pwrFDR3.2.4 package

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").