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Activity Number: 698
Type: Contributed
Date/Time: Thursday, August 4, 2016 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract #320901 View Presentation
Title: Constrained Inference for Double Cone Alternatives
Author(s): Xuechan Li* and Janice McCarthy and Zhiguo Li and Andrew Allen and Kouros Owzar
Companies: Duke University and Duke University and Duke University and Duke University and Duke University
Keywords: constrained inference ; double cone ; geometry ; likelihood ratio test

In medical studies, prior knowledge can often be used to constrain inference to clinically or biologically relevant alternative hypotheses, leading to substantial power gains relative to an unconstrained approach. For example, in cancer pharmacogenomic studies, researchers may be interested in markers for which the gene effect is present only when exposed to drug. Often the space of interesting alternatives can be described by the boundary or closure of a double cone. While single cone alternatives have been well-studied, previous studies of double cone alternatives have been limited to empirical investigations of the type I error. Here we present a detailed treatment of inference for double cone alternatives. We derive explicit mathematical formulas for calculating type I and type II error rates and illustrate how these rates relate to geometric features of the acceptance region. We provide numerical algorithms for approximating the error rates and evaluate their performance through simulations studies.

Authors who are presenting talks have a * after their name.

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