discrete.PB: Discrete Poisson-Binomial procedure

In FDX: False Discovery Exceedance Controlling Multiple Testing Procedures

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 class 'DiscreteTestResults'
DPB(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  exact = TRUE,
  select.threshold = 1,
  ...
)

discrete.PB(test.results, ...)

## Default S3 method:
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 class 'DiscreteTestResults'
discrete.PB(
  test.results,
  alpha = 0.05,
  zeta = 0.5,
  adaptive = TRUE,
  critical.values = FALSE,
  exact = TRUE,
  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.
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.

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$pCDFlist	list of the p-value supports.
Data$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.

References

Döhler, S. & Roquain, E. (2020). Controlling False Discovery Exceedance for Heterogeneous Tests. Electronic Journal of Statistics, 14(2), pp. 4244-4272. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/20-EJS1771")}

See Also

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

# 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)

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