DiscreteFDR (version 1.2)

kernel: Kernel functions for discrete.BH

Description

Kernel functions that transform observed p-values or their support according to [HSU], [HSD], [AHSU] and [AHSD]. The output is used by discrete.BH. Additionally, kernel.DBH.crit and kernel.ADBH.crit compute and return the critical constants. The end user should not use them.

Usage

kernel.DBH.fast(stepf, pv.numer, pv.denom)
kernel.DBH.crit(stepf, pv.numer, pv.denom, alpha, sorted.pv)
kernel.ADBH.fast(stepf, pv.numer, pv.denom)
kernel.ADBH.crit(stepf, pv.numer, pv.denom, alpha, sorted.pv)

Arguments

stepf

a list of the CDFs under the null hypothesis of each p-value.

pv.numer

a numeric vector. Contains all values of the p-values supports if we search for the critical constants. If not, contains only the observed p-values. Must be in increasing order.

pv.denom

a numeric vector. Identical to pv.numer for a step-down procedure. Equals c.m for a step-up procedure.

alpha

the target FDR level, a number strictly between 0 and 1.

sorted.pv

a vector of observed p-values, in increasing order.

Value

For kernel.DBH.fast and kernel.ADBH.fast, a vector of transformed p-values is returned. kernel.DBH.crit and kernel.ADBH.crit return a list object with critical constants ($crit.consts) and transformed p-values ($pval.transf), but only if pv.numer = pv.denom.

Details

When computing critical constants under step-down, that is, when using kernel.DBH.crit or kernel.ADBH.crit with pv.numer = pv.denom (i.e. the step-down case), we still need to get transformed p-values to compute the adjusted p-values.

This version: 2018-11-13.

See Also

discrete.BH, DiscreteFDR, DBR, kernel.DBR

Examples

# NOT RUN {
X1 <- c(4, 2, 2, 14, 6, 9, 4, 0, 1)
X2 <- c(0, 0, 1, 3, 2, 1, 2, 2, 2)
N1 <- rep(148, 9)
N2 <- rep(132, 9)
Y1 <- N1-X1
Y2 <- N2-X2
df <- data.frame(X1,Y1,X2,Y2)
df
#Construction of the p-values and their support
df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc")
raw.pvalues <- df.formatted$raw
pCDFlist <- df.formatted$support

m <- length(raw.pvalues)
alpha <- 0.05

# Compute the step functions from the supports
stepf <- build.stepfuns(pCDFlist)

# We stay in a step-down context, where pv.numer = pv.denom,
# for the sake of simplicity

# If not searching for critical constants, we use only the observed p-values
sorted.pvals <- sort(raw.pvalues)
y.DBH.fast <- kernel.DBH.fast(stepf, sorted.pvals, sorted.pvals)
y.ADBH.fast <- kernel.ADBH.fast(stepf, sorted.pvals, sorted.pvals)

# If searching for critical constants, we use (almost) the complete support
pv.list.all <- sort(unique(as.numeric(unlist(pCDFlist))))
# apply the shortcut drawn from Lemma 3, that is
# c.1 >= the effective critical value associated to (alpha/m)/(1 + alpha/m)
pv.list <- short.eff(pv.list.all, alpha/(m + alpha))
# then re-add the observed p-values (needed to compute the adjusted p-values),
# because we may have removed some of them by the shortcut
pv.list <- sort(unique(c(pv.list, sorted.pvals)))
# compute transformed support
y.DBH.crit <- kernel.DBH.crit(stepf, pv.list, pv.list, alpha, sorted.pvals)
y.ADBH.crit <- kernel.ADBH.crit(stepf, pv.list, pv.list, alpha, sorted.pvals)
# critical constants
y.DBH.crit$crit.consts
y.ADBH.crit$crit.consts
# The following exist only for step-down direction
y.DBH.crit$pval.transf
y.ADBH.crit$pval.transf

# }