pwrFDR (version 3.2.4)

sd.rtm.VoR: Extractor function for asymptotic sd[V_m/R_m] under selected FDP control method

Description

A function which extracts the asymptotic standard deviation for the false discovery proportion, V_m/R_m, under the selected FDP control method from the supplied pwr object, which is the result of a call to the main function, pwrFDR.

Usage

sd.rtm.VoR(object)

Value

Returns the asymptotic standard deviation of the false discovery proportion, sd[V_m/R_m], as an un-named numeric.

Arguments

object

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

Author

Grant Izmirlian <izmirlig at mail dot nih dot gov>

Details

The false discovery proportion (FDP), V_m/R_m, under the selected FDP control method, is the proportion of null distributed test statistics that were deemed significant calls by the FDP control method. The most well known of available FDP methods is the Benjamini-Hochberg False Discovery Rate (BH-FDR) procedure. It ensures that the expected value of the FDP will be less than alpha, E[FDP] < alpha. The other two included FDP control methods, "Romano" and "BHFDX", control the probability that the FDP exceeds a given value, delta:

\(P( V_m/R_m > \delta ) < \alpha\)

In most cases, the choice \(\delta=\alpha\) is appropriate but \(\delta\) is a distinct parameter to allow greater flexibility. The choice "Auto" will select the most appropriate choice from the three, BHFDR, BHFDX and Romano. If the asymptotic standard error, sd.rtm.VoR/m^0.5 is greater than a control parameter (default value 10%), then one of the choices "BHFDX" or "Romano" will be made. As the "Romano" FDP control method is more conservative, there is a preference for the "BHFDX" method, which can be used if the number of simultaneous tests, m, is larger than 50. All of this is handled internally within the function pwrFDR. These extractor functions exist to allow the user 'under the hood'.

References

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 \(\lambda\)-power in Multiple Testing Scenarios when the Benjamini-Hochberg False Discovery Rate Procedure is Used. <arXiv:1801.03989>

Kluger D. M., Owen A. B. (2023) A central limit theorem for the Benjamini-Hochberg false discovery proportion under a factor model. Bernoulli; xx:xxx-xxx.

See Also

sd.rtm.Rom sd.rtm.ToM

Examples

  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
  sdrtmVoRBHFDR  <- sd.rtm.VoR(rslt.BHFDR)

  ## Asymptotic standard deviation under BHFDX
  sdrtmVoRAuto1 <- sd.rtm.VoR(rslt.Auto.1)

  ## Asymptotic standard deviation under Romano
  sdrtmVoRAuto2 <- sd.rtm.VoR(rslt.Auto.2)