mafdr: Interpreting Q values vs. BHFDR adjusted p-values

Question

Kevin Casey 2014-7-30

4
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https://ww2.mathworks.cn/matlabcentral/answers/144113-mafdr-interpreting-q-values-vs-bhfdr-adjusted-p-values

编辑： Walter Roberson 2021-12-16

Using mafdr to produce false discovery rate adjusted Q values from lists of p-values has been working well for me with large datasets. The adjusted values appear reasonable. However, with very small datasets the Q values produced can be smaller than the initial p-values - particularly if many of the p-values are small. This seems wrong. As Q values are interpreted as p-values adjusted for the false discovery rate, shouldn't they always be larger than the initial p-value?

e.g.

if true
  >> P

P =

0.0162 0.0322 0.0888 0.0495 0.0507 0.1583

>> [FDR, Q]=mafdr(P)

FDR =

0.0023 0.0023 0.0025 0.0023 0.0018 0.0037

Q =

    0.0018    0.0018    0.0025    0.0018    0.0018    0.0037
end

A workaround for this is the 'BHFDR' option, which produces resonable looking adjustments to the p-values. It appears to use a different procedure to calculate the values

if true
 >> mafdr(P,'BHFDR', true)

ans =

    0.0761    0.0761    0.1065    0.0761    0.0761    0.1583
  end

Does anyone know why this occurs? Am I misinterpreting the meaning of the Q values? Should I switch over entirely to the 'BHFDR' procedure for both large and small datasets? Best regards, Kevin

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Pearl 2019-5-16

Thank you Kevin! This is very useful!

Mango Wang 2019-8-19

@Samaneh, They are quite similar. Based on my dataset, I calculate the correlation between fdr and q, The result is 1.

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Answer 1

Mango Wang 2019-8-19

0
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https://ww2.mathworks.cn/matlabcentral/answers/144113-mafdr-interpreting-q-values-vs-bhfdr-adjusted-p-values#answer_388114

编辑：Walter Roberson 2021-12-16

It seems FDR is suitable for the case when the dataset/hypothesis is very large due to the principle of the inherent method. https://www.mailman.columbia.edu/research/population-health-methods/false-discovery-rate check here for reference.