GeneralizedFDREstimators {fdrDiscreteNull}

Adaptive false discovery rate procedure using generalized estimator of the null proportion.

Description

Implement false discovery rate procedures of Chen, X., Doerge, R. and Heyse, J. F. (2018), the Adaptive Benjamini-Hochberg procedure, and the Adaptive Benjamini-Hochberg-Heyse procedure, using the generalized estimator of the proportion of true nulls, for discrete p-values distributions.

Usage

GeneralizedFDREstimators(data=NULL,
 Test=c("Binomial Test", "Fisher's Exact Test"),
 FET_via = c("PulledMarginals","IndividualMarginals"),
 OneSide = NULL,FDRlevel=NULL,TuningRange = c(0.5,100)) 

Arguments

data

Data to be analyzed in the form of a matrix for which observations for a single entity are in a row. Format of data will be checked by this function automatically and the functions stops execution if the format is wrong.

Test

The type of test to be conducted. It should be exactly one entry from the string c("Binomial Test", "Fisher's Exact Test"). Currently no other type of test is supported by the package.

FET_via

When the type of test is the Fisher's exact test, how the marginal counts are formed should be specified to be exactly one entry from the string c("PulledMarginals", "IndividualMarginals"). When "PulledMarginals" is used, the data matrix should have only two clumns, each row of which contains the observed counts for the two binomial distributions, whereas when "IndividualMarginals" is used the data matrix should have four columns, each row of which has the first and third entries as the observed count and total number of trials of one binomial distribution, and the second and fourth entries as the observed count and total number of trials of the other binomial distribution. For other types of test, this argument need not to be specified.

OneSide

Specify if one-sided p-value is to be computed from the test. If "OneSide= NULL", then two-sided p-value will be computed; if ‘OneSide="Left"’, then the p-value is computed using the left tail of the CDF of the test statistics; if ‘OneSide="Right" ’, then the p-value is computed using the right tail of the CDF of the test statistics.

FDRlevel

The nominal false discovery rate (FDR) no larger than which the method to be applied is to have.

TuningRange

A vector of 2 scalars (a,b). Let rho be the maximum of the minimum of each support whose minimum is smaller than 1. If rho is smaller 0.5, then the smallest guiding value is set as a times (0.5-rho) and the biggest guiding value as 0.5, and b determines the number of equally spaced guiding values. If rho is at least 0.5, then all guiding values are set to be rho and b=1.

Value

It returns the following lists:

BH

Restuls obtained by the Benjamini-Hochberg (BH) procedure.

aBH

Results obtained by the adaptive BH procedure using the generalized estimator of the proportion.

BHH

Results obtained by the Benjamini-Hochberg-Heyse (BHH) procedure.

aBHH

Results obtained by the adaptive BHH (aBHH) procedure using the generalized estimator of the proportion.

Each of the above contains:

pi0Est

The estimated proprtion of true nulls, where for the BH procedure, it is set to be 1.

Threshold

The threshold below which p-values and their associated hypotheses are rejected.

NumberOfDiscoveries

The number of rejections.

IndicesOfDiscoveries

The row indices of the data matrix for the rejections.

It also returns the following:

pvalues

Vector of p-values of the individual tests without grouping.

pvalSupp

It is a list. For binomial test, each entry of the list is a vector, whose first element is the mean of the p-value under the null, second element the p-value itself, and the rest the values at the support of the discrete cdf of the p-value without grouping; for Fisher's exact test, the structure of the list is the same except that in the vector the element denoting the p-value itself is removed.

Finally, it also returns randomized p-values (as "RndPval") and results (as "SARP") of the procedure in Habiger (2015) that is exactly the procedure of Storey et al. (2004) applied to the randomized p-values, and mid p-values (as "MidPval") and "aBHmidP" as the adaptive BH procedure of Benjamini and Hochberg (1995) applied to these mid p-values together with the estimated proportion of true null hypotheses obtained by Storey's estimator in Storey et al. (2004) applied to these mid p-values.

References

Chen, X., Doerge, R. and Heyse, J. F. (2018). Multiple testing with discrete data: proportion of true null hypotheses and two adaptive FDR procedures. Biometrial Journal 60(4): 761-779.

Habiger, J. D. (2015). Multiple test functions and adjusted p-values for test statistics with discrete distributions. J. Stat. Plan. Inference 167: 1-13.

Heyse, J. F. (2011). A false discovery rate procedure for categorical data, in M. Bhattacharjee, S. K. Dhar and S. Subramanian (eds), Recent Advances in Biostatistics: False Discovery Rates, Survival Analysis, and Related Topics, chapter 3.

Lister, R., O'Malley, R., Tonti-Filippini, J., Gregory, B. D., Berry, Charles C. Millar, A. H. and Ecker, J. R. (2008). Highly integrated single-base resolution maps of the epigenome in arabidopsis. Cell 133(3): 523-536.

See Also

GeneralizedEstimatorsGrouped

Examples

library(qvalue)
library(fdrDiscreteNull)
data(listerdata)
ResG = GeneralizedFDREstimators(listerdata[1:100,],
  Test= "Fisher's Exact Test", FET_via = "PulledMarginals",
  OneSide = NULL,FDRlevel=0.05,TuningRange = c(0.5,20))