discrete.PB {FDX}

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.

See Also

kernel, FDX-package, 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 (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)