The proportion of true nulls is estimated using the Blanchard-Roquain 1-stage procedure with parameter (alpha,lambda) via the formula
BR_pi0_est(pValues, alpha, lambda=1, truncate=TRUE)The estimated proportion of true null hypotheses.
GillesBlanchard
The raw p-values for the marginal test problems (assumed to be independent)
The FDR significance level for the BR procedure
(default 1) The parameter for the BR procedure, shoud belong to (0, 1/alpha)
(logical, default TRUE) if TRUE, output estimated is truncated to 1
estimated pi_0 = ( m - R(alpha,lambda) + 1) / ( m*( 1 - lambda * alpha ) )
where R(alpha,lambda) is the number of hypotheses rejected by the BR 1-stage procedure, alpha is the FDR level for this procedure and lambda a parameter belonging to (0, 1/alpha) with default value 1. Independence of p-values is assumed. This estimate may in some cases be larger than 1; it is truncated to 1 if the parameter truncated=TRUE. The estimate is used in the Blanchard-Roquain 2-stage step-up (using the non-truncated version)
Blanchard