# discoveries: Confidence Bound for the Number of True Discoveries In sumSome: Permutation True Discovery Guarantee by Sum-Based Tests

## Description

This function determines a lower confidence bound for the number of true discoveries within a set of interest. The bound remains valid under post-hoc selection.

## Usage

 ```1 2 3 4``` ```discoveries(object) ## S3 method for class 'sumObj' discoveries(object) ```

## Arguments

 `object` an object of class `sumObj`, as returned by the functions `sumStats` and `sumPvals`.

## Value

`discoveries` returns a lower (1-`alpha`)-confidence bound for the number of true discoveries in the set.

Anna Vesely.

## References

Goeman, J. J. and Solari, A. (2011). Multiple testing for exploratory research. Statistical Science, 26(4):584-597.

Hemerik, J. and Goeman, J. J. (2018). False discovery proportion estimation by permutations: confidence for significance analysis of microarrays. JRSS B, 80(1):137-155.

Vesely, A., Finos, L., and Goeman, J. J. (2020). Permutation-based true discovery guarantee by sum tests. Pre-print arXiv:2102.11759.

Create a `sumObj` object: `sumStats`, `sumPvals`

Lower confidence bound for the TDP: `tdp`

Upper confidence bound for the FDP: `fdp`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# generate matrix of p-values for 5 variables and 10 permutations G <- simData(prop = 0.6, m = 5, B = 10, alpha = 0.4, seed = 42) # subset of interest (variables 1 and 2) S <- c(1,2) # create object of class sumObj # combination: harmonic mean (Vovk and Wang with r = -1) res <- sumPvals(G, S, alpha = 0.4, r = -1) res summary(res) # lower confidence bound for the number of true discoveries in S discoveries(res) # lower confidence bound for the true discovery proportion in S tdp(res) # upper confidence bound for the false discovery proportion in S fdp(res) ```

sumSome documentation built on Nov. 24, 2021, 9:06 a.m.