Control of Two-Dimensional False Discovery Rate by Combining Two Univariate Multiple Testing Results with Application to Mass Spectral Data

• Activity Number: 187 - Contributed Poster Presentations: Korean International Statistical Society
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Jaesik Jeong* and Johan Lim and Yongrae Kim and Jong Soo Lee
• Companies: and Seoul National University and Seoul National University and University of Massachusetts
• Keywords: Benferroni rule; composite hypothesis; intersection/union null; mass spectral data; two-dimensional false discovery rate; two-stage procedure

Abstract

The mass spectral data feature high dimension with small number of signals and many noisy observations. This unique aspect of mass spectral data motivates the problem on testing of many composite null hypotheses simultaneously. In this paper, we develop new procedures to control the false discovery rate of the simultaneous multiple hypothesis testing of many bivariate composite null hypotheses. Two types of composite null hypothesis, the intersection-type and the union-type null, are considered; different procedure is proposed for each type. The new procedures are in two stage. In the first stage, we test simultaneously each univariate simple hypotheses of bivariate composite hypotheses at the pre-decided false discovery rate, and in the second stage, we combine the marginal univariate test results so that the two-dimensional false discovery rate for the bivariate composite null hypotheses is less than alpha, the aimed level. The new procedure provides a closed form decision rule on bivariate test statistics, unlike the existing two-dimensional local false discovery rate. We numerically compare the performance of our procedure to the existing 2d-fdr under various settings.