Ch23-criterion: BH-FDR and Romano Criterion
In pwrFDR: FDR Power

Description Usage Arguments Value Author(s) References Examples

Compute BH-FDR step up criterion, or Romano step-down criterion

1	criterion(alpha, delta, N.tests, FDP.control.method = c("BHFDR", "Romano"))

`alpha`	The false discovery rate (in the BH case) or the upper bound on the probability that the FDP exceeds lambda (Romano case)
`delta`	If the "FDP.control.method" is set to 'Romano' then the user can set the exceedance thresh-hold for the FDP tail probability control P\{ FDP > δ \} < α. The default value is α.
`N.tests`	The number of simultaneous hypothesis tests.
`FDP.control.method`	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 "Romano": use Romano's method which guarantees probability less than alpha that the FDP exceeds alpha.

The step down or step up criterion, which is a vector of length N.tests

Grant Izmirlian <izmirlian at nih dot gov>

Benjamini Y, Hochberg Y. Controlling the false discovery rate - a practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B Stat. Methodol. 1995; 57(1):289-300.

Romano J.P. and Shaikh A.M. On stepdown control of the false discovery proportion. IMS Lecture Notes–Monograph Series. 2006; 49:33-50. DOI: 10.1214/074921706000000383.

  library(pwrFDR)

  crit.b <- criterion(N.tests=1000, alpha=0.15, FDP.control.method="BHFDR")
  crit.r <- criterion(N.tests=1000, alpha=0.15, FDP.control.method="Romano")
  crit.r.17 <- criterion(N.tests=1000, alpha=0.15, delta=0.17, FDP.control.method="Romano")
  matplot(1:1000, cbind(crit.b, crit.r, crit.r.17), type="l", lty=1, col=2:4)