Understanding False Discovery Rate and q-values

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Notes

• Define pval and how it controls for FPR

• Define qval and how it controls for FDR

• P val is V/m0 because its the prop of false positives under the Ho, i.e. among null tests! Not among true alternative tests.

• The pval not the qval is not the probability of being FP.

• Comparison of pvals vs qvalues: less signif ones but less FPs when cutoff at qval

• Explain how the the qvalue is computed from the pvalue and its interpretation from R code, is it equivalent to BH method?

Sources

• Storey paper

• qvalue documentation

• p.adjust BH methd, how are pvals adjusted? is it the same as qith qvalue?

Code

Let’s generate a list of p-values from the standard normal distribution

# p <- pnorm(c(rnorm(20), rnorm(5, mean = 5)), lower.tail = F)
# 
# ## Number of tests
# m <- length(p)
# 
# ## Index of test i (= number of tests declared significant i.e. with p<=pi)
# i <- m:1
# o <- order(p, decreasing = TRUE)
# ro <- order(o)
# 
#  qvals <- pi0s$pi0 * pmin(1, cummin(p[o] * m /i ))[ro]