discrete.PB: Discrete Poisson-Binomial procedure
In FDX: False Discovery Exceedance Controlling Multiple Testing Procedures

discrete.PB

R Documentation

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

discrete.PB(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  adaptive = TRUE,
  critical.values = FALSE,
  exact = TRUE
)

DPB(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  exact = TRUE
)

NDPB(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  critical.values = FALSE,
  exact = TRUE
)

Arguments

`raw.pvalues`	vector of the raw observed p-values, as provided by the end user and before matching with their nearest neighbor in the CDFs supports.
`pCDFlist`	a list of the supports of the CDFs of the p-values. Each support is represented by a vector that must be in increasing order.
`alpha`	the target FDP, a number strictly between 0 and 1. For `*.fast` kernels, it is only necessary, if `stepUp = TRUE`.
`zeta`	the target probability of not exceeding the desired FDP, a number strictly between 0 and 1. If `zeta=NULL` (the default), then `zeta` is chosen equal to `alpha`.
`adaptive`	a boolean specifying whether to conduct an adaptive procedure or not.
`critical.values`	a boolean. If `TRUE`, critical constants are computed and returned (this is computationally intensive).
`exact`	a boolean specifying whether to compute the Poisson-Binomial distribution exactly or by a normal approximation.

Details

DPB and NDPB are wrapper functions for discrete.PB. The first one simply passes all its parameters 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 hypotheses.
`Num.rejected`	Number of rejections.
`Adjusted`	Adjusted p-values (only for step-down direction).
`Critical.values`	Critical values (if requested).
`Method`	A character string describing the used algorithm, e.g. 'Discrete Lehmann-Romano procedure (step-up)'.
`FDP.threshold`	FDP threshold `alpha`.
`Exceedance.probability`	Probability `zeta` of FDP exceeding `alpha`; thus, FDP is being controlled at level `alpha` with confidence `1 - zeta`.
`Data$raw.pvalues`	The values of `raw.pvalues`.
`Data$pCDFlist`	The values of `pCDFlist`.
`Data$data.name`	The respective variable names of `raw.pvalues` and `pCDFlist`.

References

S. Döhler and E. Roquain (2019). Controlling False Discovery Exceedance for Heterogeneous Tests. arXiv:1912.04607v1.

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 (fisher.pvalues.support
# is from 'DiscreteFDR' package!)
df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc")
raw.pvalues <- df.formatted$raw
pCDFlist <- df.formatted$support

DPB.fast <- DPB(raw.pvalues, pCDFlist)
summary(DPB.fast)

DPB.crit <- DPB(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(DPB.crit)

NDPB.fast <- NDPB(raw.pvalues, pCDFlist)
summary(NDPB.fast)

NDPB.crit <- NDPB(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(NDPB.crit)

FDX documentation built on Oct. 18, 2022, 9:09 a.m.