Optimal Designs for a Probit Model With a Quadratic Term
This article studies optimal designs to analyze dose-response functions with a downturn. Two interesting challenges are estimating the entire dose-response curve and estimating the ED50. Here, I…
Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size
In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are…
Two stage adaptive optimal design with applications to dose-finding clinical trials
It is shown that the distribution of the maximum likelihood estimates converges to a scale mixture family of normal random variables in such cases as a result of a small pilot study of fixed size being followed by a much larger experiment.
The Effects of Adaptation on Inference for Non-Linear Regression Models with Normal Errors
In this work, we assume that a response variable is explained by several controlled explanatory variables through a non-linear regression model with normal errors. The unknown parameter is the vector…
SHOWING 1-10 OF 29 REFERENCES
A geometric characterization of c-optimal designs for heteroscedastic regression
We consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the…
A note on Bayesian c- and D-optimal designs in nonlinear regression models
We present a version of Elfving's theorem for the Bayesian D-optimality criterion in nonlinear regression models. The Bayesian optimal design can be characterized as a design which allows a…
The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non‐Linear Problems
Optimal experimental designs for non-linear problems depend on the values of the underlying undknown parameters in the model. For various reasons there is interest in providing explicit formulae for…
Bayesian D-Optimal and Model Robust Designs in Linear Regression Models
- Mathematics, Computer Science
A version of Elfving's Theorem is proved for a model robust Bayesian c-optimality criterion and sufficient conditions on the precision matrices of the prior distribution are found that the Bayesian D-optimal and the classical optimal design are supported at the same set of points or are identical.
Optimal designs for the emax, log-linear and exponential models
We derive locally D- and ED p -optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and ED p -optimal designs are supported at the same set…
Optimal Designs on Tchebycheff Points
0. Summary. Kiefer and Wolfowitz (1959) proved that the optimal design for estimating the highest coefficient in polynomial regression is supported by certain Tchebycheff points. Hoel and Levine…
Optimal Experimental Design for Polynomial Regression
Abstract The problem of choosing the optimal design to estimate a regression function which can be well-approximated by a polynomial is considered, and two new optimality criteria are presented and…
Approximate Dynamic Programming and Its Applications to the Design of Phase I Cancer Trials
- Computer Science
The resulting design is a convex combination of a "treatment" design and a "learning" design, thus directly address- ing the treatment versus experimentation dilemma inherent in Phase I trials and providing a simple and intuitive design for clinical use.
Gustav Elfving's Impact on Experimental Design
Among other results, this paper demonstrated that, asymptotically, locally optimal designs for estimating one parameter require the use of no more than k of the available experiments, when the distribution of the data from these experiments involves k unknown parameters.