Description Usage Arguments Details Value Author(s) References See Also Examples
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, when using p-values as test statistics. The bounds are simultaneous over all sets, and remain valid under post-hoc selection.
1 2 |
G |
numeric matrix of p-values, 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). |
alpha |
significance level. |
truncFrom |
truncation parameter: values greater than |
truncTo |
truncation parameter: truncated values are set to |
type |
p-value combination among |
r |
parameter for Vovk and Wang's p-value combination. |
nMax |
maximum number of iterations. |
A p-value p
is transformed as following.
Edgington: -p
Fisher: -log(p)
Pearson: log(1-p)
Liptak: -qnorm(p)
Cauchy: tan(0.5 - p)/p
Vovk and Wang: - sign(r)p^r
An error message is returned if the transformation produces infinite values.
Truncation parameters should be such that truncTo
is not smaller than truncFrom
.
As Pearson's and Liptak's transformations produce infinite values in 1, for such methods
truncTo
should be strictly smaller than 1.
The significance level alpha
should be in the interval [1/B
, 1), where
B
is the number of data transformations (rows in G
).
sumPvals
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
Anna Vesely.
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.
True discovery guarantee using generic statistics: sumStats
Access a sumObj
object: discoveries
, tdp
, fdp
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)
|
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