Type: Package
Title: FDR Based Multiple Testing Procedures with Adaptation for Discrete Tests
Version: 2.1.0
Date: 2024-12-14
Description: Implementations of the multiple testing procedures for discrete tests described in the paper Döhler, Durand and Roquain (2018) "New FDR bounds for discrete and heterogeneous tests" <doi:10.1214/18-EJS1441>. The main procedures of the paper (HSU and HSD), their adaptive counterparts (AHSU and AHSD), and the HBR variant are available and are coded to take as input the results of a test procedure from package 'DiscreteTests', or a set of observed p-values and their discrete support under their nulls. A shortcut function to obtain such p-values and supports is also provided, along with a wrapper allowing to apply discrete procedures directly to data.
License: GPL-3
Language: en-US
Encoding: UTF-8
Depends: R (≥ 3.00)
Imports: Rcpp (≥ 1.0.12), DiscreteTests (≥ 0.2.1), lifecycle, checkmate, DiscreteDatasets
LinkingTo: Rcpp, RcppArmadillo
Suggests: rmarkdown, knitr, R.rsp, kableExtra
VignetteBuilder: knitr, R.rsp
URL: https://github.com/DISOhda/DiscreteFDR
BugReports: https://github.com/DISOhda/DiscreteFDR/issues
RoxygenNote: 7.3.2
NeedsCompilation: yes
Packaged: 2024-12-14 14:29:51 UTC; fjunge
Author: Sebastian Döhler ORCID iD [aut, ctb], Florian Junge ORCID iD [aut, ctb, cre], Guillermo Durand ORCID iD [aut, ctb], Etienne Roquain [ctb], Christina Kihn [ctb]
Maintainer: Florian Junge <diso.fbmn@h-da.de>
Repository: CRAN
Date/Publication: 2024-12-14 14:50:02 UTC

FDR-based Multiple Testing Procedures with Adaptation for Discrete Tests

Description

This package implements the [HSU], [HSD], [AHSU], [AHSD] and [HBR-\lambda] procedures for discrete tests (see References).

Details

The functions are reorganized from the reference paper in the following way. discrete.BH() (for Discrete Benjamini-Hochberg) implements [HSU], [HSD], [AHSU] and [AHSD], while DBR() (for Discrete Blanchard-Roquain) implements [HBR-\lambda]. DBH() and ADBH() are wrapper functions for discrete.BH() to access [HSU] and [HSD], as well as [AHSU] and [AHSD] directly.

This package is part of a package family to which the DiscreteDatasets and DiscreteTests packages also belong. The latter allows to compute p-values and their respective supports for various tests. The objects that contain these results can be used directly by the discrete.BH(), DBH(), ADBH() and DBR() functions. Alternatively, these functions also accept a vector of raw observed p-values and a list of the respective discrete supports of the CDFs of the p-values.

Note: The former function fisher.pvalues.support(), which allows to compute such p-values and supports in the framework of a Fisher's exact test, is now deprecated and should not be used anymore. It has been replaced by generate.pvalues().

The same applies for the function fast.Discrete(), which is a wrapper for fisher.pvalues.support() and discrete.BH() and allows to apply discrete procedures directly to a data set of contingency tables and perform data preprocessing before p-values are computed. It is also now deprecated and has been replaced by direct.discrete.BH(), but for more flexibility, users may employ pipes, e.g.
⁠data |>⁠
⁠ DiscreteDatasets::reconstruct_*(<args>) |>⁠
⁠ DiscreteTests::*.test.pv(<args>) |>⁠
⁠ discrete.BH(<args>)⁠.

Author(s)

Maintainer: Florian Junge diso.fbmn@h-da.de (ORCID) [contributor]

Authors:

Other contributors:

References

Döhler, S., Durand, G., & Roquain, E. (2018). New FDR bounds for discrete and heterogeneous tests. Electronic Journal of Statistics, 12(1), pp. 1867-1900. doi:10.1214/18-EJS1441

G. Blanchard and E. Roquain (2009). Adaptive false discovery rate control under independence and dependence. Journal of Machine Learning Research, 10, pp. 2837-2871. doi:10.48550/arXiv.0707.0536

Döhler, S. (2018). A discrete modification of the Benjamini–Yekutieli procedure. Econometrics and Statistics, 5, pp. 137-147. doi:10.1016/j.ecosta.2016.12.002

See Also

Useful links:

Wrapper Functions for the Adaptive Discrete Benjamini-Hochberg Procedure

Description

ADBH() is a wrapper function of discrete.BH() for computing [AHSU] and [AHSD], which are more powerful than [HSU] and [HSD], respectively. It simply passes its arguments to discrete.BH() with fixed adaptive = TRUE and is computationally more demanding than DBH().

Usage

ADBH(test.results, ...)

## Default S3 method:
ADBH(
  test.results,
  pCDFlist,
  alpha = 0.05,
  direction = "su",
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)

## S3 method for class 'DiscreteTestResults'
ADBH(
  test.results,
  alpha = 0.05,
  direction = "su",
  ret.crit.consts = 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.

...

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 indicating the target FDR level.

direction

single character string specifying whether to perform a step-up ("su"; the default) or step-down procedure ("sd").

ret.crit.consts

single boolean specifying 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 (ret.crit.consts = 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 set in a plot or other theoretical reasons.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values (only for step-down direction).

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

References

Döhler, S., Durand, G., & Roquain, E. (2018). New FDR bounds for discrete and heterogeneous tests. Electronic Journal of Statistics, 12(1), pp. 1867-1900. doi:10.1214/18-EJS1441

See Also

discrete.BH(), DBH(), DBR(), DBY()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# ADBH (step-up) without critical values; using test results object
ADBH.su.fast <- ADBH(test.result)
summary(ADBH.su.fast)

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

# ADBH (step-up) with critical values; using extracted p-values and supports
ADBH.su.crit <- ADBH(raw.pvalues, pCDFlist, ret.crit.consts = TRUE)
summary(ADBH.su.crit)

# ADBH (step-down) with critical values; using test results object
ADBH.sd.crit <- ADBH(test.result, direction = "sd", ret.crit.consts = TRUE)
summary(ADBH.sd.crit)

Wrapper Functions for the Discrete Benjamini-Hochberg Procedure

Description

DBH() is a wrapper function of discrete.BH() for computing [HSU] and [HSD]. It simply passes its arguments to discrete.BH() with fixed adaptive = FALSE.

Usage

DBH(test.results, ...)

## Default S3 method:
DBH(
  test.results,
  pCDFlist,
  alpha = 0.05,
  direction = "su",
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)

## S3 method for class 'DiscreteTestResults'
DBH(
  test.results,
  alpha = 0.05,
  direction = "su",
  ret.crit.consts = 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.

...

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 indicating the target FDR level.

direction

single character string specifying whether to perform a step-up ("su"; the default) or step-down procedure ("sd").

ret.crit.consts

single boolean specifying 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 (ret.crit.consts = 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 set in a plot or other theoretical reasons.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values (only for step-down direction).

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

References

Döhler, S., Durand, G., & Roquain, E. (2018). New FDR bounds for discrete and heterogeneous tests. Electronic Journal of Statistics, 12(1), pp. 1867-1900. doi:10.1214/18-EJS1441

See Also

discrete.BH(), ADBH(), DBR(), DBY()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# DBH (step-up) without critical values; using test results object
DBH.su.fast <- DBH(test.result)
summary(DBH.su.fast)

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

# DBH (step-up) with critical values; using extracted p-values and supports
DBH.su.crit <- DBH(raw.pvalues, pCDFlist, ret.crit.consts = TRUE)
summary(DBH.su.crit)

# DBH (step-down) with critical values; using test results object
DBH.sd.crit <- DBH(test.result, direction = "sd", ret.crit.consts = TRUE)
summary(DBH.sd.crit)

The Discrete Blanchard-Roquain Procedure

Description

Applies the [HBR-\lambda] procedure, with or without computing the critical constants, to a set of p-values and their respective discrete supports.

Usage

DBR(test.results, ...)

## Default S3 method:
DBR(
  test.results,
  pCDFlist,
  alpha = 0.05,
  lambda = NULL,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)

## S3 method for class 'DiscreteTestResults'
DBR(
  test.results,
  alpha = 0.05,
  lambda = NULL,
  ret.crit.consts = 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.

...

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 indicating the target FDR level.

lambda

real number strictly between 0 and 1 specifying the DBR tuning parameter; if lambda = NULL (the default), lambda is chosen to be equal to alpha.

ret.crit.consts

single boolean specifying 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

[DBR-\lambda] is the discrete version of the [Blanchard-Roquain-\lambda] procedure (see References). The authors of the latter suggest to take lambda = alpha (see their Proposition 17), which explains the choice of the default value here.

Computing critical constants (ret.crit.consts = 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 set in a plot or other theoretical reasons.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values.

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$DBR.Tuning

value of the tuning parameter lambda.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

References

: G. Blanchard and E. Roquain (2009). Adaptive false discovery rate control under independence and dependence. Journal of Machine Learning Research, 10, pp. 2837-2871. doi:10.48550/arXiv.0707.0536

See Also

discrete.BH(), DBH(), ADBH(), DBY()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

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

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

The Discrete Benjamini-Yekutieli Procedure

Description

Applies the Discrete Benjamini-Yekutieli procedure, with or without computing the critical constants, to a set of p-values and their respective discrete supports.

Usage

DBY(test.results, ...)

## Default S3 method:
DBY(
  test.results,
  pCDFlist,
  alpha = 0.05,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)

## S3 method for class 'DiscreteTestResults'
DBY(
  test.results,
  alpha = 0.05,
  ret.crit.consts = 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.

...

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 indicating the target FDR level.

ret.crit.consts

single boolean specifying 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 (ret.crit.consts = 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 set in a plot or other theoretical reasons.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values (only for step-down direction).

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

References

Döhler, S. (2018). A discrete modification of the Benjamini–Yekutieli procedure. Econometrics and Statistics, 5, pp. 137-147. doi:10.1016/j.ecosta.2016.12.002

See Also

discrete.BH(), DBH(), ADBH(), DBR()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

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

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

Direct Application of Multiple Testing Procedures to Dataset

Description

Apply the [HSU], [HSD], [AHSU] or [AHSD] procedure, with or without computing the critical constants, to a data set of 2x2 contingency tables using Fisher's exact tests which may have to be transformed before computing p-values.

Usage

direct.discrete.BH(
  dat,
  test.fun,
  test.args = NULL,
  alpha = 0.05,
  direction = "su",
  adaptive = FALSE,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  preprocess.fun = NULL,
  preprocess.args = NULL
)

Arguments

dat

input data; must be suitable for the first parameter of the provided preprocess.fun function or, if preprocess.fun is NULL, for the first parameter of the test.fun function.

test.fun

function from package DiscreteTests, i.e. one whose name ends with ⁠*_test_pv⁠ and which performs hypothesis tests and provides an object with p-values and their support sets; can be specified by a single character string (which is automatically checked for being a suitable function from that package and may be abbreviated) or a single function object.

test.args

optional named list with arguments for test.fun; the names of the list fields must match the test function's parameter names. The first parameter of the test function (i.e. the data) MUST NOT be included!

alpha

single real number strictly between 0 and 1 indicating the target FDR level.

direction

single character string specifying whether to perform a step-up ("su"; the default) or step-down procedure ("sd").

adaptive

single boolean specifying whether to conduct an adaptive procedure or not.

ret.crit.consts

single boolean specifying 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.

preprocess.fun

optional function for pre-processing the input data; its result must be suitable for the first parameter of the test.fun function.

preprocess.args

optional named list with arguments for preprocess.fun; the names of the list fields must match the pre-processing function's parameter names. The first parameter of the test function (i.e. the data) MUST NOT be included!

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

DBH.su <- direct.discrete.BH(df, "fisher", direction = "su")
summary(DBH.su)

DBH.sd <- direct.discrete.BH(df, "fisher", direction = "sd")
DBH.sd$Adjusted
summary(DBH.sd)

ADBH.su <- direct.discrete.BH(df, "fisher", direction = "su",
                              adaptive = TRUE)
summary(ADBH.su)

ADBH.sd <- direct.discrete.BH(df, "fisher", direction = "sd",
                              adaptive = TRUE)
ADBH.sd$Adjusted
summary(ADBH.sd)

The Discrete Benjamini-Hochberg Procedure

Description

Applies the [HSU], [HSD], [AHSU] and [AHSD] procedures at a given FDR level, with or without computing the critical constants, to a set of p-values and their respective discrete supports.

Usage

discrete.BH(test.results, ...)

## Default S3 method:
discrete.BH(
  test.results,
  pCDFlist,
  alpha = 0.05,
  direction = "su",
  adaptive = FALSE,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)

## S3 method for class 'DiscreteTestResults'
discrete.BH(
  test.results,
  alpha = 0.05,
  direction = "su",
  adaptive = FALSE,
  ret.crit.consts = 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.

...

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 indicating the target FDR level.

direction

single character string specifying whether to perform a step-up ("su"; the default) or step-down procedure ("sd").

adaptive

single boolean specifying whether to conduct an adaptive procedure or not.

ret.crit.consts

single boolean specifying 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

The adaptive variants [AHSU] and [AHSD], which are executed via adaptive = TRUE, are often slightly more powerful than [HSU] and [HSD], respectively. But they are also computationally more demanding.

Computing critical constants (ret.crit.consts = 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 set in a plot or other theoretical reasons.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values (only for step-down direction).

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

References

Döhler, S., Durand, G., & Roquain, E. (2018). New FDR bounds for discrete and heterogeneous tests. Electronic Journal of Statistics, 12(1), pp. 1867-1900. doi:10.1214/18-EJS1441

See Also

DBH(), ADBH(), DBR(), DBY()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# DBH (step-up) without critical values; using test results object
DBH.su.fast <- discrete.BH(test.result)
summary(DBH.su.fast)

# DBH (step-down) without critical values; using extracted p-values
# and supports
DBH.sd.fast <- discrete.BH(raw.pvalues, pCDFlist, direction = "sd")
summary(DBH.sd.fast)

# DBH (step-up) with critical values; using extracted p-values and supports
DBH.su.crit <- discrete.BH(raw.pvalues, pCDFlist, ret.crit.consts = TRUE)
summary(DBH.su.crit)

# DBH (step-down) with critical values; using test results object
DBH.sd.crit <- discrete.BH(test.result, direction = "sd",
                           ret.crit.consts = TRUE)
summary(DBH.sd.crit)

# ADBH (step-up) without critical values; using test results object
ADBH.su.fast <- discrete.BH(test.result, adaptive = TRUE)
summary(ADBH.su.fast)

# ADBH (step-down) without critical values; using extracted p-values
# and supports
ADBH.sd.fast <- discrete.BH(raw.pvalues, pCDFlist, direction = "sd",
                             adaptive = TRUE)
summary(ADBH.sd.fast)

# ADBH (step-up) with critical values; using extracted p-values and supports
ADBH.su.crit <- discrete.BH(raw.pvalues, pCDFlist, adaptive = TRUE,
                            ret.crit.consts = TRUE)
summary(ADBH.su.crit)

# ADBH (step-down) with critical values; using test results object
ADBH.sd.crit <- discrete.BH(test.result, direction = "sd", adaptive = TRUE,
                            ret.crit.consts = TRUE)
summary(ADBH.sd.crit)

Fast Application of Discrete Multiple Testing Procedures

Description

[Deprecated]

Apply the [HSU], [HSD], [AHSU] or [AHSD] procedure, without computing the critical constants, to a data set of 2x2 contingency tables which may have to be preprocessed in order to have the correct structure for computing p-values using Fisher's exact test.

Note: This function is deprecated and will be removed in a future version. Please use direct.discrete.BH() with test.fun = DiscreteTests::fisher.test.pv and (optional) preprocess.fun = DiscreteDatasets::reconstruct_two or preprocess.fun = DiscreteDatasets::reconstruct_four instead. Alternatively, use a pipeline, e.g.
⁠data |>⁠
⁠ DiscreteDatasets::reconstruct_*(<args>) |>⁠
⁠ DiscreteTests::*.test.pv(<args>) |>⁠
⁠ discrete.BH(<args>)⁠.

Usage

fast.Discrete(
  counts,
  alternative = "greater",
  input = "noassoc",
  alpha = 0.05,
  direction = "su",
  adaptive = FALSE,
  select.threshold = 1
)

Arguments

counts

a data frame of two or four columns and any number of lines; each line representing a 2x2 contingency table to test. The number of columns and what they must contain depend on the value of the input argument (see Details section of fisher.pvalues.support()).

alternative

same argument as in stats::fisher.test(). The three possible values are "greater" (default), "two.sided" or "less" (may be abbreviated).

input

the format of the input data frame (see Details section of fisher.pvalues.support(). The three possible values are "noassoc" (default), "marginal" or "HG2011" (may be abbreviated).

alpha

single real number strictly between 0 and 1 indicating the target FDR level.

direction

single character string specifying whether to perform a step-up ("su"; the default) or step-down procedure ("sd").

adaptive

single boolean specifying whether to conduct an adaptive procedure or not.

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.

Value

A DiscreteFDR S3 class object whose elements are:

Rejected

rejected raw p-values.

Indices

indices of rejected hypotheses.

Num.rejected

number of rejections.

Adjusted

adjusted p-values (only for step-down direction).

Critical.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed p-values.

Data$pCDFlist

list of the p-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to p-value selection; only exists if select.threshold < 1.

Select$Threshold

p-value selection threshold (select.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.

See Also

fisher.pvalues.support(), discrete.BH()

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

DBH.su <- fast.Discrete(df, input = "noassoc", direction = "su")
summary(DBH.su)

DBH.sd <- fast.Discrete(df, input = "noassoc", direction = "sd")
DBH.sd$Adjusted
summary(DBH.sd)

ADBH.su <- fast.Discrete(df, input = "noassoc", direction = "su",
                         adaptive = TRUE)
summary(ADBH.su)

ADBH.sd <- fast.Discrete(df, input = "noassoc", direction = "sd",
                         adaptive = TRUE)
ADBH.sd$Adjusted
summary(ADBH.sd)

Computing Discrete P-Values and Their Supports for Fisher's Exact Test

Description

[Deprecated]

Computes discrete raw p-values and their support for Fisher's exact test applied to 2x2 contingency tables summarizing counts coming from two categorical measurements.

Note: This function is deprecated and will be removed in a future version. Please use generate.pvalues() with test.fun = DiscreteTests::fisher.test.pv and (optional) preprocess.fun = DiscreteDatasets::reconstruct_two or preprocess.fun = DiscreteDatasets::reconstruct_four instead. Alternatively, use a pipeline like
⁠data |>⁠
⁠ DiscreteDatasets::reconstruct_*(<args>) |>⁠
⁠ DiscreteTests::fisher.test.pv(<args>)⁠

Usage

fisher.pvalues.support(counts, alternative = "greater", input = "noassoc")

Arguments

counts

a data frame of two or four columns and any number of lines; each line represents a 2x2 contingency table to test. The number of columns and what they must contain depend on the value of the input argument, see Details.

alternative

same argument as in stats::fisher.test(). The three possible values are "greater" (default), "two.sided" or "less" and you can specify just the initial letter.

input

the format of the input data frame, see Details. The three possible values are "noassoc" (default), "marginal" or "HG2011" and you can specify just the initial letter.

Details

Assume that each contingency tables compares two variables and resumes the counts of association or not with a condition. This can be resumed in the following table:

Association No association Total
Variable 1 X_1 Y_1 N_1
Variable 2 X_2 Y_2 N_2
Total X_1 + X_2 Y_1 + Y_2 N_1 + N_2

If input="noassoc", counts has four columns which respectively contain, X_1, Y_1, X_2 and Y_2. If input="marginal", counts has four columns which respectively contain X_1, N_1, X_2 and N_2.

If input="HG2011", we are in the situation of the amnesia data set as in Heller & Gur (2011, see References). Each contingency table is obtained from one variable which is compared to all other variables of the study. That is, counts for "second variable" are replaced by the sum of the counts of the other variables:

Association No association Total
Variable j X_j Y_j N_j
Variables \neq j \sum_{i \neq j} X_i \sum_{i \neq j} Y_i \sum_{i \neq j} N_i
Total \sum X_i \sum Y_i \sum N_i

Hence counts needs to have only two columns which respectively contain X_j and Y_j.

The code for the computation of the p-values of Fisher's exact test is inspired by the example in the help page of p.discrete.adjust of package discreteMTP, which is no longer available on CRAN.

See the Wikipedia article about Fisher's exact test, paragraph Example, for a good depiction of what the code does for each possible value of alternative.

Value

A list of two elements:

raw

raw discrete p-values.

support

a list of the supports of the CDFs of the p-values. Each support is represented by a vector in increasing order.

References

R. Heller and H. Gur (2011). False discovery rate controlling procedures for discrete tests. arXiv preprint. arXiv:1112.4627v2.

"Fisher's exact test", Wikipedia, The Free Encyclopedia, accessed 2024-12-14, link.

See Also

fisher.test()

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

# Compute p-values and their supports of Fisher's exact test
df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc")
raw.pvalues <- df.formatted$raw
pCDFlist <- df.formatted$support

Generation of P-Values and Their Supports After Data Transformations

Description

Simple wrapper for generating p-values of discrete tests and their supports after preprocessing the input data. The user only has to provide 1.) a function that generates p-values and supports and 2.) an optional function that preprocesses (i.e. transforms) the input data (if necessary) before it can be used for p-value calculations. The respective arguments are provided

Usage

generate.pvalues(
  dat,
  test.fun,
  test.args = NULL,
  preprocess.fun = NULL,
  preprocess.args = NULL
)

Arguments

dat

input data; must be suitable for the first parameter of the provided preprocess.fun function or, if preprocess.fun is NULL, for the first parameter of the test.fun function.

test.fun

function from package DiscreteTests, i.e. one whose name ends with ⁠*_test_pv⁠ and which performs hypothesis tests and provides an object with p-values and their support sets; can be specified by a single character string (which is automatically checked for being a suitable function from that package and may be abbreviated) or a single function object.

test.args

optional named list with arguments for test.fun; the names of the list fields must match the test function's parameter names. The first parameter of the test function (i.e. the data) MUST NOT be included!

preprocess.fun

optional function for pre-processing the input data; its result must be suitable for the first parameter of the test.fun function.

preprocess.args

optional named list with arguments for preprocess.fun; the names of the list fields must match the pre-processing function's parameter names. The first parameter of the test function (i.e. the data) MUST NOT be included!

Value

A DiscreteTestResults R6 class object.

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# Compute p-values and their supports of Fisher's exact test 
# with preprocessing
df2 <- data.frame(X1, N1, X2, N2)
generate.pvalues(
  dat = df2,
  test.fun = "fisher_test_pv",
  preprocess.fun = function(tab) {
    for(col in c(2, 4)) tab[, col] <- tab[, col] - tab[, col - 1]
    return(tab)
  }
)

# Compute p-values and their supports of a binomial test with preprocessing
generate.pvalues(
  dat = rbind(c(5, 2, 7), c(3, 4, 0)), 
  test.fun = "binom_test_pv",
  test.args = list(n = c(9, 8, 11), p = 0.6, alternative = "two.sided"),
  preprocess.fun = colSums
)

Histogram of Raw P-Values

Description

Computes a histogram of the raw p-values of a DiscreteFDR object.

Usage

## S3 method for class 'DiscreteFDR'
hist(x, breaks = "FD", mode = c("raw", "selected"), ...)

Arguments

x

an object of class DiscreteFDR.

breaks

as in graphics::hist(); here, the Friedman-Diaconis algorithm ("FD") is used as default.

mode

single character string specifying for which $p$-values the histogram is to be generated; must either be "raw" or "selected".

...

further arguments to graphics::hist() or graphics::plot.histogram(), respectively.

Details

If x does not contain results of a selection approach, a warning is issued and a histogram of the raw p-values is drawn.

Value

An object of class histogram.

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# DBH (SU)
DBH <- DBH(raw.pvalues, pCDFlist)
hist(DBH)

Kernel Functions

Description

Kernel functions that transform observed p-values or their support according to [HSU], [HSD], [AHSU], [AHSD] and [HBR-\lambda]. The output is used by discrete.BH or DBR, respectively. kernel_DBH_crit, kernel_ADBH_crit and kernel_DBR_crit additionally compute and return the critical constants. The end user should not use these functions directly.

Note: As of version 2.0, these functions are purely internal functions! As a consequence, they have to be called directly via :::, e.g. DiscreteFDR:::kernel_DBH_fast(). But users should not rely on them, as parameters (including their names, order, etc.) may be changed without notice!

Usage

kernel_DBH_fast(
  pCDFlist,
  pvalues,
  stepUp = FALSE,
  tau_max = NULL,
  alpha = 0.05,
  support = numeric(),
  pCDFcounts = NULL
)

kernel_DBH_crit(
  pCDFlist,
  support,
  sorted_pv,
  stepUp = FALSE,
  alpha = 0.05,
  pCDFcounts = NULL
)

kernel_ADBH_fast(
  pCDFlist,
  sorted_pv,
  stepUp = FALSE,
  alpha = 0.05,
  support = numeric(),
  pCDFcounts = NULL
)

kernel_ADBH_crit(
  pCDFlist,
  support,
  sorted_pv,
  stepUp = FALSE,
  alpha = 0.05,
  pCDFcounts = NULL
)

kernel_DBR_fast(pCDFlist, sorted_pv, lambda = 0.05, pCDFcounts = NULL)

kernel_DBR_crit(
  pCDFlist,
  support,
  sorted_pv,
  lambda = 0.05,
  alpha = 0.05,
  pCDFcounts = NULL
)

kernel_DBY_fast(pCDFlist, pvalues, pCDFcounts = NULL)

kernel_DBY_crit(pCDFlist, support, sorted_pv, alpha = 0.05, pCDFcounts = NULL)

Arguments

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.

pvalues

numeric vector, sorted in increasing order, that either must contain the entirety of all observable values of the p-value supports (when computing critical constants) or only the sorted raw p-values.

stepUp

boolean specifying whether to conduct the step-up (TRUE) or step-down (FALSE; the default) procedure.

tau_max

single real number strictly between 0 and 1 indicating the largest critical value for step-up procedures; if NULL (the default), it is computed automatically, otherwise it needs to be computed manually by the user; ignored if stepUp = FALSE.

alpha

single real number strictly between 0 and 1 indicating the target FDR level; for ⁠*_fast⁠ kernels, it is only needed, if stepUp = TRUE.

support

numeric vector, sorted in increasing order, that contains the entirety of all observable values of the p-value supports; for ⁠*_fast⁠ kernels, it is ignored if stepUp = FALSE.

pCDFcounts

integer vector of counts that indicates to how many p-values each unique p-value distributions belongs.

sorted_pv

numeric vector containing the raw p-values, sorted in increasing order.

lambda

real number strictly between 0 and 1 specifying the DBR tuning parameter.

Details

When computing critical constants under step-down, that is, when using kernel_DBH_crit, kernel_ADBH_crit or kernel_DBR_crit with stepUp = FALSE (i.e. the step-down case), we still need to get transformed p-values to compute the adjusted p-values.

Value

For kernel_DBH_fast(), kernel_ADBH_fast() and kernel_DBR_fast(), a vector of transformed p-values is returned. kernel_DBH_crit, kernel_ADBH_crit and kernel_DBR_crit return a list with critical constants (⁠$crit.consts⁠) and transformed p-values (⁠$pval.transf⁠), but if stepUp = FALSE, there are critical values only.

See Also

discrete.BH(), direct.discrete.BH(), DBR()

Matching Raw P-Values with Supports

Description

Constructs the observed p-values from the raw observed p-values, by rounding them to their nearest neighbor matching with the supports of their respective CDFs (as in function p.discrete.adjust() of package discreteMTP, which is no longer available on CRAN).

Note: This is an internal function and has to be called directly via :::, i.e. DiscreteFDR:::match.pvals().

Usage

match.pvals(test.results, pCDFlist, pCDFlist.indices = NULL)

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.

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.

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

Well computed raw p-values should already belong to their respective CDF support. So this function is called at the beginning of discrete.BH(), DBH(), ADBH() and DBR(), just in case raw p-values are biased.

For each raw p-value that needs to be rounded, a warning is issued.

Value

A vector where each raw p-value has been replaced by its nearest neighbor, if necessary.

See Also

discrete.BH(), DBR()

Plot Method for DiscreteFDR objects

Description

Plots raw p-values of a DiscreteFDR object and highlights rejected and accepted p-values. If present, the critical values are plotted, too.

Usage

## S3 method for class 'DiscreteFDR'
plot(
  x,
  col = c(2, 4, 1),
  pch = c(20, 20, 17),
  lwd = rep(par()$lwd, 3),
  cex = rep(par()$cex, 3),
  type.crit = "b",
  legend = NULL,
  ...
)

Arguments

x

object of class DiscreteFDR.

col

numeric or character vector of length 3 indicating the colors of the

  1. rejected p-values

  2. accepted p-values

  3. critical values (if present).

pch

numeric or character vector of length 3 indicating the point characters of the

  1. rejected p-values

  2. accepted p-values

  3. critical values (if present and type.crit is a plot type like 'p', 'b' etc.).

lwd

numeric vector of length 3 indicating the thickness of the points and lines; defaults to current par()$lwd setting.

cex

numeric vector of length 3 indicating the size of point characters or lines of the

  1. rejected p-values

  2. accepted p-values

  3. critical values (if present).

defaults to current par()$cex setting.

type.crit

1-character string giving the type of plot desired for the critical values (e.g.: 'p', 'l' etc; see plot()).

legend

if NULL, no legend is plotted; otherwise expecting a character string like "topleft" etc. or a numeric vector of two elements indicating (x, y) coordinates.

...

further arguments to plot.default().

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

DBH.su.fast <- DBH(raw.pvalues, pCDFlist)
DBH.su.crit <- DBH(raw.pvalues, pCDFlist, ret.crit.consts = TRUE)
DBH.sd.fast <- DBH(test.result, direction = "sd")
DBH.sd.crit <- DBH(test.result, direction = "sd", ret.crit.consts = TRUE)

plot(DBH.sd.fast)
plot(DBH.sd.crit, xlim = c(1, 5), ylim = c(0, 0.4))
plot(DBH.su.fast, col = c(2, 4), pch = c(2, 3), lwd = c(2, 2), 
     legend = "topleft", xlim = c(1, 5), ylim = c(0, 0.4))
plot(DBH.su.crit, col = c(2, 4, 1), pch = c(1, 1, 4), lwd = c(1, 1, 2), 
     type.crit = 'o', legend = c(1, 0.4), lty = 1, xlim = c(1, 5), 
     ylim = c(0, 0.4))

Printing DiscreteFDR results

Description

Prints the results of discrete FDR analysis, stored in a DiscreteFDR class object.

Usage

## S3 method for class 'DiscreteFDR'
print(x, ...)

Arguments

x

an object of class "DiscreteFDR".

...

further arguments to be passed to or from other methods. They are ignored in this function.

Value

The input object x is invisibly returned via invisible(x).

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

DBH.su.crit <- DBH(raw.pvalues, pCDFlist, direction = "su",
                   ret.crit.consts = TRUE)
print(DBH.su.crit)

Summarizing Discrete FDR Results

Description

summary method for class DiscreteFDR.

Usage

## S3 method for class 'DiscreteFDR'
summary(object, ...)

## S3 method for class 'summary.DiscreteFDR'
print(x, max = NULL, ...)

Arguments

object

an object of class DiscreteFDR.

...

further arguments passed to or from other methods.

x

an object of class summary.DiscreteFDR.

max

numeric or NULL, specifying the maximal number of rows of the p-value table to be printed. By default, when NULL, getOption("max.print") is used.

Details

summary.DiscreteFDR objects contain all data of an DiscreteFDR object, but also include an additional table which includes the raw p-values, their indices, the respective critical values (if present), the adjusted p-values (if present) and a logical column to indicate rejection. The table is sorted in ascending order by the raw p-values.

print.summary.DiscreteFDR simply prints the same output as print.DiscreteFDR, but also prints the p-value table.

Value

summary.DiscreteFDR computes and returns a list that includes all the data of an input DiscreteFDR object, plus

Table

data.frame, sorted by the raw p-values, that contains the indices, the raw p-values themselves, their respective critical values (if present), their adjusted p-values (if present) and a logical column to indicate rejection.

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

DBH.sd.crit <- DBH(raw.pvalues, pCDFlist, direction = "sd",
                   ret.crit.consts = TRUE)
summary(DBH.sd.crit)