An evaluation of population D-optimal designs via pharmacokinetic simulations

New Horizons of Model Informed Drug Development in Rare Diseases Drug Development

Model-informed approaches provide a quantitative framework to integrate all available nonclinical and clinical data, thus furnishing a totality of evidence approach to drug development and regulatory evaluation. Maximizing the use of all available data and information about the drug enables a more robust characterization of the risk-benefit profile and reduces uncertainty in both technical and regulatory success. This offers the potential to transform rare diseases drug development, where conducting large well-controlled clinical trials is impractical and/or unethical due to a small patient population, a significant portion of which could be children. Additionally, the totality of evidence generated by model-informed approaches can provide confirmatory evidence for regulatory approval without the need for additional clinical data. In the article, applications of novel quantitative approaches such as quantitative systems pharmacology, disease progression modeling, artificial intelligence, machine learning, modeling of real-world data using model-based meta-analysis and strategies such as external control and patient-reported outcomes as well as clinical trial simulations to optimize trials and sample collection are discussed. Specific case studies of these modeling approaches in rare diseases are provided to showcase applications in drug development and regulatory review. Finally, perspectives are shared on the future state of these modeling approaches in rare diseases drug development along with challenges and opportunities for incorporating such tools in the rational development of drug products.

Pharmacometric estimation methods for aggregate data, including data simulated from other pharmacometric models

Lack of data is an obvious limitation to what can be modelled. However, aggregate data in the form of means and possibly (co)variances, as well as previously published pharmacometric models, are often available. Being able to use all available data is desirable, and therefore this paper will outline several methods for using aggregate data as the basis of parameter estimation. The presented methods can be used for estimation of parameters from aggregate data, and as a computationally efficient alternative for the stochastic simulation and estimation procedure. They also allow for population PK/PD optimal design in the case when the data-generating model is different from the data-analytic model, a scenario for which no solutions have previously been available. Mathematical analysis and computational results confirm that the aggregate-data FO algorithm converges to the same estimates as the individual-data FO and yields near-identical standard errors when used in optimal design. The aggregate-data MC algorithm will asymptotically converge to the exactly correct parameter estimates if the data-generating model is the same as the data-analytic model. The performance of the aggregate-data methods were also compared to stochastic simulations and estimations (SSEs) when the data-generating model is different from the data-analytic model. The aggregate-data FO optimal design correctly predicted the sampling distributions of 200 models fitted to simulated datasets with the individual-data FO method.

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.

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.

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.

Using Animal Instincts to Design Efficient Biomedical Studies via Particle Swarm Optimization

Particle swarm optimization (PSO) is an increasingly popular metaheuristic algorithm for solving complex optimization problems. Its popularity is due to its repeated successes in finding an optimum or a near optimal solution for problems in many applied disciplines. The algorithm makes no assumption of the function to be optimized and for biomedical experiments like those presented here, PSO typically finds the optimal solutions in a few seconds of CPU time on a garden-variety laptop. We apply PSO to find various types of optimal designs for several problems in the biological sciences and compare PSO performance relative to the differential evolution algorithm, another popular metaheuristic algorithm in the engineering literature.

A model-based meta-analysis of monoclonal antibody pharmacokinetics to guide optimal first-in-human study design

The objectives of this retrospective analysis were (1) to characterize the population pharmacokinetics (popPK) of four different monoclonal antibodies (mAbs) in a combined analysis of individual data collected during first-in-human (FIH) studies and (2) to provide a scientific rationale for prospective design of FIH studies with mAbs. The data set was composed of 171 subjects contributing a total of 2716 mAb serum concentrations, following intravenous (IV) and subcutaneous (SC) doses. mAb PK was described by an open 2-compartment model with first-order elimination from the central compartment and a depot compartment with first-order absorption. Parameter values obtained from the popPK model were further used to generate optimal sampling times for a single dose study. A robust fit to the combined data from four mAbs was obtained using the 2-compartment model. Population parameter estimates for systemic clearance and central volume of distribution were 0.20 L/day and 3.6 L with intersubject variability of 31% and 34%, respectively. The random residual error was 14%. Differences (> 2-fold) in PK parameters were not apparent across mAbs. Rich designs (22 samples/subject), minimal designs for popPK (5 samples/subject), and optimal designs for non-compartmental analysis (NCA) and popPK (10 samples/subject) were examined by stochastic simulation and estimation. Single-dose PK studies for linear mAbs executed using the optimal designs are expected to yield high-quality model estimates, and accurate capture of NCA estimations. This model-based meta-analysis has determined typical popPK values for four mAbs with linear elimination and enabled prospective optimization of FIH study designs, potentially improving the efficiency of FIH studies for this class of therapeutics.

A general model-based design of experiments approach to achieve practical identifiability of pharmacokinetic and pharmacodynamic models

The use of pharmacokinetic (PK) and pharmacodynamic (PD) models is a common and widespread practice in the preliminary stages of drug development. However, PK-PD models may be affected by structural identifiability issues intrinsically related to their mathematical formulation. A preliminary structural identifiability analysis is usually carried out to check if the set of model parameters can be uniquely determined from experimental observations under the ideal assumptions of noise-free data and no model uncertainty. However, even for structurally identifiable models, real-life experimental conditions and model uncertainty may strongly affect the practical possibility to estimate the model parameters in a statistically sound way. A systematic procedure coupling the numerical assessment of structural identifiability with advanced model-based design of experiments formulations is presented in this paper. The objective is to propose a general approach to design experiments in an optimal way, detecting a proper set of experimental settings that ensure the practical identifiability of PK-PD models. Two simulated case studies based on in vitro bacterial growth and killing models are presented to demonstrate the applicability and generality of the methodology to tackle model identifiability issues effectively, through the design of feasible and highly informative experiments.

Application of ED-optimality to screening experiments for analgesic compounds in an experimental model of neuropathic pain

In spite of the evidence regarding high variability in the response to evoked pain, little attention has been paid to its impact on the screening of drugs for inflammatory and neuropathic pain. In this study, we explore the feasibility of introducing optimality concepts to experimental protocols, enabling estimation of parameter and model uncertainty. Pharmacokinetic (PK) and pharmacodynamic data from different experiments in rats were pooled and modelled using nonlinear mixed effects modelling. Pain data on gabapentin and placebo-treated animals were generated in the complete Freund's adjuvant model of neuropathic pain. A logistic regression model was applied to optimise sampling times and dose levels to be used in an experimental protocol. Drug potency (EC(50)) and interindividual variability (IIV) were considered the parameters of interest. Different experimental designs were tested and validated by SSE (stochastic simulation and estimation) taking into account relevant exposure ranges. The pharmacokinetics of gabapentin was described by a two-compartment PK model with first order absorption (CL = 0.159 l h(-1), V(2) = 0.118 l, V(3) = 0.253 l, Ka = 0.26 h(-1), Q = 1.22 l h(-1)). Drug potency (EC(50)) for the anti-allodynic effects was estimated to be 1400 ng ml(-1). Protocol optimisation improved bias and precision of the EC50 by 6 and 11.9. %, respectively, whilst IIV estimates showed improvement of 31.89 and 14.91 %, respectively. Our results show that variability in behavioural models of evoked pain response leads to uncertainty in drug potency estimates, with potential impact on the ranking of compounds during screening. As illustrated for gabapentin, ED-optimality concepts enable analysis of discrete data taking into account experimental constraints.

Translation of drug effects from experimental models of neuropathic pain and analgesia to humans

Neuropathic pain research remains a challenging undertaking owing to: (i) the lack of understanding about the underlying disease processes; and (ii) poor predictive validity of the current models of evoked pain used for the screening of novel compounds. Common consensus is that experimental models replicate symptoms (i.e. have face validity but no construct validity). Another issue that requires attention is the sensitivity of endpoints to discriminate drug effects that are relevant to the disease in humans. In this paper we provide an overview of the pre-clinical models that can be used in conjunction with a model-based approach to facilitate the prediction of drug effects in humans. Our review strongly suggests that evidence of the concentration-effect relationship is necessary for translational purposes.

Nonnucleoside reverse transcriptase inhibitor pharmacokinetics in a large unselected cohort of HIV-infected women

BACKGROUND

Small intensive pharmacokinetic (PK) studies of medications in early-phase trials cannot identify the range of factors that influence drug exposure in heterogenous populations. We performed PK studies in large numbers of HIV-infected women on nonnucleoside reverse transcriptase inhibitors (NNRTIs) under conditions of actual use to assess patient characteristics that influence exposure and evaluated the relationship between exposure and response.

METHODS

Two hundred twenty-five women on NNRTI-based antiretroviral regimens from the Women's Interagency HIV Study were enrolled into 12-hour or 24-hour PK studies. Extensive demographic, laboratory, and medication covariate data were collected before and during the visit to be used in multivariate models. Total NNRTI drug exposure was estimated by area under the concentration-time curves.

RESULTS

Hepatic inflammation and renal insufficiency were independently associated with increased nevirapine exposure in multivariate analysis: crack cocaine, high fat diets, and amenorrhea were associated with decreased levels (n = 106). Higher efavirenz exposure was seen with increased transaminase, albumin levels, and orange juice consumption; tenofovir use, increased weight, being African American, and amenorrhea were associated with decreased exposure (n = 119). With every 10-fold increase in nevirapine or efavirenz exposure, participants were 3.3 and 3.6 times likely to exhibit virologic suppression, respectively. Patients with higher drug exposure were also more likely to report side effects on therapy.

CONCLUSIONS

Our study identifies and quantitates previously unrecognized factors modifying NNRTI exposure in the "real-world" setting. Comprehensive PK studies in representative populations are feasible and may ultimately lead to dose optimization strategies in patients at risk for failure or adverse events.

Robust population pharmacokinetic experiment design

The population approach to estimating mixed effects model parameters of interest in pharmacokinetic (PK) studies has been demonstrated to be an effective method in quantifying relevant population drug properties. The information available for each individual is usually sparse. As such, care should be taken to ensure that the information gained from each population experiment is as efficient as possible by designing the experiment optimally, according to some criterion. The classic approach to this problem is to design "good" sampling schedules, usually addressed by the D-optimality criterion. This method has the drawback of requiring exact advanced knowledge (expected values) of the parameters of interest. Often, this information is not available. Additionally, if such prior knowledge about the parameters is misspecified, this approach yields designs that may not be robust for parameter estimation. In order to incorporate uncertainty in the prior parameter specification, a number of criteria have been suggested. We focus on ED-optimality. This criterion leads to a difficult numerical problem, which is made tractable here by a novel approximation of the expectation integral usually solved by stochastic integration techniques. We present two case studies as evidence of the robustness of ED-optimal designs in the face of misspecified prior information. Estimates from replicate simulated population data show that such misspecified ED-optimal designs recover parameter estimates that are better than similarly misspecified D-optimal designs, and approach estimates gained from D-optimal designs where the parameters are correctly specified.

Simultaneous population optimal design for pharmacokinetic-pharmacodynamic experiments

Multiple outputs or measurement types are commonly gathered in biological experiments. Often, these experiments are expensive (such as clinical drug trials) or require careful design to achieve the desired information content. Optimal experimental design protocols could help alleviate the cost and increase the accuracy of these experiments. In general, optimal design techniques ignore between-individual variability, but even work that incorporates it (population optimal design) has treated simultaneous multiple output experiments separately by computing the optimal design sequentially, first finding the optimal design for one output (eg, a pharmacokinetic [PK] measurement) and then determining the design for the second output (eg, a pharmacodynamic [PD] measurement). Theoretically, this procedure can lead to biased and imprecise results when the second model parameters are also included in the first model (as in PK-PD models). We present methods and tools for simultaneous population D-optimal experimental designs, which simultaneously compute the design of multiple output experiments, allowing for correlation between model parameters. We then apply these methods to simulated PK-PD experiments. We compare the new simultaneous designs to sequential designs that first compute the PK design, fix the PK parameters, and then compute the PD design in an experiment. We find that both population designs yield similar results in designs for low sample number experiments, with simultaneous designs being possibly superior in situations in which the number of samples is unevenly distributed between outputs. Simultaneous population D-optimality is a potentially useful tool in the emerging field of experimental design.

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.

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.