FDX (version 2.0.0)

continuous.LR: 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
)

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 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 \(\leq\) 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.

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.

References

Lehmann, E. L. & Romano, J. P. (2005). Generalizations of the familywise error rate. The Annals of Statistics, 33(3), pp. 1138-1154. 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)