DPB.DiscreteTestResults: Discrete Poisson-Binomial procedure

Description

Apply the [DPB] procedure, with or without computing the critical values, to a set of p-values and their discrete support. A non-adaptive version is available as well. Additionally, the user can choose between exact computation of the Poisson-Binomial distribution or a refined normal approximation.

Usage

# S3 method for DiscreteTestResults
DPB(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  exact = TRUE,
  select.threshold = 1,
  ...
)
discrete.PB(test.results, ...)
# S3 method for default
discrete.PB(
  test.results,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  adaptive = TRUE,
  critical.values = FALSE,
  exact = TRUE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)
# S3 method for DiscreteTestResults
discrete.PB(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  adaptive = TRUE,
  critical.values = FALSE,
  exact = TRUE,
  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$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$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.
critical.values: single boolean indicating whether critical constants are to be computed.
exact: single boolean indicating whether to compute the Poisson-Binomial distribution exactly or by normal approximation.
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.
...: 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.
adaptive: single boolean indicating whether to conduct an adaptive procedure or not.
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

DPB and NDPB are wrapper functions for discrete.PB. The first one simply passes all its arguments to discrete.PB with adaptive = TRUE and NDPB does the same with adaptive = FALSE.

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()

# DPB (exact) without critical values; using results object
DPB.exact.fast <- discrete.PB(test.results)
summary(DPB.exact.fast)

# DPB (exact) with critical values; using extracted p-values and supports
DPB.exact.crit <- discrete.PB(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(DPB.exact.crit)

# DPB (normal approximation) without critical values; using extracted p-values and supports
DPB.norm.fast <- discrete.PB(raw.pvalues, pCDFlist, exact = FALSE)
summary(DPB.norm.fast)

# DPB (normal approximation) with critical values; using results object
DPB.norm.crit <- discrete.PB(test.results, critical.values = TRUE,
                             exact = FALSE)
summary(DPB.norm.crit)

# Non-adaptive DPB (exact) without critical values; using results object
NDPB.exact.fast <- discrete.PB(test.results, adaptive = FALSE)
summary(NDPB.exact.fast)

# Non-adaptive DPB (exact) with critical values; using extracted p-values and supports
NDPB.exact.crit <- discrete.PB(raw.pvalues, pCDFlist, adaptive = FALSE,
                               critical.values = TRUE)
summary(NDPB.exact.crit)

# Non-adaptive DPB (normal approx.) without critical values; using extracted p-values and supports
NDPB.norm.fast <- discrete.PB(raw.pvalues, pCDFlist, adaptive = FALSE,
                              exact = FALSE)
summary(NDPB.norm.fast)

# Non-adaptive DPB (normal approx.) with critical values; using results object
NDPB.norm.crit <- discrete.PB(test.results, adaptive = FALSE,
                              critical.values = TRUE, exact = FALSE)
summary(NDPB.norm.crit)

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