Title
Confidence Sets in Genetics and Toxicology
Speaker
James Rogers, Department of Statistics, Ohio State University
Abstract
We consider two problems where a multiple action / confidence set framework is desirable, but traditional approaches have tested only a universal point null hypothesis. The two action (accept / reject) inferences available from the traditional formulation are not particularly informative.
Our first example arises from a common genetic linkage experiment known as the phase unknown double backcross. In this context, we construct a confidence set which is guaranteed (with probability 1-alpha) to contain the locus of the trait gene if such a gene exists, but also has a high probability of being empty if the trait is not genetic. We explain why construction of this confidence set does not require adjustment for multiplicity, even if an infinite number of markers are tested.
We also consider a non-inferiority problem from toxicology, where the response is taxonomic diversity as measured by Simpson's Index. We take advantage of marginal Edgeworth Expansions to construct a confidence set which is guaranteed (with probability 1-alpha) to include all unsafe doses, but also has a high probability of being empty if all doses are sufficiently safe.
