# Ch02-controlFDF: Calculates a reduced FDR required to control the FDF In pwrFDR: FDR Power

## Description

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

## Usage

 ```1 2``` ``` 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'.

## 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.

## 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.

## Author(s)

Grant Izmirlian <izmirlian at nih dot gov>

## References

Izmirlian G. (2017) Average Power and λ-power in Multiple Testing Scenarios when the Benjamini-Hochberg False Discovery Rate Procedure is Used. arXiv:1801.03989

`pwrFDR`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## 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! ```

pwrFDR documentation built on May 2, 2019, 7:53 a.m.