Description
Computing Average and TPX Power under various BHFDR type sequential
procedures. All of these procedures involve control of some summary of the
distribution of the FDP, e.g. the proportion of discoveries which are false
in a given experiment. The most widely known of these, the BH-FDR procedure,
controls the FDR which is the mean of the FDP. A lesser known procedure, due
to Lehmann and Romano, controls the FDX, or probability that the FDP exceeds
a user provided threshold. This is less conservative than FWE control
procedures but much more conservative than the BH-FDR proceudre. This
package and the references supporting it introduce a new procedure for
controlling the FDX which we call the BH-FDX procedure. This procedure
iteratively identifies, given alpha and lower threshold delta, an alpha*
less than alpha at which BH-FDR guarantees FDX control. This uses
asymptotic approximation and is only slightly more conservative than the
BH-FDR procedure. Likewise, we can think of the power in multiple testing
experiments in terms of a summary of the distribution of the True Positive
Proportion (TPP), the portion of tests truly non-null distributed that are
called significant. The package will compute power, sample size or any other
missing parameter required for power defined as (i) the mean of the TPP
(average power) or (ii) the probability that the TPP exceeds a given value,
lambda, (TPX power) via asymptotic approximation. All supplied theoretical
results are also obtainable via simulation. The suggested approach is to
narrow in on a design via the theoretical approaches and then make final
adjustments/verify the results by simulation. The theoretical results are
described in Izmirlian, G (2020) Statistics and Probability letters,
"", and an applied paper describing the
methodology with a simulation study is in preparation.
See citation("pwrFDR").