pwrFDR on a grid.Function for evaluating pwrFDR on a factorial design of
possible parameters.
pwrFDR.grid(effect.size, n.sample, r.1, alpha, delta, groups, N.tests,
average.power, TPX.power, lambda, type, grpj.per.grp1,
corr.struct, FDP.control.method, distopt, control)A list having two components:
A data.frame with one column for each argument listing the distinct settings for all parameters.
A list with components objects of class pwr,
the results of the calls to pwrFDR
A vector of effect sizes to be looped over. 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.
A vector of sample sizes to be looped over. The sample size is the number of experimental replicates. Required for calculation of power
A vector of mixing proportions to be looped over. The mixing proportion is 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)
If the "FDP.control.method" is set to 'Romano' or 'BHFDX', then this optional argument can be set to the exceedance thresh-hold in defining the FDP-tp: \(P\{ FDP > \delta \} < \alpha\). The default value is \(\alpha\).
The number of experimental groups to compare. Must be integral and >=1. The default value is 2.
The number of simultaneous hypothesis tests.
The desired average power. Calculation of sample size, effect size mixing proportion or alpha requires specification of either 'average.power' or 'TPX.power'.
The desired tp-power (see pwrFDR documentation).
Calculation of sample size, effect size mixing proportion or alpha
requires specification of either 'average.power' or 'TPX.power'.
The tp-power threshold, required when calculating the tp-power
(see pwrFDR documentation) or when calculating the
sample size, effect size mixing proportion or alpha required for
tp-power.
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.
Specifies a block correlation structure between test
statistics which is used in both the simulation routine, and in the
computations based upon asymptotic approximation, e.g. the AFDX
control and the ATPP method. Its form is specified via the following
named elements.
"type": "CS-Blocks" for compound symmetry within blocks, or
"Toeplitz-Blocks" for toeplitz blocks.
"block.size": the size of the correlated blocks
"rho": When type="CS-Blocks", then 'rho' is a correlation of length 1
when type="Toeplitz-Blocks", then 'rho' is a vector of
correlations of length 'block.size' - 1
A character string specifying how the false discovery proportion (FDP) is to be
controlled. You may specify the whole word or any shortened uniquely
identifying truncation.
"BHFDR": the usual BH-FDR
"BHFDX": guarantees control of the FDX e.g. probability that the FDP exceeds
delta will be less than alpha. Uses asymptotic approximationto the
distribution of the FDP to find alpha* such that the BHFDR
procedure controls the FDX at alpha. Only slightly more conservative
than BHFDR control at alpha. Allows dependence which must be specified.
Not guaranteed to have a solution in all cases, in which case Romano's
procedure is used as a fall-back.
"Romano": use Romano's method which guarantees control of the FDX,
e.g. the probability that the FDP exceeds delta will
be less than alpha.
"Auto": in 'FixedPoint' mode, the program will use its own
wisdom to determine which choice above to make. The
order of conservatism is
Bonferroni > Holm > Hochberg > Romano > BHFDX > BHFDR,
but BHFDR offers only expected control, the most
conservative 3 control the FWER and the other two
guarantee bounds on the excedance probabilty. If the
distribution of the FDP is nearly degenerate, then BHFDR
is the best option. Otherwise, if it can be reliably used,
BHFDX would be the best choice. The 'effective' denominator,
gamma*N.tests, in the CLT determines when the approximation
is good enough and the asymptotic standard error of the FDP
determines when the distribution is dispersed enough to matter.
Use "Auto" to run through these checks and determine the best.
A return argument, 'Auto', displays the choice made. See
output components and details.
"both": in 'simulation' mode, compute statistics R and T under BHFDX
and Romano (in addition to BHFDR). Corresponding
statistics are denoted R.st, T.st corresponding to BHFDX
control of the FDP, and R.R and T.R corresponding to
Romano control of the FDP. If sim.level is set to 2,
(default) the statistics R.st.ht and T.st.ht, which are
the number rejected and number true positives under BHFDX
where r_0 = 1-r_1, gamma, and alpha.star have been estimated
from the P-value data and then alpha.star computed from
these.
"Holm": Use Holm's step-down procedure which guarantees control of the
family-wise error rate (FWER)
"Hochberg": Use Hochberg's step-up procedure which guarantees control
of the FWER if the tests are independent. Less conservative
than Holm and Bonferroni but more conservative than all other
procedures here.
"Bonferroni": Use the Bonferroni procedure. Guarantees control of the FWER.
the most conservative of procedures offered here.
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)
Optionally, a list with components with the following
components:
'tol' is a convergence criterion used in iterative
methods which is set to 1e-8 by default.
'max.iter' is an iteration limit, set to 20 for the iterated
function limit and 1000 for all others by default.
'sim.level' sim level 2 (default) stipulates, when FDP.control.method
is set to "BHFDX", or "both", R.st.ht and T.st.ht are
computed in addition to R.st and T.st (see above).
'low.power.stop' in simulation option, will result in an error message
if the power computed via FixedPoint method is too low, which
result in no solution for the BHFDX option. Default setting is TRUE.
Set to FALSE to over-ride this behavior.
'FDP.meth.thresh' fine-tunes the 'Auto' voodoo (see above). Leave
this alone.
'verb' vebosity level.
'ast.le.a' leaving this at the default value TRUE forces
'alpha.star', the solution under FDP.method.control="BHFDX",
to be less than the specified 'alpha'.
Grant Izmirlian <izmirlian at nih dot gov>
Arguments may be specified as vectors of possible values or can be set to a single constant value.
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.
pwrFDR.grid
controlFDP
tst <- pwrFDR.grid(effect.size=c(0.6,0.9), n.sample=c(50,60,70), r.1=0.4+0.2*(0:1),
alpha=0.05+0.05*(0:3), N.tests=1000, FDP.control.method="Auto")
Run the code above in your browser using DataLab