Article ID Journal Published Year Pages File Type
1148434 Journal of Statistical Planning and Inference 2008 12 Pages PDF
Abstract

This paper reviews two types of geometric methods proposed in recent years for defining statistical decision rules based on two-dimensional parameters that characterize treatment effect in a medical setting. A common example is that of making decisions, such as comparing treatments or selecting a best dose, based on both the probability of efficacy and the probability of toxicity. In most applications, the two-dimensional parameter is defined in terms of a model parameter of higher dimension including effects of treatment and possibly covariates. Each method uses a geometric construct in the two-dimensional parameter space based on a set of elicited parameter pairs as a basis for defining decision rules. The first construct is a family of contours that partitions the parameter space, with the contours constructed so that all parameter pairs on a given contour are equally desirable. The partition is used to define statistical decision rules that discriminate between parameter pairs in term of their desirabilities. The second construct is a convex two-dimensional set of desirable parameter pairs, with decisions based on posterior probabilities of this set for given combinations of treatments and covariates under a Bayesian formulation. A general framework for all of these methods is provided, and each method is illustrated by one or more applications.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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