D-Optimality for Regression Designs: A Review

Optimal design of sampling schedules for studying glucose kinetics with tracers

Minimum size sampling schedules for estimating glucose kinetic parameters from an impulsive (bolus) tracer injection in normal humans and rats are presented. Glucose kinetics are described by a two-compartment linear model, and reference values of the parameters are estimated from a data base with many samples. The optimal sampling schedule (OSS) is determined in each individual by using a D-optimal criterion and consists of four samples. A population optimal sampling schedule (POSS) applicable to all the individuals of a given population is then determined, and its reliability and efficiency in recovering kinetic parameters (e.g., rate constants, plasma clearance rate, and mean residence time) is assessed. The influence of model and measurement error on OSS is discussed. Moreover, the adoption of an enhanced POSS (EPOSS, 8 samples) is shown to improve accuracy and precision of parameter estimates in a predictable manner. Finally some suggestions are given for obtaining more information from turnover studies using a constant infusion of tracer, with or without a priming pulse of tracer.

Experimental design optimisation: theory and application to estimation of receptor model parameters using dynamic positron emission tomography

The general framework and various criteria for experimental design optimisation are presented. The methodology is applied to the estimation of receptor-ligand reaction model parameters with dynamic positron emission tomography data. The possibility of improving parameter estimation using a new experimental design combining an injection of the beta+-labelled ligand and an injection of the cold ligand is investigated. Numerical simulations predict a remarkable improvement in the accuracy of the parameter estimates with this new experimental design and particularly the possibility of separate estimations of the association constant (k+1) and of the receptor density (B'max) in a single experiment. Simulation predictions are validated using experimental PET data in which parameter uncertainties are reduced by factors ranging from 17 to 1000.

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. I. Homologous and heterologous binding to one or two classes of sites

We have developed a versatile computer program for optimization of ligand binding experiments (e.g., radioreceptor assay system for hormones, drugs, etc.). This optimization algorithm is based on an overall measure of precision of the parameter estimates (D-optimality). The program DESIGN uses an exact mathematical model of the equilibrium ligand binding system with up to two ligands binding to any number of classes of binding sites. The program produces a minimal list of the optimal ligand concentrations for use in the binding experiment. This potentially reduces the time and cost necessary to perform a binding experiment. The program allows comparison of any proposed experimental design with the D-optimal design or with assay protocols in current use. The level of nonspecific binding is regarded as an unknown parameter of the system, along with the affinity constant (Kd) and binding capacity (Bmax). Selected parameters can be fixed at constant values and thereby excluded from the optimization algorithm. Emphasis may be placed on improving the precision of a single parameter or on improving the precision of all the parameters simultaneously. We present optimal designs for several of the more commonly used assay protocols (saturation binding with a single labeled ligand, competition or displacement curve, one or two classes of binding sites), and evaluate the robustness of these designs to changes in parameter values of the underlying models. We also derive the theoretical D-optimal design for the saturation binding experiment with a homogeneous receptor class.

Confidence intervals for multiple-dose concentrations in the one-compartment open model with rapid intravenous injection

The parameters in a multiple-dose compartmental model can be estimated from plasma concentration observations after a single dose of drug. These estimates can be used to obtain confidence intervals for the multiple-dose concentrations. However, since the models are non-linear functions of the parameters, no exact confidence interval procedures are available. In this paper a conservative interval estimation procedure is applied to the one-compartment open model with rapid intravenous injection. Also, extended tables required in the estimation procedure are provided.