokinetic model, simulations were performed to suggest dosing regimens that achieved in vitro target selenite levels, and optimal pharmacokinetic sampling times for a subsequent study were proposed using PopED.

Results

A one-compartment model characterized selenite pharmacokinetics. Parameter estimates were absorption rate constant (0.64 h⁻¹), apparent clearance (1.58 L/h), apparent volume of distribution (42.3 L), and baseline selenium amount (5270 μg). A logarithmic function characterized the inverse relationship between dose level and bioavailability. Four regimens to reach in vitro target selenite levels were proposed: 33 mg daily, 16.5 mg twice daily (BID), 11 mg BID, and 5.5 mg thrice daily (TID). Optimal sampling times were 1, 2, 6, and 24 h.

Discussion

The population model described the pharmacokinetic data well. Three regimens (33 mg daily, 11 mg BID, 5.5 mg TID) achieved in vitro target selenite levels after one dose. The model and optimal sampling times may inform future studies evaluating the efficacy of selenite for metastatic cancer treatment.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40268-021-00340-9.

Optimal sampling strategies for darunavir and external validation of the underlying population pharmacokinetic model

Purpose

A variety of diagnostic methods are available to validate the performance of population pharmacokinetic models. Internal validation, which applies these methods to the model building dataset and to additional data generated through Monte Carlo simulations, is often sufficient, but external validation, which requires a new dataset, is considered a more rigorous approach, especially if the model is to be used for predictive purposes. Our first objective was to validate a previously published population pharmacokinetic model of darunavir, an HIV protease inhibitor boosted with ritonavir or cobicistat. Our second objective was to use this model to derive optimal sampling strategies that maximize the amount of information collected with as few pharmacokinetic samples as possible.

Methods

A validation dataset comprising 164 sparsely sampled individuals using ritonavir-boosted darunavir was used for validation. Standard plots of predictions and residuals, NPDE, visual predictive check, and bootstrapping were applied to both the validation set and the combined learning/validation set in NONMEM to assess model performance. D-optimal designs for darunavir were then calculated in PopED and further evaluated in NONMEM through simulations.

Results

External validation confirmed model robustness and accuracy in most scenarios but also highlighted several limitations. The best one-, two-, and three-point sampling strategies were determined to be pre-dose (0 h); 0 and 4 h; and 1, 4, and 19 h, respectively. A combination of samples at 0, 1, and 4 h was comparable to the optimal three-point strategy. These could be used to reliably estimate individual pharmacokinetic parameters, although with fewer samples, precision decreased and the number of outliers increased significantly.

Conclusions

Optimal sampling strategies derived from this model could be used in clinical practice to enhance therapeutic drug monitoring or to conduct additional pharmacokinetic studies.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00228-020-03036-2.

Optimal Designs for Model-Based Assessment of Insulin Sensitivity and Glucose Effectiveness

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (S_I ) and glucose effectiveness (S_G ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of S_I and S_G . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing S_I and S_G as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing S_I and S_G than the sparse standard design.

Clinical implementation of pharmacogenetics and model-informed precision dosing to improve patient care

Providing maximal therapeutic efficacy without toxicity is a universal goal of rational drug therapy. However, substantial between-patient variability in drug response often impedes such successful treatments and brings the necessity of tailoring drug dose to individual needs for more precise therapy. In many cases plenty of patient characteristics, such as body size, genetic makeup and environmental factors, need to be taken into consideration to find the optimal dose in clinical practice. A pharmacokinetics and pharmacodynamics (PK/PD) model-informed approach offers integration of various patient information to provide an expectation of drug response and derive practical dose estimates to support clinicians' dosing decisions. Such an approach was pioneered in the late 1970s, but its broad clinical acceptance and implementation have been hampered by the lack of widespread computer technology, including user-friendly software tools. This has significantly changed in recent years. With the advent of electronic health records (EHRs) and the ubiquity of user-friendly software tools, we now experience a convergence of clinical information, pharmacogenetics, systems pharmacology and pharmacometrics, and technology. Advanced pharmacometrics research is now more appliable and implementable to improve health care. This article presents examples of successful development and implementation of pharmacogenetics-guided and PK/PD model-informed decision support to facilitate precision dosing, including the development of an EHR-embedded decision support tool. Through the integration of clinical decision support tools in EHRs, clinical pharmacometrics support can be brought directly to the clinical team and the bedside.

Optimal Sampling Strategies for Irinotecan (CPT-11) and its Active Metabolite (SN-38) in Cancer Patients

Irinotecan (CPT-11) is an anticancer agent widely used in the treatment of a variety of adult solid tumors. The objective of this study was to develop an optimal sampling strategy model that accurately estimates pharmacokinetic parameters of CPT-11 and its active metabolite, SN-38. This study included 221 patients with advanced solid tumors or lymphoma receiving CPT-11 single or combination therapy with 5-fluorouracil (5-FU)/leucovorin (LV) (FOLFIRI) plus bevacizumab from 4 separate clinical trials. Population pharmacokinetic analysis of CPT-11 and SN-38 was performed by non-linear mixed effects modeling. The optimal sampling strategy model was developed using D-optimality with expected distribution approach. The pharmacokinetic profiles of CPT-11 and SN-38 were best described by a 3- and 2-compartment model, respectively, with first-order elimination. Body surface area and co-administration with 5-FU/LV plus bevacizumab were significant covariates (p < 0.01) for volumes of the central compartment of CPT-11 and SN-38, and clearance of CPT-11. Pre-treatment total bilirubin and co-administration with 5-FU/LV and bevacizumab were significant covariates (p < 0.01) for clearance of SN-38. Accurate and precise predictive performance (r² > 0.99, -2 < bias (%ME) < 0, precision (% RMSE) < 12) of both CPT-11 and SN-38 was achieved using: (i) 6 fixed sampling times collected at 1.5, 3.5, 4, 5.75, 22, 23.5 hours post-infusion; or (ii) 1 fixed time and 2 sampling windows collected at 1.5, [3-5.75], [22-23.5] hours post-infusion. The present study demonstrates that an optimal sampling design with three blood samples achieves accurate and precise pharmacokinetic parameter estimates for both CPT-11 and SN-38.

Quantitative Systems Pharmacology and Physiologically-Based Pharmacokinetic Modeling With mrgsolve: A Hands-On Tutorial

mrgsolve is an open-source R package available on the Comprehensive R Archive Network. It combines R and C++ coding for simulation from hierarchical, ordinary differential equation-based models. Its efficient simulation engine and integration into a parallelizable, R-based workflow makes mrgsolve a convenient tool both for simple and complex models and thus is ideal for physiologically-based pharmacokinetic (PBPK) and quantitative systems pharmacology (QSP) model. This tutorial will first introduce the basics of the mrgsolve simulation workflow, including model specification, the introduction of interventions (dosing events) into the simulation, and simulated results postprocessing. An applied simulation example is then presented using a PBPK model for voriconazole, including a model validation step against adult and pediatric data sets. A final simulation example is then presented using a previously published QSP model for mitogen-activated protein kinase signaling in colorectal cancer, illustrating population simulation of different combination therapies.

Use of prior knowledge and extrapolation in paediatric drug development: A case study with deferasirox

The characterisation of pharmacokinetics, pharmacodynamics and dose-exposure-response relationships requires data arising from well-designed study protocols and a relatively large sample from the target patient population. Such a prerequisite is unrealistic for paediatric rare diseases, where the patient population is often vulnerable and very small. In such cases, different sources of data and knowledge need to be considered to ensure trial designs are truly informative and oncoming data can be analysed efficiently. Here, we use clinical trial simulations to assess the contribution of historical data for (1) the analysis of sparse samples from a limited number of children and (2) the optimisation of study design when an increase in the number of subjects is not feasible. The evaluation of the pharmacokinetics of deferasirox in paediatric patients affected by haemoglobinopathies was used as case study. Our investigation shows that the incorporation of prior knowledge increases parameter precision and probability of successful convergence from only 12% with no priors to 56% and 75% for weakly and highly informative priors, respectively. In addition, results suggest that even when only one sample is collected per subject, as implemented in the original trial and in many other examples in clinical research, there is a 60% probability of biased parameter estimates (>25%). In conjunction with adult prior information and optimisation techniques, the probability of bias could be limited to <20% by increasing the number of samples/subject from 1 to 3. The methodology described here can be easily applied to other studies in small populations.

Reduced and optimized trial designs for drugs described by a target mediated drug disposition model

Monoclonal antibodies against soluble targets are often rich and include the sampling of multiple analytes over a lengthy period of time. Predictive models built on data obtained in such studies can be useful in all drug development phases. If adequate model predictions can be maintained with a reduced design (e.g. fewer samples or shorter duration) the use of such designs may be advocated. The effect of reducing and optimizing a rich design based on a published study for Omalizumab (OMA) was evaluated as an example. OMA pharmacokinetics were characterized using a target-mediated drug disposition model considering the binding of OMA to free IgE and the subsequent formation of an OMA–IgE complex. The performance of the reduced and optimized designs was evaluated with respect to: efficiency, parameter uncertainty and predictions of free target. It was possible to reduce the number of samples in the study by 30% while still maintaining an efficiency of almost 90%. A reduction in sampling duration by two-thirds resulted in an efficiency of 75%. Omission of any analyte measurement or a reduction of the number of dose levels was detrimental to the efficiency of the designs (efficiency ≤ 51%). However, other metrics were, in some cases, relatively unaffected, showing that multiple metrics may be needed to obtain balanced assessments of design performance.

Population Pharmacokinetics of Piperacillin in Sepsis Patients: Should Alternative Dosing Strategies Be Considered?

Sufficient antibiotic dosing in septic patients is essential for reducing mortality. Piperacillin-tazobactam is often used for empirical treatment, but due to the pharmacokinetic (PK) variability seen in septic patients, optimal dosing may be a challenge. We determined the PK profile for piperacillin given at 4 g every 8 h in 22 septic patients admitted to a medical ward. Piperacillin concentrations were compared to the clinical breakpoint MIC for Pseudomonas aeruginosa (16 mg/liter), and the following PK/pharmacodynamic (PD) targets were evaluated: the percentage of the dosing interval that the free drug concentration is maintained above the MIC (fTMIC) of 50% and 100%. A two-compartment population PK model described the data well, with clearance being divided into renal and nonrenal components. The renal component was proportional to the estimated creatinine clearance (eCLCR) and constituted 74% of the total clearance in a typical individual (eCLCR, 83.9 ml/min). Patients with a high eCLCR (>130 ml/min) were at risk of subtherapeutic concentrations for the current regimen, with a 90% probability of target attainment being reached at MICs of 2.0 (50% fTMIC) and 0.125 mg/liter (100% fTMIC). Simulations of alternative dosing regimens and modes of administration showed that dose increment and prolonged infusion increased the chance of achieving predefined PK/PD targets. Alternative dosing strategies may therefore be needed to optimize piperacillin exposure in septic patients. (This study has been registered at ClinicalTrials.gov under identifier NCT02569086.).

Model-Based Approach for Optimizing Study Design and Clinical Drug Performances of Extended-Release Formulations of Methylphenidate for the Treatment of ADHD

Methylphenidate (MPH) is currently used to treat children with attention deficit hyperactivity disorder (ADHD). Several extended-release (ER) formulations characterized by a dual release process were developed to improve efficacy over an extended duration. In this study, a model-based approach using literature data was developed to: 1) evaluate the most efficient pharmacokinetic (PK) model to characterize the complex PK profile of MPH ER formulations; 2) provide PK endpoint metrics for comparing ER formulations; 3) define criteria for optimizing development of ER formulations using a convolution-based model linking in vitro release, in vivo release, and hour-by-hour behavioral ratings of ADHD symptoms; and 4) define an optimized trial design for assessing the activity of MPH in pediatric populations. The convolution-based model accurately described the complex PK profiles of a variety of ER MPH products, providing a natural framework for establishing an in vitro/in vivo correlation and for defining criteria for assessing comparative bioequivalence of MPH ER products.

Opportunities for model-based precision dosing in the treatment of sickle cell anemia

Hydroxyurea is the primary pharmacotherapy to prevent complications of sickle cell anemia (SCA). Accumulated clinical experience across multiple age ranges has suggested that the use of an individualized maximum tolerated dose (MTD) will achieve optimal benefit of hydroxyurea treatment. However, the current empirical and trial-and-error approach for dose escalation often results in a lengthy titration process and is not strictly implemented in many clinics. Opportunities exist for pharmacokinetics model-based precision dosing of hydroxyurea to quickly achieve individual MTD. This review intends to introduce the use of a quantitative modeling approach including a Bayesian adaptive control strategy for the precision dosing of hydroxyurea. The rationale and practical considerations for the implementation of this approach are discussed. Future research directions with a focus on integrating specific safety and other clinical outcome endpoints into dose selection decision making are also discussed.

The effect of using a robust optimality criterion in model based adaptive optimization

Optimizing designs using robust (global) optimality criteria has been shown to be a more flexible approach compared to using local optimality criteria. Additionally, model based adaptive optimal design (MBAOD) may be less sensitive to misspecification in the prior information available at the design stage. In this work, we investigate the influence of using a local (lnD) or a robust (ELD) optimality criterion for a MBAOD of a simulated dose optimization study, for rich and sparse sampling schedules. A stopping criterion for accurate effect prediction is constructed to determine the endpoint of the MBAOD by minimizing the expected uncertainty in the effect response of the typical individual. 50 iterations of the MBAODs were run using the MBAOD R-package, with the concentration from a one-compartment first-order absorption pharmacokinetic model driving the population effect response in a sigmoidal EMAX pharmacodynamics model. The initial cohort consisted of eight individuals in two groups and each additional cohort added two individuals receiving a dose optimized as a discrete covariate. The MBAOD designs using lnD and ELD optimality with misspecified initial model parameters were compared by evaluating the efficiency relative to an lnD-optimal design based on the true parameter values. For the explored example model, the MBAOD using ELD-optimal designs converged quicker to the theoretically optimal lnD-optimal design based on the true parameters for both sampling schedules. Thus, using a robust optimality criterion in MBAODs could reduce the number of adaptations required and improve the practicality of adaptive trials using optimal design.

The effect of Fisher information matrix approximation methods in population optimal design calculations

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

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

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

Optimal Design for Informative Protocols in Xenograft Tumor Growth Inhibition Experiments in Mice

Tumor growth inhibition (TGI) models are increasingly used during preclinical drug development in oncology for the in vivo evaluation of antitumor effect. Tumor sizes are measured in xenografted mice, often only during and shortly after treatment, thus preventing correct identification of some TGI model parameters. Our aims were (i) to evaluate the importance of including measurements during tumor regrowth and (ii) to investigate the proportions of mice included in each arm. For these purposes, optimal design theory based on the Fisher information matrix implemented in PFIM4.0 was applied. Published xenograft experiments, involving different drugs, schedules, and cell lines, were used to help optimize experimental settings and parameters using the Simeoni TGI model. For each experiment, a two-arm design, i.e., control versus treatment, was optimized with or without the constraint of not sampling during tumor regrowth, i.e., "short" and "long" studies, respectively. In long studies, measurements could be taken up to 6 g of tumor weight, whereas in short studies the experiment was stopped 3 days after the end of treatment. Predicted relative standard errors were smaller in long studies than in corresponding short studies. Some optimal measurement times were located in the regrowth phase, highlighting the importance of continuing the experiment after the end of treatment. In the four-arm designs, the results showed that the proportions of control and treated mice can differ. To conclude, making measurements during tumor regrowth should become a general rule for informative preclinical studies in oncology, especially when a delayed drug effect is suspected.

An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models

Non-linear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. In recent years, estimation algorithms for NLMEMs have transitioned from linearization toward more exact higher-order methods. Optimal design, on the other hand, has mainly relied on first-order (FO) linearization to calculate the FIM. Although efficient in general, FO cannot be applied to complex non-linear models and with difficulty in studies with discrete data. We propose an approach to evaluate the expected FIM in NLMEMs for both discrete and continuous outcomes. We used Markov Chain Monte Carlo (MCMC) to integrate the derivatives of the log-likelihood over the random effects, and Monte Carlo to evaluate its expectation w.r.t. the observations. Our method was implemented in R using Stan, which efficiently draws MCMC samples and calculates partial derivatives of the log-likelihood. Evaluated on several examples, our approach showed good performance with relative standard errors (RSEs) close to those obtained by simulations. We studied the influence of the number of MC and MCMC samples and computed the uncertainty of the FIM evaluation. We also compared our approach to Adaptive Gaussian Quadrature, Laplace approximation, and FO. Our method is available in R-package MIXFIM and can be used to evaluate the FIM, its determinant with confidence intervals (CIs), and RSEs with CIs.

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Sampling Optimization in Pharmacokinetic Bridging Studies: Example of the Use of Deferiprone in Children With β-Thalassemia

Despite wide clinical experience with deferiprone, the optimum dosage in children younger than 6 years remains to be established. This analysis aimed to optimize the design of a prospective clinical study for the evaluation of deferiprone pharmacokinetics in children. A 1-compartment model with first-order oral absorption was used for the purposes of the analysis. Different sampling schemes were evaluated under the assumption of a constrained population size. A sampling scheme with 5 samples per subject was found to be sufficient to ensure accurate characterization of the pharmacokinetics of deferiprone. Whereas the accuracy of parameters estimates was high, precision was slightly reduced because of the small sample size (CV% >30% for Vd/F and KA). Mean AUC ± SD was found to be 33.4 ± 19.2 and 35.6 ± 20.2 mg · h/mL, and mean Cmax ± SD was found to be 10.2 ± 6.1 and 10.9 ± 6.7 mg/L based on sparse and frequent sampling, respectively. The results showed that typical frequent sampling schemes and sample sizes do not warrant accurate model and parameter identifiability. Expectation of the determinant (ED) optimality and simulation-based optimization concepts can be used to support pharmacokinetic bridging studies. Of importance is the accurate estimation of the magnitude of the covariate effects, as they partly determine the dose recommendation for the population of interest.

Development of a pharmacokinetic-guided dose individualization strategy for hydroxyurea treatment in children with sickle cell anaemia

AIMS

Hydroxyurea has emerged as the primary disease-modifying therapy for patients with sickle cell anaemia (SCA). The laboratory and clinical benefits of hydroxyurea are optimal at maximum tolerated dose (MTD), but the current empirical dose escalation process often takes up to 12 months. The purpose of this study was to develop a pharmacokinetic-guided dosing strategy to reduce the time required to reach hydroxyurea MTD in children with SCA.

METHODS

Pharmacokinetic (PK) data from the HUSTLE trial (NCT00305175) were used to develop a population PK model using non-linear mixed effects modelling (nonmem 7.2). A D-optimal sampling strategy was developed to estimate individual PK and hydroxyurea exposure (area under the concentration-time curve (AUC)). The initial AUC target was derived from HUSTLE clinical data and defined as the mean AUC at MTD.

RESULTS

PK profiles were best described by a one compartment with Michaelis-Menten elimination and a transit absorption model. Body weight and cystatin C were identified as significant predictors of hydroxyurea clearance. The following clinically feasible sampling times are included in a new prospective protocol: pre-dose (baseline), 15-20 min, 50-60 min and 3 h after an initial 20 mg kg(-1) oral dose. The mean target AUC(0,∞) for initial dose titration was 115 mg l(-1)  h.

CONCLUSION

We developed a PK model-based individualized dosing strategy for the prospective Therapeutic Response Evaluation and Adherence Trial (TREAT, ClinicalTrials.gov NCT02286154). This approach has the potential to optimize the dose titration of hydroxyurea therapy for children with SCA, such that the clinical benefits at MTD are achieved more quickly.

Influence of the Size of Cohorts in Adaptive Design for Nonlinear Mixed Effects Models: An Evaluation by Simulation for a Pharmacokinetic and Pharmacodynamic Model for a Biomarker in Oncology

PURPOSE

In this study we aimed to evaluate adaptive designs (ADs) by clinical trial simulation for a pharmacokinetic-pharmacodynamic model in oncology and to compare them with one-stage designs, i.e., when no adaptation is performed, using wrong prior parameters.

METHODS

We evaluated two one-stage designs, ξ0 and ξ*, optimised for prior and true population parameters, Ψ0 and Ψ*, and several ADs (two-, three- and five-stage). All designs had 50 patients. For ADs, the first cohort design was ξ0. The next cohort design was optimised using prior information updated from the previous cohort. Optimal design was based on the determinant of the Fisher information matrix using PFIM. Design evaluation was performed by clinical trial simulations using data simulated from Ψ*.

RESULTS

Estimation results of two-stage ADs and ξ * were close and much better than those obtained with ξ 0. The balanced two-stage AD performed better than two-stage ADs with different cohort sizes. Three- and five-stage ADs were better than two-stage with small first cohort, but not better than the balanced two-stage design.

CONCLUSIONS

Two-stage ADs are useful when prior parameters are unreliable. In case of small first cohort, more adaptations are needed but these designs are complex to implement.

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 scheme for estimation of intraocular pressure diurnal curves in glaucoma trials

BACKGROUND AND OBJECTIVE

Effective control of intraocular pressure (IOP) is essential for the successful management of glaucoma. IOP exhibits diurnal variation, yet continuous monitoring is impractical. To date, no clear evidence exists on the number of sampling timepoints required to characterize diurnal IOP and when those measurements should be collected. The objective of this study was to develop an optimized sampling scheme to estimate diurnal IOP and to provide sampling windows for practicality.

METHODS

Baseline IOP values for glaucoma patients were collected from the published literature. A population model-based meta-analysis was performed to develop a model for diurnal IOP that accounts for covariates and inter-study variability. Optimization was performed using the D-optimality criteria to determine optimal sampling times. In addition, various reduced sampling designs were tested to investigate the minimum number of sampling timepoints to precisely estimate diurnal IOP. Also, sampling windows were calculated around the final optimal sampling times to allow flexibility in data collection. The final reduced optimized model was validated by simulating and estimating 500 datasets with reduced optimal sampling times.

RESULTS

The final baseline IOP model included type of glaucoma as a covariate. Bootstrap analysis and visual predictive check plots revealed the adequacy of the model to describe the observed IOP data. Optimization results indicated an increasing trend in bias with decreasing sampling timepoints. A reduced model with four sampling times resulted in acceptable precision (<40 %). Restricting the sampling time between 8 a.m. and 4 p.m. underestimates the fluctuation in diurnal IOP. Sampling windows with ≥95 % efficiency were calculated around the optimized sampling times. Validation results indicated acceptable precision and relative bias for model estimates in the reduced optimized model.

CONCLUSION

A physiologically based mechanistic model was developed to describe the diurnal variation in baseline IOP and inter-study variability was estimated on key diurnal model parameters. Optimization of the final covariate model indicated a reduced sampling time of at least four samples should be collected at 5:45 a.m., 2:15 p.m., 8:00 p.m., and 12:00 a.m. for reliable estimation of diurnal IOP variation.

Improved precision of exposure-response relationships by optimal dose-selection. Examples from studies of receptor occupancy using PET and dose finding for neuropathic pain treatment

An understanding of the relationship between drug exposure and response is a fundamental basis for any dosing recommendation. We investigate optimal dose-selection for two different types of studies, a receptor occupancy study assessed by positron emission tomography (PET) and a dose-finding study in neuropathic pain treatment. For the PET-study, an inhibitory E-max model describes the relationship between drug exposure and displacement of a radioligand from specific receptors in the brain. The model has a mechanistic basis in the law of mass action and the affinity parameter (Ki PL ) is of primary interest. For optimization of the neuropathic pain study, the model is empirical and the exposure response curve itself is of primary interest. An alternative parameterization of the sigmoid Emax model was therefore used where the plasma concentration corresponding to the minimum relevant efficacy was estimated as a parameter. Optimal design methodology was applied using the D-optimal criterion as well as the Ds-optimal criterion where parameters of interest were defined. For the PET-study it was shown that the precision of Ki PL can be improved by inclusion of brain regions with both high and low receptor density and that the need for high doses is reduced when a brain region with low receptor density is included in the analysis. In the case of the neuropathic pain study it was shown that a Ds-optimal study design using the reparameterized Emax model can improve the precision in the minimum effective dose compared to a D-optimal design.

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.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Optimizing disease progression study designs for drug effect discrimination

Investigate the possibility to directly optimize a clinical trial design for statistical power to detect a drug effect and compare to optimal designs that focus on parameter precision. An improved statistic derived from the general formulation of the Wald approximation was used to predict the statistical power for given trial designs of a disease progression study. The predicted value was compared, together with the classical Wald statistic, to a type I error-corrected model-based power determined via clinical trial simulations. In a second step, a study design for maximal power was determined by directly maximizing the new statistic. The resulting power-optimal designs and their corresponding performance based on empirical power calculations were compared to designs focusing on parameter precision. Comparisons of empirically determined power and the newly developed statistic, showed excellent agreement across all scenarios investigated. This was in contrast to the classical Wald statistic, which consistently over-predicted the reference power with deviations of up to 90 %. Designs maximized using the proposed metric differed from traditional optimal designs and showed equal or up to 20 % higher power in the subsequent clinical trial simulations. Furthermore, the proposed method was used to minimize the number of individuals required to achieve 80 % power through a simultaneous optimization of study size and study design. The targeted power of 80 % was confirmed in subsequent simulation study. A new statistic was developed, allowing for the explicit optimization of a clinical trial design with respect to statistical power.

Simultaneous optimal experimental design for in vitro binding parameter estimation

Simultaneous optimization of in vitro ligand binding studies using an optimal design software package that can incorporate multiple design variables through non-linear mixed effect models and provide a general optimized design regardless of the binding site capacity and relative binding rates for a two binding system. Experimental design optimization was employed with D- and ED-optimality using PopED 2.8 including commonly encountered factors during experimentation (residual error, between experiment variability and non-specific binding) for in vitro ligand binding experiments: association, dissociation, equilibrium and non-specific binding experiments. Moreover, a method for optimizing several design parameters (ligand concentrations, measurement times and total number of samples) was examined. With changes in relative binding site density and relative binding rates, different measurement times and ligand concentrations were needed to provide precise estimation of binding parameters. However, using optimized design variables, significant reductions in number of samples provided as good or better precision of the parameter estimates compared to the original extensive sampling design. Employing ED-optimality led to a general experimental design regardless of the relative binding site density and relative binding rates. Precision of the parameter estimates were as good as the extensive sampling design for most parameters and better for the poorly estimated parameters. Optimized designs for in vitro ligand binding studies provided robust parameter estimation while allowing more efficient and cost effective experimentation by reducing the measurement times and separate ligand concentrations required and in some cases, the total number of samples.