FDR adjustments of Microarray Experiments (FDR-AME)

Purpose This R package adjusts p-values generated in multiple hypothe-ses testing of gene expression data obtained by a microarray experiment. The software applies multiple testing procedures that control the False Discovery Rate (FDR) criterion introduced by Benjamini and Hochberg (1995). It applies both theoretical-distribution-based and resampling-based multiple testing pro-cedures, and presents as output adjusted p-values and p-value plots, as described in Reiner et al (2003). It goes beyond Reiner et al in offering adjustments ac-cording to the adaptive two stage FDR controlling procedures in Benjamini et al (2001, submitted), and in addressing differences in expression between many classes using one-way ANOVA. The False Discovery Rate (FDR) Criterion The FDR is the expected proportion of erroneously rejected null hypotheses among the rejected ones. Consider a family of m simultaneously tested null hypotheses of which m0 are true. For each hypothesis Hi a test statistic is calculated along with the cor-responding p-value Pi. Let R denote the number of hypotheses rejected by a procedure, V the number of true null hypotheses erroneously rejected, and S the number of false hypotheses rejected. Now let Q denote V/R when R>0 and 0 otherwise. Then the FDR is defined as FDR=E(Q). The Linear Step-Up Procedure (BH) This procedure makes use of the ordered p-values P(1)≤... ≤P (m). Denote the corresponding null hypotheses H(1),...,H (m). For a desired FDR level q, the ordered p-value P(i) is compared to the critical value q·i/m. Let k = max { i: P (i) ≤ q ·i/m}. Then reject H(1),...,H (k), if such a k exists. Benjamini and Hochberg (1995) show that when the test statistics are inde-pendent, this procedure controls the FDR at the level q. Actually, the FDR is controlled at level FDR ≤ q·m0/m ≤ q. 1 Benjamini and Yekutieli (2001) further show that FDR ≤ q·m0/m for pos-itively dependent test statistics as well. The technical condition under which the control holds is that of positive regression dependency on each test statistic corresponding the true null hypotheses. Reiner et al (2003) and Reiner (unpub-lished thesis) shows FDR ≤ q for two sided tests under positive and negative correlations