Ch29-backsolve-seFDPoalpha: Find missing argument giving required se[FDP]/alpha (or...

In pwrFDR: FDR Power

Find missing argument giving required se[FDP]/alpha (or se[TPP]/average.power)

Description

backsolve.seFDPoalpha finds the missing argument, one of 'N.tests', 'r.1', 'n.sample' or 'effect size' giving the specified value of se[FDP]/alpha under the BH-FDR procedure.

backsolve.seTPPoavgpwr finds the missing argument, one of 'N.tests', 'r.1', 'n.sample' or 'effect size' giving the specified value of se[TPP]/average.power under the BH-FDR procedure.

Usage

backsolve.seFDPoalpha(seFDPoalpha, effect.size, n.sample, r.1, alpha, groups = 2, N.tests,
                      type = "balanced", grpj.per.grp1 = 1, distopt = 1, rho, k.bs)

backsolve.seTPPoavgpwr(seTPPoavgpwr, effect.size, n.sample, r.1, alpha, groups = 2,
                       N.tests, type = "balanced", grpj.per.grp1 = 1, distopt = 1, rho,
                       k.bs)

Arguments

seFDPoalpha	In backsolve.seFDPoalpha, the user specified value of se[FDP]/alpha
seTPPoavgpwr	In backsolve.seTPPoavgpwr, the user specified value of se[TPP]/average.power
effect.size	The effect size (mean over standard deviation) for test statistics having non-zero means. Assumed to be a constant (in magnitude) over non-zero mean test statistics.
n.sample	The number of experimental replicates. Required for calculation of power
r.1	The proportion of simultaneous tests that are non-centrally located
alpha	The false discovery rate (in the BH case) or the upper bound on the probability that the FDP exceeds delta (BHFDX and Romano case)
groups	The number of experimental groups to compare. Must be integral and >=1. The default value is 2.
N.tests	The number of simultaneous hypothesis tests.
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)
rho	This can be done under the assumption of tests that are correlated identically in pair within blocks of given size.
k.bs	When 'rho' is specified, the common block-size for correlated test statistics.

Value

A numeric vector having components

<missing argument>	Value of missing argument giving required se[FDP]/alpha (backsolve.seFDPoalpha) or se[TPP]/average.power (backsolve.seTPPoavgpwr).
average.power	The average power at the given set of conditions
se.VoR/se.ToM	The standard error of the FDP (backsolve.seFDPoalpha) or standard error of the TPP (backsolve.seTPPoavgpwr).
value	Value returned by the solver. Should be near zero if a solution was found.

Author(s)

Grant Izmirlian Jr <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.

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.

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.

Lehmann E. L., Romano J. P.. Generalizations of the familywise error rate. Ann. Stat.. 2005;33(3):1138-1154.

Romano Joseph P., Shaikh Azeem M.. Stepup procedures for control of generalizations of the familywise error rate. Ann. Stat.. 2006;34(4):1850-1873.

Examples

backsolve.seFDPoalpha(seFDPoalpha=0.50, n.sample=50, alpha=0.05, effect.size=0.8,
                      r.1=0.20)

backsolve.seTPPoavgpwr(seTPPoavgpwr=0.20, n.sample=30, alpha=0.05, effect.size=0.8,
                       r.1=0.20)

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