Bayesian Optimal Designs for Pharmacokinetic Models: Sensitivity to Uncertainty

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.

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

Several developments have facilitated the practical application and increased the general use of optimal design for nonlinear mixed effects models. These developments include new methodology for utilizing advanced pharmacometric models, faster optimization algorithms and user friendly software tools. In this paper we present the extension of the optimal design software PopED, which incorporates many of these recent advances into an easily useable enhanced GUI. Furthermore, we present new solutions to problems related to the design of experiments such as: faster and more robust FIM calculations and optimizations, optimizing over cost/utility functions and diagnostic tools and plots to evaluate design performance. Examples for; (i) Group size optimization and efficiency translation, (ii) Cost/constraint optimization, (iii) Optimizations with different FIM approximations and (iv) optimization with parallel computing demonstrate the new features in PopED and underline the potential use of this tool when designing experiments.

Serial correlation in optimal design for nonlinear mixed effects models

In population modeling two sources of variability are commonly included; inter individual variability and residual variability. Rich sampling optimal design (more samples than model parameters) using these models will often result in a sampling schedule where some measurements are taken at exactly the same time point, thereby maximizing the signal-to-noise ratio. This behavior is a result of not appropriately taking into account error generation mechanisms and is often clinically unappealing and may be avoided by including intrinsic variability, i.e. serially correlated residual errors. In this paper we extend previous work that investigated optimal designs of population models including serial correlation using stochastic differential equations to optimal design with the more robust, and analytic, AR(1) autocorrelation model. Further, we investigate the importance of correlation strength, design criteria and robust designs. Finally, we explore the optimal design properties when estimating parameters with and without serial correlation. In the investigated examples the designs and estimation performance differs significantly when handling serial correlation.

Optimal sampling strategy development methodology using maximum a posteriori Bayesian estimation

Maximum a posteriori Bayesian (MAPB) pharmacokinetic parameter estimation is an accurate and flexible method of estimating individual pharmacokinetic parameters using individual blood concentrations and prior information. In the past decade, many studies have developed optimal sampling strategies to estimate pharmacokinetic parameters as accurately as possible using either multiple regression analysis or MAPB estimation. This has been done for many drugs, especially immunosuppressants and anticancer agents. Methods of development for optimal sampling strategies (OSS) are diverse and heterogeneous. This review provides a comprehensive overview of OSS development methodology using MAPB pharmacokinetic parameter estimation, determines the transferability of published OSSs, and compares sampling strategies determined by MAPB estimation and multiple regression analysis. OSS development has the following components: 1) prior distributions; 2) reference value determination; 3) optimal sampling time identification; and 4) validation of the OSS. Published OSSs often lack all data necessary for the OSS to be clinically transferable. MAPB estimation is similar to multiple regression analysis in terms of predictive performance but superior in flexibility.

An example of optimal phase II design for exposure response modelling

This paper presents an example of how optimal design methodology was used to help design a phase II clinical study. The planned analysis would relate the clinical endpoint to exposure (measured via the area under the curve (AUC)), rather than dose. Optimal design methodology was used to compare a number of candidate phase II designs, and an algorithm for finding optimal designs was employed. The sigmoidal E(max) with baseline (E₀) model was used to relate the clinical endpoint to individual subject AUCs, and the primary metrics were D optimality and the standard error (SE) of the AUC required to yield a clinically relevant change in the clinical endpoint. The performance of the candidate designs were compared across four different 'true' exposure response relationships (determined from the analysis of an earlier proof of concept (PoC) study). The results suggested the total sample size should be increased from the planned 540 individuals, and that the optimal design with 700 individuals would be equivalent to 812 individuals with the reference design (a 16% gain). The performance with this design was considered acceptable, although all designs performed poorly if the true exposure response relationship was very flat. This work allowed a prospective assessment of the likely performance and precision from the exposure response modelling prior to the start of the phase II study, and hence allowed the design to be revised to ensure the subsequent analysis would be of most value.

Application of optimal design methodologies in clinical pharmacology experiments

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

Optimization of the intravenous glucose tolerance test in T2DM patients using optimal experimental design

Intravenous glucose tolerance test (IVGTT) provocations are informative, but complex and laborious, for studying the glucose-insulin system. The objective of this study was to evaluate, through optimal design methodology, the possibilities of more informative and/or less laborious study design of the insulin modified IVGTT in type 2 diabetic patients. A previously developed model for glucose and insulin regulation was implemented in the optimal design software PopED 2.0. The following aspects of the study design of the insulin modified IVGTT were evaluated; (1) glucose dose, (2) insulin infusion, (3) combination of (1) and (2), (4) sampling times, (5) exclusion of labeled glucose. Constraints were incorporated to avoid prolonged hyper- and/or hypoglycemia and a reduced design was used to decrease run times. Design efficiency was calculated as a measure of the improvement with an optimal design compared to the basic design. The results showed that the design of the insulin modified IVGTT could be substantially improved by the use of an optimized design compared to the standard design and that it was possible to use a reduced number of samples. Optimization of sample times gave the largest improvement followed by insulin dose. The results further showed that it was possible to reduce the total sample time with only a minor loss in efficiency. Simulations confirmed the predictions from PopED. The predicted uncertainty of parameter estimates (CV) was low in all tested cases, despite the reduction in the number of samples/subject. The best design had a predicted average CV of parameter estimates of 19.5%. We conclude that improvement can be made to the design of the insulin modified IVGTT and that the most important design factor was the placement of sample times followed by the use of an optimal insulin dose. This paper illustrates how complex provocation experiments can be improved by sequential modeling and optimal design.

Simultaneous optimal experimental design on dose and sample times

Optimal experimental design can be used for optimizing new pharmacokinetic (PK)-pharmacodynamic (PD) studies to increase the parameter precision. Several methods for optimizing non-linear mixed effect models has been proposed previously but the impact of optimizing other continuous design parameters, e.g. the dose, has not been investigated to a large extent. Moreover, the optimization method (sequential or simultaneous) for optimizing several continuous design parameters can have an impact on the optimal design. In the sequential approach the time and dose where optimized in sequence and in the simultaneous approach the dose and time points where optimized at the same time. To investigate the sequential approach and the simultaneous approach; three different PK-PD models where considered. In most of the cases the optimization method did change the optimal design and furthermore the precision was improved with the simultaneous approach.