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.
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)
A numeric vector having components
Value of missing argument giving required se[FDP]/alpha (backsolve.seFDPoalpha) or se[TPP]/average.power (backsolve.seTPPoavgpwr).
The average power at the given set of conditions
The standard error of the FDP (backsolve.seFDPoalpha) or standard error of the TPP (backsolve.seTPPoavgpwr).
Value returned by the solver. Should be near zero if a solution was found.
In backsolve.seFDPoalpha, the user specified value of se[FDP]/alpha
In backsolve.seTPPoavgpwr, the user specified value of se[TPP]/average.power
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.
The number of experimental replicates. Required for calculation of power
The proportion of simultaneous tests that are non-centrally located
The false discovery rate (in the BH case) or the upper bound on the probability that the FDP exceeds delta (BHFDX and Romano case)
The number of experimental groups to compare. Must be integral and >=1. The default value is 2.
The number of simultaneous hypothesis tests.
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.
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.
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)
This can be done under the assumption of tests that are correlated identically in pair within blocks of given size.
When 'rho' is specified, the common block-size for correlated test statistics.
Grant Izmirlian Jr <izmirlian at 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 \(\lambda\)-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.
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)
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