GetStabilityDistance: Stability measures for gene rankings

Description

The similarity of two rankings is assessed by computing a weighted distance measure. This function implements weighted absolute- and squared distance, a weighted versions of Spearman's rank correlation coefficient and Kendall's tau. Note that Spearman's rank correlation coefficient is not a distance measure in the classical sense, but can be obtained as transformation of the squared distance.

Usage

GetStabilityDistance(RR, scheme = c("original", "pairwise"), measure = c("l1", "l2", "spearman", "kendall"),
decay = c("linear", "quadratic", "exponential"), alpha = 1, ...)

Arguments

An object of class RepeatedRanking

scheme

If scheme = "original", a reference ranking is compared with alternative rankings. If scheme = "pairwise", all possible pairs of rankings are compared. The latter is normally used in the absence of a reference ranking, e.g. if the agreement of different ranking procedures is of interest.

measure

The measure to be used. measure = "l1" computes a weighted absolute distance, measure = "l2" a weighted squared distance. measure = "spearman" computes a weighted version of Spearman's rank correlation coefficient. measure = "kendall" computes a weighted version of Kendall's tau. Note that, unlike in the function cor in R base, Kendall's tau ranges from 0 to 1, and not from -1 to 1, which is the case when measure = "spearman". Absolute- and squared distance are suitably normalized to fall into the unit interval for the sake of better interpretability, with zero corresponding to maximal instability.

decay

Argument controlling the weight decay of the weights of the summands contributing to the stability measure. If decay="linear", then we have weight 1/r for rank r, if decay="quadratic", then the weight is 1/r^2 and if decay="exponential", then the weight is exp(-alpha*r) where alpha is a tuning parameter, specified via the argument alpha.

alpha

s. decay.

...

Currently unused argument.

Value

StabilityDistance

References

Jurman, G., Merler, S., Barla, A., Paoli, S., Galea, A., Furlanello, C. (2008). Algebraic stability indicators for ranked lists in molecular profiling. Bioinformatics 24, 258-264

DeConde, R. P., Hawley, S., Falcon, S., Clegg, N., Knudsen, B., Etzioni, R. (2006). Combining results of microarray experiments: a rank aggregation approach. Statistical Applications in Genetics and Molecular Biology 5, 15

Examples

Run this code

 ## Load toy gene expression data
data(toydata)
### class labels
yy <- toydata[1,]
### gene expression
xx <- toydata[-1,]
### get ranking 
ordT <- RankingTstat(xx, yy, type="unpaired")
### Generate Leave-One-Out
loo <- GenerateFoldMatrix(y = yy, k=1)
### Repeat Ranking with t-statistic
loor_ordT <- RepeatRanking(ordT, loo)
### assess stability
stab_dis_ordT <- GetStabilityDistance(loor_ordT, scheme  = "original", measure = "spearman", decay="linear")
### for a short summary
summary(stab_dis_ordT, display = "all")