Title: Control of 2d-fdr by combining two univariate multiple testing results with application to mass spectral data
Authors: Jaesik Jeong - Chonnam National University (Korea, South) [presenting]
Abstract: The mass spectral data feature high dimension with small number of signals (peaks) and many noisy observations. This unique aspect of mass spectral data motivates the problem on testing of many composite null hypotheses simultaneously. 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 (bivariate) composite null hypothesis, the intersection-type and the union-type null, are considered; a different procedure is proposed for each type. The new procedures (for both types of composite null hypotheses) are in two stages. 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 (2d-fdr). We numerically compare the performance of our procedure (for the union-type composite null) to the existing 2d-fdr under various settings. We then apply the procedure to the problem of differentiating origins of herbal medicine using gas chromatography-mass spectrometry (GC-MS).