JSM 2005 Online Program

Abstract #303462

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Activity Number:	135
Type:	Contributed
Date/Time:	Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor:	IMS
Abstract - #303462
Title:	Sharp Simultaneous Intervals for the Means of Selected Populations with Application to Microarray Data Analysis
Author(s):	Jing Qiu*+
Companies:	University of Missouri, Columbia
Address:	134I Middlebush Hall, Columbia, MO, 65211, United States
Keywords:	Empirical Bayes approach ; mixed effect models ; inference after selection ; Bonferroni's simultaneous intervals ; differential expression
Abstract:	Simultaneous inference is a challenge when the number of populations, N, or the dimensionality is large. In some situations, including microarray experiments, the scientists are interested in only the K populations with parameters (such as means) that have the most extreme estimates. In these cases, can we construct simultaneous intervals for the means corresponding to these K selected populations? The answer is yes as demonstrated here, and the approach allows us to cut down the dimensionality of the problem from N to K. The naïve simultaneous intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an Empirical Bayes approach (or an approach based on the mixed effect model) and construct simultaneous intervals with good coverage probabilities. For N=10,000 and K=100, typical for microarray data, the lengths of our intervals could be 82% shorter than those of the Bonferroni's N-dimensional simultaneous intervals and 77% shorter than those of the naive K-dimensional simultaneous intervals.

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