pwrFDR - FDR Power
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,
"<doi:10.1016/j.spl.2020.108713>", and an applied paper
describing the methodology with a simulation study is in
preparation. See citation("pwrFDR").
