I've been using the R package
qvalue to estimate q-values based on p-values, and in most cases I have been observing results consistent with what one would expect from multiple testing correction.
However, in one particular instance,
qvalue appears to estimate a strangely low
pi0est (the estimate of the proportion of true null hypotheses). This vector of p-values is as follows (rounded):
0.014 0.424 0.249 0.706 0.705 0.502 0.359 0.830 0.695 0.447
pi0est in this instance is 0.033, while the corresponding q-values are (rounded): 0.004 0.026 0.0260 0.026 0.026 0.026 0.026 0.026 0.026 0.027
I am aware that q-values can in some cases be lower than the corresponding p-value, however in this instance I feel that the decrease is far too low to be justifiable. This can be seen in the following plot of q-values (y-axis) vs p-values (x-axis). Further, I don't understand how such a relatively uniform distribution of p-values can lead to such a small
pi0 and FDR.