sumSome (version 1.1.0)

sumStats: True Discovery Guarantee for Generic Statistics

Description

This function determines confidence bounds for the number of true discoveries, the true discovery proportion and the false discovery proportion within a set of interest. The bounds are simultaneous over all sets, and remain valid under post-hoc selection.

Usage

sumStats(G, S = NULL, alternative = "greater", alpha = 0.05,
         truncFrom = NULL, truncTo = NULL, nMax = 50)

Arguments

G

numeric matrix of statistics, where columns correspond to variables, and rows to data transformations (e.g. permutations). The first transformation is the identity.

S

vector of indices for the variables of interest (if not specified, all variables).

alternative

direction of the alternative hypothesis (greater, lower, two.sided).

alpha

significance level.

truncFrom

truncation parameter: values less extreme than truncFrom are truncated. If NULL, statistics are not truncated.

truncTo

truncation parameter: truncated values are set to truncTo. If NULL, statistics are not truncated.

nMax

maximum number of iterations.

Value

sumStats returns an object of class sumObj, containing

• total: total number of variables (columns in G)

• size: size of S

• alpha: significance level

• TD: lower (1-alpha)-confidence bound for the number of true discoveries in S

• maxTD: maximum value of TD that could be found under convergence of the algorithm

• iterations: number of iterations of the algorithm

Details

Truncation parameters should be such that truncTo is not more extreme than truncFrom.

The significance level alpha should be in the interval [1/B, 1), where B is the number of data transformations (rows in G).

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.

See Also

True discovery guarantee using p-values: sumPvals

Access a sumObj object: discoveries, tdp, fdp

Examples

# NOT RUN {
# generate matrix of t-scores for 5 variables and 10 permutations
G <- simData(prop = 0.6, m = 5, B = 10, alpha = 0.4, p = FALSE, seed = 42)
 
# subset of interest (variables 1 and 2)
S <- c(1,2)
 
# create object of class sumObj
res <- sumStats(G, S, alpha = 0.4, truncFrom = 0.7, truncTo = 0)
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)
# }