We consider the problem
of experimental design when the response is modeled by a generalized linear
model (GLM) and the experimental plan can be determined sequentially. Most
prior research on this problem has been limited to the case of one-factor,
binary response experiments, which are encountered in dose-response
studies and sensitivity testing. We suggest a new procedure for the sequential
choice of observations, that improves on existing methods in four important
ways:

(1) It can be applied to multi-factor
experiments and is not limited to the one-factor setting;

(2) It can be used with any GLM, not
just binary responses;

(3) Both fully sequential and group
sequential settings are treated; and

(4) The experimenter is not constrained
to specify a single model and can use the prior to reflect uncertainty as to
the link function and the form of the linear predictor.

Our procedure is based
on a D-optimality criterion, and on a Bayesian analysis that exploits a
discretization of the parameter space to efficiently represent the posterior
distribution. In the one-factor setting, a simulation study shows that our
method is superior in efficiency to commonly used procedures, such as
the"Bruceton" test (Dixon and Mood, 1948), the Langlie (1965) test or
Neyer's (1994) procedure. We also present a comparison of results obtained
with the new algorithm versus the "Bruceton" method on an actual
sensitivity test conducted recently at an industrial plant.

Publication

Hovav A. Dror and David
M. Steinberg (2008). Sequential
Experimental Designs for Generalized Linear Models, *
Journal of the American Statistical Association, * **103**, 288-298.

Source Code for
algorithms and Examples

Source code is written on MATLAB and requires the Statistical Toolbox. Most of the files are given in two versions: “regular” and “auto”. When the name of the file includes “auto”, the file demonstrates the algorithm by running automatically, with observations randomized in accordance to a chosen “true” reality. The “regular” files require the user to either accept or change the algorithm’s recommendation for the location of the next observation(s), and then to enter the outcome of the observation.

Most files require the files: GLMDAUG.m, canddaugm.m and InfoMtrxGLM.m.

Sensitivity Test. This source code is the
choice for “dose-response” experiments and “sensitivity tests”, and utilizes
the example from section 4.1 of the paper. Files: SensitivityTest.m,
SensitivityTestAUTO.m, Screenshot: SensitivityTestScreenshot.jpg

Extension to multivariate cases, as in section 4.3, is
provided here: MultivariateTest.m, MultivariateTestAUTO.m

Extension to Group Sequential multivariate design, as in
section 4.4, is provided here: GroupSequential.m,
GroupSequentialAUTO.m

Extension for a Poisson response model,
with different possible models (with and without interactions) is provided
here: TwoModelsAndPoissonSequential.m,
TwoModelsAndPoissonSequentialAuto.m

Bayesian analysis
is utilized within all these files, but can also be found here

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