Viatcheslav B. Melas

Optimal Design for Goodness-of-Fit of the Michaelis–Menten Enzyme Kinetic Function

We construct efficient designs for the Michaelis–Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis–Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis–Menten model against the EMAX model by maximizing a minimum of the D or D1 efficiencies taken over a range of values for the nonlinear parameters. In particular, we show that such designs are (a) efficient for estimating parameters in the EMAX model, (b) about 70% efficient for estimating parameters in the Michaelis–Menten model, (c) efficient for testing the Michaelis–Menten model against the EMAX model, and (d) robust with respect to misspecification of the unknown parameters in the nonlinear model.

Optimal designs for exponential regression

This paper is concerned with the optimal design problem for the particular case of non-linear parametrisation:the parameters to be estimated are included in exponents.Some properties of locally optimal designs as functions of estimated parameters are investigated and a table of such designs in given.We consider also designs to be optimal in the sense of minimax approach.

Optimal Designs for a Class of Nonlinear Regression Models

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f 0 ≡ 0 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational, logistic and exponential models and for the rational regression models the E- and c-optimal design problem is solved explicitly in many cases.

Standardized Maximin E-optimal Designs for the Michaelis Menten Model

In the Michaelis-Menten model we determine efficient designs by maximizing a minimum of standardized

Optimal designs for estimating individual coefficients in polynomial regression—a functional approach

E

Locally E-optimal designs for exponential regression models

-efficiencies. It is shown in many cases that optimal designs are supported at only two points and that the support points and corresponding weights can be characterized explicitly. Moreover, a numerical study indicates that two point designs are usually very efficient, even if they are not optimal. Some practical recommendations for the design of experiments in the Michaelis-Menten model are given.

T-optimal designs for discrimination between two polynomial models

Abstract In this paper the optimal design problem for the estimation of the individual coefficients in a polynomial regression on an arbitrary interval [a,b] (−∞ is considered. Recently, Sahm (Ann. Statist. 2000, accepted for publication) demonstrated that the optimal design is one of four types depending on the symmetry parameter s ∗ =(a+b)/(a−b) and the specific coefficient which has to be estimated. In the same paper the optimal design was identified explicitly in three cases. It is the basic purpose of the present paper to study the remaining open fourth case. It will be proved that in this case the support points and weights are real analytic functions of the boundary points of the design space. This result is used to provide a Taylor expansion for the weights and support points as functions of the parameters a and b, which can easily be used for the numerical calculation of the optimal designs in all cases, which were not treated by Sahm (Ann. Statist. 2000, accepted for publication).

D-optimal designs for trigonometric regression models on a partial circle

In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two results. First we consider the limit ?i ? ? and show that the optimal designs converge weakly to the optimal designs in a heteroscedastic polynomial regression model. It is then demonstrated that in this model the optimal designs can be easily determined by standard numerical software. Secondly, it is proved that the support points and weights of the locally optimal designs in the exponential regression model are analytic functions of the nonlinear parameters ?1, . . . , ?k. This result is used for the numerical calculation of the locally E-optimal designs by means of a Taylor expansion for any vector (?1, . . . , ?k). It is also demonstrated that in the models under consideration E-optimal designs are usually more efficient for estimating individual parameters than D-optimal designs.

Robust T-optimal discriminating designs

This paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree

Optimal design of experiments with simulation models of nearly saturated queues

n-2