Sergei L. Leonov

OPTIMAL POPULATION DESIGNS FOR PK MODELS WITH SERIAL SAMPLING

ABSTRACT In various pharmaceutical applications, repeated measurements are taken from each subject, and model parameters are estimated from the collected data. Examples include dose response modeling and PK/PD studies with serial blood sampling, among others. The quality of the information in an experiment is reflected in the precision of estimates of model parameters, which is traditionally measured by their variance–covariance matrix. In this article, we concentrate on the example of a clinical PK study where multiple blood samples are taken for each enrolled patient, which leads to nonlinear mixed effects regression models with multiple responses. The sampling scheme for each patient is considered a multidimensional point in the space of admissible sampling sequences. We demonstrate how to optimize the precision of parameter estimates by finding the best number and allocation of sampling times. It is shown that a reduced number of samples may be taken without significant loss of precision of parameter estimates. Moreover, our approach allows for taking experimental costs into account, which leads to a more meaningful comparison of sampling schemes and to potential cost savings.

Optimal Design of Dose Response Experiments: A Model-Oriented Approach*

We discuss optimal experimental design issues for nonlinear models arising in dose response studies. The optimization is performed with respect to various criteria which depend on the Fisher information matrix. Special attention is given to models with a variance component that depends on unknown parameters.

An Adaptive Optimal Design for the E max Model and Its Application in Clinical Trials

A project team working on a compound to treat Alzheimers disease is carrying out a first-time-in-human dose-escalation study in patients. The team wished to maximize the efficiency of the study by using doses targeted at maximizing information about the dose-response relationship within certain safety constraints. We have developed an adaptive optimal design tool to recommend doses when the response follows an E max model, with functionality for pretrial simulation and in-stream analysis. We present the results of a simulation to investigate the operating characteristics of the applied algorithm.

Parameter Estimation for Models with Unknown Parameters in Variance

Abstract We discuss estimation methods for multiresponse models with a variance matrix that depends on unknown parameters. An iterated estimator is proposed that is asymptotically equivalent to a maximum likelihood estimator. Numerically, this estimator is close to the iteratively reweighted least squares method. However, in the situations when the information contained in the variance component is significant, the new iterated estimator outperforms the traditional iteratively reweighted estimator. The performance of the various numerical procedures is illustrated in the simulation study.

Optimal Design of Pharmacokinetic Studies Described by Stochastic Differential Equations

Pharmacokinetic (PK) studies with serial sampling which are described by compartmental models are discussed. We focus on intrinsic variability induced by the noise terms in stochastic differential equations (SDE). For several models of intrinsic randomness, we find explicit expressions for mean and covariance functions of the solution of the system of SDE. This, in turn, allows us to construct optimal designs, i.e. find sequences of sampling times that guarantee the most precise estimation of unknown model parameters. The performance of optimal designs is illustrated with several examples, including cost-based designs.

Pharmacokinetic Studies Described by Stochastic Differential Equations: Optimal Design for Systems with Positive Trajectories

In compartmental pharmacokinetic (PK) modelling, ordinary differential equations (ODE) are traditionally used with two sources of randomness: measurement error and population variability. In this paper we focus on intrinsic (within-subject) variability modelled with stochastic differential equations (SDE), and consider stochastic systems with positive trajectories which are important from a physiological perspective. We derive mean and covariance functions of solutions of SDE models, and construct optimal designs, i.e. find sampling schemes that provide the most precise estimation of model parameters under cost constraints.

Population Pharmacokinetic Measures, Their Estimation and Selection of Sampling Times

In pharmacokinetic (PK) studies, including bioavailability assessment, various population PK measures, such as area under the curve (AUC), maximal concentration (C max ) and time to maximal concentration (T max ) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model are estimated and the explicit formulae for PK measures are used, and a model-independent approach, where numerical integration algorithms are used for AUC and sample estimates for C max and T max . Since regulatory agencies usually require the model-independent estimation of PK measures, we focus on the empirical approach while using the model-based approach and corresponding measures as a benchmark. We show how to “split” a single sampling grid into two or more subsets, which substantially reduces the number of samples taken for each patient, but often has little effect on the precision of estimation of PK measures in terms of mean squared error (MSE). We give explicit formulae for the MSE of the empirical estimator of AUC for a simple example and discuss how costs may be taken into account.

Component-wise dimension reduction

Principal components methods and factor analysis are popular tools for the dimension-reduction problem. These techniques can be used to obtain a smaller number of new variables. However, the new variables may include all or most of the original variables. In this study, two methods are given which will select the most informative subset of variables from the variables which are directly measured. The different approaches are compared in a concluding example.

Discussion of the “White Paper of the PhRMA PISC Working Group on Adaptive Dose-Ranging Designs”

First, I would like to thank the authors for putting together this important survey paper. They have covered a wide range of methods that are applied in dose ranging studies, with the emphasis on model-based techniques, from Bayesian modeling to multiple comparison-modeling approach to model-based optimal designs to nonparametric estimation techniques. These methods are of personal interest to me and I expect that the paper will generate a lot of interest from the readers of the journal. Still there is one specific area which, in my opinion, should have been covered in more detail – namely, what the authors call “D-optimal response-adaptive”, or “Dopt approach”. I understand that the authors address a variety of methods, and the goals of this paper are different from providing a comprehensive review of each method. However a complete lack of references on optimal model-based designs seems rather strange.