pwrFDR (version 1.95)

controlFDF: Calculates a reduced FDR required to control the FDF

Description

Calculates a reduced FDR required to bound the the false discovery rate in probability.

Usage

controlFDF(groups=2, FDR, r.1, N.tests, effect.size, n.sample,
             use.prob=c("f*","f","user"), prob=NULL)

Arguments

groups

The number of experimental groups to compare. Default value is 2.

FDR

The false discovery rate.

r.1

The proportion of simultaneous tests that are non-centrally located

N.tests

The number of simultaneous hypothesis tests.

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.

use.prob

This sets the value of the probability that the FDF exceeds lambda*. Set this to the character string 'f*' (default) and the routine uses the value of f*. Set this to 'f' and the routine uses the value of the FDR. Set this to 'user' and then you can specify any desired probability in the argument 'prob'.

prob

The desired probability that the FDF exceeds lambda* that is user specified when the argument 'use.prob' is set to 'user'.

Value

f.star

The reduced FDR required to bound the FDF in probability

obj

Result of optimization yielding 'f.star' should be close to 0

L.star

The bound on the FDF, should be (1-r) f. See above.

P.star

The probability that the FDF is greater than L.star. See above.

average.power

Resulting average power.

c.g

The BH-FDR threshold on the scale of the test statistics.

gamma

The proportion of all 'm' tests declared significant.

objective

Result of optimization yielding the 'average.power'.

err.III

Mass on the wrong side of the threshold.

sigma.rtm.SoM

Asymptotic variance of the true positive fraction.

Details

Calculates a reduced FDR required to bound the the false discovery rate in probability...e.g. finds f* so that when the BH-FDR procedure at FDR, f*, is used, we ensure that

Pr( T/J > (1-r) f ) < (1-r) f*

where 'f' is the original false discovery rate and 'r' is the proportion of non-null distributed test statistics.

References

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

See Also

pwrFDR

Examples

# NOT RUN {
## at FDR=0.15 and other parameters, it takes n.sample=46 replicates for 
## average power > 80%
pwr.46.15 <- pwrFDR(FDR=0.15, r.1=0.03, N.tests=1000, effect.size=0.79, n.sample=46)

## when there are 'only' N.tests=1000 simultaneous tests, the distribution of the
## false discovery fraction, FDF, is not so highly spiked at the FDR=0.15
## You need to set the FDR down to FDR=0.0657 to ensure that  Pr( T/J > 0.145 ) < 0.0657
fstr <- controlFDF(FDR=0.15, r.1=0.03, N.tests=1000, effect.size=0.8, n.sample=46)

## at all the above settings, with FDR=0.0657 at an n.sample of 46, we only have 69% 
## average power.
pwr.46.0657 <- pwrFDR(FDR=0.065747, r.1=0.03, N.tests=1000, effect.size=0.79, n.sample=46)

## it'll cost 7 more replicates to get the average power up over 80%.
pwr.53.0657 <- pwrFDR(FDR=0.065747, r.1=0.03, N.tests=1000, effect.size=0.8, n.sample=53)

## it costs only 8.75% more to get it right!
# }