27 research outputs found
Optimal designs for comparing curves
We consider the optimal design problem for a comparison of two regression
curves, which is used to establish the similarity between the dose response
relationships of two groups. An optimal pair of designs minimizes the width of
the confidence band for the difference between the two regression functions.
Optimal design theory (equivalence theorems, efficiency bounds) is developed
for this non standard design problem and for some commonly used dose response
models optimal designs are found explicitly. The results are illustrated in
several examples modeling dose response relationships. It is demonstrated that
the optimal pair of designs for the comparison of the regression curves is not
the pair of the optimal designs for the individual models. In particular it is
shown that the use of the optimal designs proposed in this paper instead of
commonly used "non-optimal" designs yields a reduction of the width of the
confidence band by more than 50%.Comment: 27 pages, 3 figure
Complete classes of designs for nonlinear regression models and principal representations of moment spaces
In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave
sufficient conditions for complete classes of designs for nonlinear regression
models. In this note we demonstrate that there is an alternative way to
validate this result. Our main argument utilizes the fact that boundary points
of moment spaces generated by Chebyshev systems possess unique representations.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1108 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bayesian optimal designs for dose-response curves with common parameters
The issue of determining not only an adequate dose but also a dosing frequency
of a drug arises frequently in Phase II clinical trials. This results in the comparison
of models which have some parameters in common. Planning such studies based on
Bayesian optimal designs offers robustness to our conclusions since these designs,
unlike locally optimal designs, are efficient even if the parameters are misspecified.
In this paper we develop approximate design theory for Bayesian D-optimality for
nonlinear regression models with common parameters and investigate the cases of
common location or common location and scale parameters separately. Analytical
characterisations of saturated Bayesian D-optimal designs are derived for frequently
used dose-response models and the advantages of our results are illustrated via a
numerical investigation
Model Selection versus Model Averaging in Dose Finding Studies
Phase II dose finding studies in clinical drug development are typically
conducted to adequately characterize the dose response relationship of a new
drug. An important decision is then on the choice of a suitable dose response
function to support dose selection for the subsequent Phase III studies. In
this paper we compare different approaches for model selection and model
averaging using mathematical properties as well as simulations. Accordingly, we
review and illustrate asymptotic properties of model selection criteria and
investigate their behavior when changing the sample size but keeping the effect
size constant. In a large scale simulation study we investigate how the various
approaches perform in realistically chosen settings. Finally, the different
methods are illustrated with a recently conducted Phase II dosefinding study in
patients with chronic obstructive pulmonary disease.Comment: Keywords and Phrases: Model selection; model averaging; clinical
trials; simulation stud
Optimal designs for enzyme inhibition kinetic models
In this paper we present a new method for determining optimal designs for
enzyme inhibition kinetic models, which are used to model the influence of the
concentration of a substrate and an inhibition on the velocity of a reaction.
The approach uses a nonlinear transformation of the vector of predictors such
that the model in the new coordinates is given by an incomplete response
surface model. Although there exist no explicit solutions of the optimal design
problem for incomplete response surface models so far, the corresponding design
problem in the new coordinates is substantially more transparent, such that
explicit or numerical solutions can be determined more easily. The designs for
the original problem can finally be found by an inverse transformation of the
optimal designs determined for the response surface model. We illustrate the
method determining explicit solutions for the -optimal design and for the
optimal design problem for estimating the individual coefficients in a
non-competitive enzyme inhibition kinetic model
Optimal designs for active controlled dose finding trials with efficacy-toxicity outcomes
Nonlinear regression models addressing both efficacy and toxicity outcomes
are increasingly used in dose-finding trials, such as in pharmaceutical drug
development. However, research on related experimental design problems for
corresponding active controlled trials is still scarce. In this paper we derive
optimal designs to estimate efficacy and toxicity in an active controlled
clinical dose finding trial when the bivariate continuous outcomes are modeled
either by polynomials up to degree 2, the Michaelis- Menten model, the Emax
model, or a combination thereof. We determine upper bounds on the number of
different doses levels required for the optimal design and provide conditions
under which the boundary points of the design space are included in the optimal
design. We also provide an analytical description of the minimally supported
-optimal designs and show that they do not depend on the correlation between
the bivariate outcomes. We illustrate the proposed methods with numerical
examples and demonstrate the advantages of the -optimal design for a trial,
which has recently been considered in the literature.Comment: Keywords and Phrases: Active controlled trials, dose finding, optimal
design, admissible design, Emax model, Equivalence theorem, Particle swarm
optimization, Tchebycheff syste