  OGTT is a common test, frequently used to diagnose insulin resistance or
diabetes, in which a patient's blood sugar is measured at various times over
the course of a few hours. Recent developments in the study of OGTT results
have framed it as an inverse problem which has been the subject of Bayesian
inference. This is a powerful new tool for analyzing the results of an OGTT
test,and the question arises as to whether the test itself can be improved. It
is of particular interest to discover whether the times at which a patient's
glucose is measured can be changed to improve the effectiveness of the test.
The purpose of this paper is to explore the possibility of finding a better
experimental design, that is, a set of times to perform the test. We review the
theory of Bayesian experimental design and propose an estimator for the
expected utility of a design. We then study the properties of this estimator
and propose a new method for quantifying the uncertainty in comparisons between
designs. We implement this method to find a new design and the proposed design
is compared favorably to the usual testing scheme.
