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Limitations of Global FDR Less likely to be false positive Global FDR 0 More likely to be false positive threshold rejection region 1 Single hypothesis testing P-values Global FDR method • cannot associate the corrected significance with each hypothesis testing • cannot distinguish p-values that are close to the threshold and those that are not How to assess to each feature its own measure of significance ? Storey and Tibshirani method 2001 q value = mˆ 0 Pi Ri • Pi is the p value of the ordered gene i, Ri is the total number of rejected genes whose p-values are less than the threshold t=Pi and m̂0 Is an estimate of the total number of non-differentially expressed genes, m0 • the q-value tries to attach each feature with a significance measure • the q-value does not estimate the probability of the feature to be false positive Local FDR introduced by Efron 2004 lFDR (t ) Pr( H 0 | T t ) H = 0 if the null hypothesis H0 is true (non-differential) T is the test statistic considered for all hypotheses T = t, a particular value of the test statistic Local FDR Definition f 0(t ) lFDR (t ) 0 f (t ) 0 Pr( H 0) f (t ) 0 f 0(t ) (1 0) f 1(t ) H = 0 if the null hypothesis H0 is true (non-differential) f0, f1 is the conditional density function corresponding to null hypothesis and alternative hypothesis, respectively Different lFDR methods through different estimations of π0, f0 and f Efron’s Aubert et al Sheid & Sprang’s Broberg’s Dalmasso et al 2004 2004 2004 2005 2007 restricted to π0 > 90% yields an estimator of large variance computational extensive can substantially underestimate lFDR efficient and also compute gFDR Different lFDR methods Efron’s Aubert et al Sheid & Sprang’s J. Am. Stat Assoc 2004, 99:96 BMC Bioinformatics 2004, 5:125 IEEE Transactions on computational biology and Bioinformatics 2004, 1:98 Broberg’s Dalmasso et al BMC Bioinformatics 2005, 6:199 BMC Bioinformatics 2007, 8:229