DLR: Wrapper Functions for the Discrete Guo-Romano Procedure

Description

DLR() is a wrapper function of discrete.LR() for computing [DLR]. It simply passes its arguments to discrete.LR() with fixed adaptive = TRUE.

Usage

DLR(test.results, ...)
# S3 method for default
DLR(
  test.results,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  direction = "sd",
  critical.values = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)
# S3 method for DiscreteTestResults
DLR(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  direction = "sd",
  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 (only for step-down direction).
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$pCDFlist: list of the $p$-value supports.
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.
...: further arguments to be passed to or from other methods. They are ignored here.
pCDFlist: list of the supports of the CDFs of the p-values; each list item must be a numeric vector, which is sorted in increasing order and whose last element equals 1.
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.
direction: single character string specifying whether to perform the step-up ("su) or step-down ("sd"; the default) version of the Lehmann-Romano procedure.
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.
pCDFlist.indices: list of numeric vectors containing the test indices that indicate to which raw p-value each unique support in pCDFlist belongs; ignored if the lengths of test.results and pCDFlist are equal.

Details

Computing critical constants (critical.values = TRUE) requires considerably more execution time, especially if the number of unique supports is large. We recommend that users should only have them calculated when they need them, e.g. for illustrating the rejection area in a plot or other theoretical reasons.

References

Döhler, S. & Roquain, E. (2020). Controlling False Discovery Exceedance for Heterogeneous Tests. Electronic Journal of Statistics, 14(2), pp. 4244-4272. tools:::Rd_expr_doi("10.1214/20-EJS1771")

Examples

Run this code

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()

# DLR without critical values; using results object
DLR.sd.fast <- DLR(test.results)
summary(DLR.sd.fast)

# DLR with critical values; using extracted p-values and supports
DLR.sd.crit <- DLR(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(DLR.sd.crit)

# DLR (step-up) without critical values; using extracted p-values and supports
DLR.su.fast <- DLR(raw.pvalues, pCDFlist, direction = "su")
summary(DLR.su.fast)

# DLR (step-up) with critical values; using test results object
DLR.su.crit <- DLR(test.results, direction = "su", critical.values = TRUE)
summary(DLR.su.crit)

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