Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics (original) (raw)
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Optimal Designs for Two Nested Pharmacokinetic Models with Correlated Observations
Communications in Statistics - Simulation and Computation, 2012
Two nested pharmacokinetic models are considered in this work. Several observations are taken on the same subject so they are correlated. The covariance function assumed is an exponential covariance function. Optimal exact designs are computed with different criteria, both for discriminating between models and estimating parameters. Compound criteria to estimate the parameters and nonlinear functions of the parameters are used. An iterative algorithm based on T-optimality and an algorithm from Brimkulov, Krug and Savanov [?] are combined in order to compute T-optimal designs with correlated observations. Finally, compound designs to discriminate between the models and estimate the nonlinear functions are considered. A test power study is performed to adjust the compound parameter.
An Evaluation of Population D-Optimal Designs Via Pharmacokinetic Simulations
Annals of biomedical …, 2003
One goal of large scale clinical trials is to determine how a drug is processed by, and cleared from, the human body [i.e., its pharmacokinetic (PK) properties] and how these PK properties differ between individuals in a population (i.e., its population PK properties). Due to the high cost of these studies and the limited amount of data (e.g., blood samples) available from each study subject, it would be useful to know how many measurements are needed and when those measurements should be taken to accurately quantify population PK model parameters means and variances. Previous studies have looked at optimal design strategies of population PK experiments by developing an optimal design for an individual study (i.e., no interindividual variability was considered in the design), and then applying that design to each individual in a population study (where interindividual variability is present). A more algorithmically and informationally intensive approach is to develop a population optimal design, which inherently includes the assessment of interindividual variability. We present a simulation-based evaluation of these two design methods based on nonlinear Gaussian population PK models. Specifically, we compute standard individual and population D-optimal designs and compare population PK model parameter estimates based on simulated optimal design measurements. Our results show that population and standard D-optimal designs are not significantly different when both designs have the same number of samples per individual. However, population optimal designs allow for sampling schedules where the number of samples per individual is less than the number of model parameters, the theoretical limit allowed in standard optimal design. These designs with a low number of samples per individual are shown to be nearly as robust in parameter estimation as standard D-optimal designs. In the limit of just one sample per individual, however, population D-optimal designs are shown to be inadequate. © 2003 Biomedical Engineering Society.
A geometric characterization of optimal designs for regression models with correlated observations
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2011
We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals can be assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated in a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics.
Journal of Biopharmaceutical Statistics, 2014
Nonlinear mixed-effect models are used increasingly during drug development. For design, an alternative to simulations is based on the Fisher information matrix. Its expression was derived using a first-order approach, was then extended to include covariance and implemented into the R function PFIM. The impact of covariance on standard errors, amount of information and optimal designs was studied. It was also shown how standard errors can be predicted analytically within the framework of rich individual data without the model. The results were illustrated by applying this extension to the design of a pharmacokinetic study of a drug in paediatric development.
Optimal designs for composed models in pharmacokinetic–pharmacodynamic experiments
Journal of Pharmacokinetics and Pharmacodynamics, 2012
We discuss design issues for pharmacokinetic and pharmacodynamic (PK/PD) models and provide closed form descriptions for locally optimal designs for estimating individual parameter in two frequently used models. We propose standardized maximin optimal designs that remove dependence on the particular parameter of interest by maximizing the minimal efficiency across all parameters. Further, robust designs are proposed to overcome the dependence on the parameters of interest and the nominal values of the parameters. We compare performance of these optimal designs with designs used in four real studies from the pharmacokinetic/pharmacodynamic literature and show that our proposed designs provide definite advantages over those used in practice.
A pragmatic approach to the design of population pharmacokinetic studies
The AAPS Journal, 2005
The publication of a seminal article on nonlinear mixedeffect 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.
Optimal Design for Nonlinear Response Models
Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors’ many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design—such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints—are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The...
Prospective Evaluation of a D-Optimal Designed Population Pharmacokinetic Study
Journal of Pharmacokinetics and Pharmacodynamics, 2000
Recently, methods for computing D-optimal designs for population pharmacokinetic studies haûe become aûailable. Howeûer there are few publications that haûe prospectiûely eûaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB ûersion 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject ûariability and proportional residual ûariability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11-12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectiûely represented the entire dose interûal. Each patient was assigned to haûe one blood sample taken from three different windows. Windows for blood sampling times were also proûided for the optimal design. Ninety six patients were recruited into the study who were currently receiûing enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (ûersion 5). The empirical design supported a one compartment linear model with additiûe residual error, while the optimal design supported a two compartment linear model with additiûe residual error as did the model deriûed from the full data set. A posterior predictiûe check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This reûealed the ''optimal'' design deriûed model was superior to the empirical design model in terms of precision and was similar to the model deûeloped from the full dataset. This study suggests optimal design techniques may be useful, eûen when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deûiated from the nominal design.