continuous.LR: Continuous Lehmann-Romano procedure

In FDX: False Discovery Exceedance Controlling Multiple Testing Procedures

Continuous Lehmann-Romano procedure

Description

Apply the usual (continuous) [LR] procedure, with or without computing the critical values, to a set of p-values. A non-adaptive version is available as well.

Usage

continuous.LR(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  adaptive = TRUE,
  critical.values = FALSE,
  select.threshold = 1
)

LR(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  select.threshold = 1
)

NLR(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  select.threshold = 1
)

Arguments

test.results	either a numeric vector with p-values or an R6 object of class DiscreteTestResults from package DiscreteTests for which a discrete FDR procedure is to be performed.
alpha	single real number strictly between 0 and 1 specifying the target FDP.
zeta	single real number strictly between 0 and 1 specifying the target probability of not exceeding the desired FDP. If zeta = NULL (the default), then zeta is chosen equal to alpha.
adaptive	single boolean indicating whether to conduct an adaptive procedure or not.
critical.values	single boolean indicating whether critical constants are to be computed.
select.threshold	single real number strictly between 0 and 1 indicating the largest raw p-value to be considered, i.e. only p-values below this threshold are considered and the procedures are adjusted in order to take this selection effect into account; if threshold = 1 (the default), all raw p-values are selected.

Details

LR and NLR are wrapper functions for continuous.LR. The first one simply passes all its arguments to continuous.LR with adaptive = TRUE and NLR does the same with adaptive = FALSE.

Value

A FDX S3 class object whose elements are:

Rejected	rejected raw p-values.
Indices	indices of rejected p-values.
Num.rejected	number of rejections.
Adjusted	adjusted p-values.
Critical.values	critical values (only exists if computations where performed with critical.values = TRUE).
Select	list with data related to p-value selection; only exists if select.threshold < 1.
Select$Threshold	p-value selection threshold.
Select$Effective.Thresholds	results of each p-value CDF evaluated at the selection threshold.
Select$Pvalues	selected p-values that are \leq selection threshold.
Select$Indices	indices of p-values \leq selection threshold.
Select$Scaled	scaled selected p-values.
Select$Number	number of selected p-values \leq selection threshold.
Data	list with input data.
Data$Method	character string describing the used algorithm, e.g. 'Discrete Lehmann-Romano procedure (step-up)'.
Data$Raw.pvalues	all observed raw p-values.
Data$FDP.threshold	FDP threshold alpha.
Data$Exceedance.probability	probability zeta of FDP exceeding alpha; thus, FDP is being controlled at level alpha with confidence 1 - zeta.
Data$Adaptive	boolean indicating whether an adaptive procedure was conducted or not.
Data$Data.name	the respective variable name(s) of the input data.

References

Lehmann, E. L. & Romano, J. P. (2005). Generalizations of the familywise error rate. The Annals of Statistics, 33(3), pp. 1138-1154. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/009053605000000084")}

See Also

kernel(), FDX, continuous.GR(), discrete.LR(), discrete.GR(), discrete.PB(), weighted.LR(), weighted.GR(), weighted.PB()

Examples

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 supports with Fisher's exact test
library(DiscreteTests)  # for Fisher's exact test
test.results <- fisher_test_pv(df)
raw.pvalues <- test.results$get_pvalues()
pCDFlist <- test.results$get_pvalue_supports()

# LR without critical values; using extracted p-values
LR.fast <- LR(raw.pvalues)
summary(LR.fast)

# LR with critical values; using test results object
LR.crit <- LR(test.results, critical.values = TRUE)
summary(LR.crit)

# Non-adaptive LR without critical values; using test results object
NLR.fast <- NLR(test.results)
summary(NLR.fast)

# Non-adaptive LR with critical values; using extracted p-values
NLR.crit <- NLR(raw.pvalues, critical.values = TRUE)
summary(NLR.crit)

FDX documentation built on April 4, 2025, 4:08 a.m.