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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