Ch12-sd-rtm-ToM: Extractor function for asymptotic sd[T_m/M_m] under selected...
In pwrFDR: FDR Power

Description Usage Arguments Details Value Author(s) References See Also Examples

A function which extracts the asymptotic standard deviation for the true positive proportion, T_m/M_m, under the selected FDP control method from the supplied pwr object, which is the result of a call to the main function, pwrFDR.

1	sd.rtm.ToM(object)

object

An object of class, pwr, which is the result of a call to the main function, pwrFDR

The true positive proportion (TPP), T_m/M_m, is the proportion of all test statistics distributed according to the alternative that are declared significant by the selected FDP control method. Whereas the ensemble type I error in the multiple testing experiment is handled via control of the distribution of the FDP, V_m/R_m, the ensemble power is optimized via the distribution of the TPP. The most commonly used ensemble power is based upon the expected TPP, or true postive rate, E[TPP], which also called the average power. In situations of just adequate power or near adequate power, especially when testing less than 1000 simultaneous tests or so, the distribution of the TPP will be non-negligiby dispersed and this means that the TPP in a given multiple testing experiment for which sample size was based on the average power will likely not be close to the promised average power. For this reason, it is preferable to use a concept of ensemble power which is based upon the excedance probability for the TPP, or tail probability of the TPP (tp-TPP).

P(TPP > λ) >= 1- ε_{II}

This package uses asymptotic approximation to derive the tp-TPP ensemble power under any one of the avaialbe FDP control methods, BHFDR, BHCLT or Romano.

Returns the asymptotic standard deviation of the true postive proportion, sd[T_m/M_m], as an un-named numeric.

Grant Izmirlian <izmirlig at mail dot nih dot gov>

Izmirlian G. (2020) Strong consistency and asymptotic normality for quantities related to the Benjamini-Hochberg false discovery rate procedure. Statistics and Probability Letters; 108713, <doi:10.1016/j.spl.2020.108713>.

Izmirlian G. (2017) Average Power and λ-power in Multiple Testing Scenarios when the Benjamini-Hochberg False Discovery Rate Procedure is Used. <arXiv:1801.03989>

sd.rtm.Rom sd.rtm.VoR

  rslt.BHFDR  <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15)
  rslt.Auto.1 <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15, N.tests=51,
                       FDP.control.method="Auto")
  rslt.Auto.2 <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15, N.tests=49,
                       FDP.control.method="Auto")

  ## Asymptotic standard deviation under BHFDR
  sdrtmToMBHFDR  <- sd.rtm.ToM(rslt.BHFDR)

  ## Asymptotic standard deviation under BHCLT
  sdrtmToMAuto1 <- sd.rtm.ToM(rslt.Auto.1)

  ## Asymptotic standard deviation under Romano
  sdrtmToMAuto2 <- sd.rtm.ToM(rslt.Auto.2)