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. 2008;18(3):881-904.

SOME STEP-DOWN PROCEDURES CONTROLLING THE FALSE DISCOVERY RATE UNDER DEPENDENCE

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Free PMC article

SOME STEP-DOWN PROCEDURES CONTROLLING THE FALSE DISCOVERY RATE UNDER DEPENDENCE

Yongchao Ge et al. Stat Sin. .
Free PMC article

Abstract

Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the familywise error rate (FWER) in multiple testing problems. Since then, researchers have been increasingly interested in developing methodologies for controlling the FDR under different model assumptions. In a later paper, Benjamini and Yekutieli (2001) developed a conservative step-up procedure controlling the FDR without relying on the assumption that the test statistics are independent.In this paper, we develop a new step-down procedure aiming to control the FDR. It incorporates dependence information as in the FWER controlling step-down procedure given by Westfall and Young (1993). This new procedure has three versions: lFDR, eFDR and hFDR. Using simulations of independent and dependent data, we observe that the lFDR is too optimistic for controlling the FDR; the hFDR is very conservative; and the eFDR a) seems to control the FDR for the hypotheses of interest, and b) suggests the number of false null hypotheses. The most conservative procedure, hFDR, is proved to control the FDR for finite samples under the subset pivotality condition and under the assumption that joint distribution of statistics from true nulls is independent of the joint distribution of statistics from false nulls.

Figures

Figure 1
Figure 1. Different FDR procedures
The independent case: ρ = 0 and δ = 2; the dotted vertical line is x = m1; the dotted horizontal line is y = m0/m, the overall proportion of false null hypotheses. Different panels are for different values of m1 (100, 500, 900).
Figure 2
Figure 2
The negatively dependent case ρ = −0.1 and δ = 1: different FDR procedures and different values of m1 (100, 500, 900).
Figure 3
Figure 3. Apo AI
Plot of FDR adjusted p-values when the top 1, 2, … genes are rejected. We only plot the total number of genes rejected up to 100 among 6,356 genes. The adjusted p-values were estimated using all B = 16!/(8! × 8!) = 12,870 permutations.
Figure 4
Figure 4. Leukemia
Plot of FDR adjusted p-values when the top 1, 2, …, genes among 3,051 ones are rejected. The adjusted p-values were estimated using B = 10,000 random permutations.

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