Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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'. |

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.

`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. |

Grant Izmirlian <izmirlian at nih dot gov>

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

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!
``` |

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