Ch19-CDF-Pval-au-eq-u: Function which solves the implicit equation u = G( u alpha)

In pwrFDR: FDR Power

Function which solves the implicit equation u = G( u alpha)

Description

Function which solves the implicit equation u = G( u alpha) where G is the pooled P-value CDF and alpha is the FDR

Usage

  CDF.Pval.au.eq.u(effect.size, n.sample, r.1, alpha, groups, type, 
                   grpj.per.grp1, distopt, control)
  

Arguments

effect.size	The per statistic effect size
n.sample	The per statistic sample size
r.1	The proportion of Statistics distributed according to the alternative distribution
alpha	The false discovery rate.
groups	Number of experimental groups from which the test statistic is calculated
type	A character string specifying, in the groups=2 case, whether the test is 'paired', 'balanced', or 'unbalanced' and in the case when groups >=3, whether the test is 'balanced' or 'unbalanced'. The default in all cases is 'balanced'. Left unspecified in the one sample (groups=1) case.
grpj.per.grp1	Required when type="unbalanced", specifies the group 0 to group 1 ratio in the two group case, and in the case of 3 or more groups, the group j to group 1 ratio, where group 1 is the group with the largest effect under the alternative hypothesis.
distopt	Test statistic distribution in among null and alternatively distributed sub-populations. distopt=0 gives normal (2 groups), distop=1 gives t- (2 groups) and distopt=2 gives F- (2+ groups)
control	Optionally, a list with components with the following components: 'groups', used when distop=3 (F-dist), specifying number of groups. 'max.iter' is an iteration limit, set to 1000 by default

Value

A list with a single component,

gamma

The solution of the implicit equation u = G( u alpha), where G is the pooled P-value CDF. This represents the infinite tests limiting proportion of hypothesis tests that are called significant by the BH-FDR procedure at alpha.

Author(s)

Grant Izmirlian <izmirlian at nih dot gov>

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>

Jung S-H. (2005) Sample size for FDR-control in microarray data analysis. Bioinformatics; 21:3097-3104.

Liu P. and Hwang J-T. G. (2007) Quick calculation for sample size while controlling false discovery rate with application to microarray analysis. Bioinformatics; 23:739-746.

See Also

CDF.Pval.apsi.eq.u

Examples

  ## An example showing that the Romano method is more conservative than the BHFDX method
  ## which is in turn more conservative than the BH-FDR method based upon ordering of the
  ## significant call proportions, R_m/m

  ## First find alpha.star for the BH-CLT method at level alpha=0.15
  a.st.BHFDX <-controlFDP(effect.size=0.8,r.1=0.05,N.tests=1000,n.sample=70,alpha=0.15)$alpha.star

  ## now find the significant call fraction under the BH-FDR method at level alpha=0.15
  gamma.BHFDR <- CDF.Pval.au.eq.u(effect.size = 0.8, n.sample = 70, r.1 = 0.05, alpha=0.15)

  ## now find the significant call fraction under the Romano method at level alpha=0.15
  gamma.romano <- CDF.Pval.apsi.eq.u(effect.size = 0.8, n.sample = 70, r.1 = 0.05, alpha=0.15)

  ## now find the significant call fraction under the BH-CLT method at level alpha=0.15
  gamma.BHFDX <- CDF.Pval.au.eq.u(effect.size = 0.8, n.sample = 70, r.1 = 0.05, alpha=a.st.BHFDX)

pwrFDR documentation built on April 11, 2025, 5:47 p.m.