qtlhot (version 1.2.10)

ww.perm: Conduct West-Wu (Q) permutation tests

Description

This function computes the West/Wu permutation thresholds. The output is a nlod (number of LOD thresholds) by nalpha (number of significance levels) matrix, where each entry shows the hotspot size significance threshold of the West/Wu approach. Note we have two "alphas" here, one for the QTL mapping (the LOD thresholds) and one for the permutation significance (alpha levels of lod.thrs).

Usage

ww.perm(highobj, n.perm, lod.thrs, alpha.levels, verbose = FALSE)
# S3 method for ww.perm
print(x, ...)
# S3 method for ww.perm
summary(object, alpha.levels = attr(object, "alpha.levels"), ...)

Arguments

highobj

object of class highlod

n.perm

number of permutations

lod.thrs

vector of LOD thresholds

alpha.levels

vector of significance levels

verbose

verbose output if TRUE

x, object

object of class ww.perm

...

ignored

Author

Elias Chaibub Neto and Brian S Yandell

Details

Note that I separated the original ww.permutations() into a piece that do the actual permutations [ww.perm.matrix() function] and a piece that summarizes it [the ww.summary() function] in the same way you did with the NL.N.permutations() function.

Perform permutation tests to assess the statistical significance of the hotspots detected using the West-Wu Q-method permutations. The ww.perm function implements the Q-method's permutation scheme (see the Method's section of Chaibub Neto et a. 2012, for details). The n.perm parameter specifies the number of simulations. Here we set it to 100 in order to save time. In practice, we recommend at least 1,000 permutations. The function's output is a matrix with 100 rows representing the permutations, and 10 columns representing the QTL mapping thresholds. Each entry ij, represents the maximum number of significant linkages across the entire genome detected at permutation i, using the LOD threshold j. The ww.summary function computes the Q-method's hotspot size permutation thresholds, that is, the 1-alpha quantiles for each one of the QTL mapping LOD thrsholds in lod.thrs. For instance, the entry at row 10 and column 1 of the Q.1.thr matrix tells us that the 99% percentile of the permutation distribution of genome wide maximum hotspot size based on a QTL mapping threshold of 2.11 is 27.00. In other words, any hotspot greater than 27 is considered statistically significant at a 0.01 significance level when QTL mapping is done using a 2.11 LOD threshold. In general, we are often interested in using the same error rates for the QTL mapping and hotspot analysis. That is, if we adopt a QTL mapping threshold that controls GWER at a 1% level (in our case, 3.11) we will also want to consider alpha = 0.01 for the hotspot analysis, leading to a hotspot threshold of 12.00. Therefore, we are usually more interested in the diagonal of Q.1.thr. We adopted a GWER of 5%, and the corresponding Q-method's permutation threshold is 18. According to this threshold, all hotspots are significant.

Examples

if (FALSE) {
## All unspecified objects come from vignette qtlhot.
set.seed(12345)
Q.1 <- ww.perm(high1, n.perm = 100, lod.thrs, alphas)
Q.1.thr <- summary(Q.1, alphas)
Q.1.thr
diag(Q.1.thr)

set.seed(12345)
Q.2 <- ww.perm(high2, 100, lod.thrs, alphas)
Q.2.thr <- summary(Q.2, alphas)
}