shrinkcat.stat: Correlation-Adjusted t Score (CAT score) In st: Shrinkage t Statistic and Correlation-Adjusted t-Score

Description

`shrinkcat.stat` and `shrinkcat.fun` compute a shrinkage estimate of the “correlation-adjusted t score” of Zuber and Strimmer (2009).

Usage

 ```1 2 3 4``` ```shrinkcat.stat(X, L, lambda, lambda.var, lambda.freqs, var.equal=TRUE, paired=FALSE, verbose=TRUE) shrinkcat.fun(L, lambda, lambda.var, lambda.freqs, var.equal=TRUE, verbose=TRUE) ```

Arguments

 `X` data matrix. Note that the columns correspond to variables (“genes”) and the rows to samples. `L` factor with class labels for the two groups. If only a single label is given then a one-sample CAT score against 0 is computed. `lambda` Shrinkage intensity for the correlation matrix. If not specified it is estimated from the data. `lambda=0` implies no shrinkage and `lambda=1` complete shrinkage. `lambda.var` Shrinkage intensity for the variances. If not specified it is estimated from the data. `lambda.var=0` implies no shrinkage and `lambda.var=1` complete shrinkage. `lambda.freqs` Shrinkage intensity for the frequencies. If not specified it is estimated from the data. `lambda.freqs=0` implies no shrinkage (i.e. empirical frequencies). `var.equal` assume equal (default) or unequal variances in each group. `paired` compute paired CAT score (default is to use unpaired CAT score). `verbose` print out some (more or less useful) information during computation.

Details

The CAT (“correlation-adjusted t”) score is the product of the square root of the inverse correlation matrix with a vector of t scores. The CAT score thus describes the contribution of each individual feature in separating the two groups, after removing the effect of all other features.

In Zuber and Strimmer (2009) it is shown that the CAT score is a natural criterion to rank features in the presence of correlation. If there is no correlation, the CAT score reduces to the usual t score (hence in this case the estimate from `shrinkcat.stat` equals that from `shrinkt.stat`).

The function `catscore` implements multi-class CAT scores.

Value

`shrinkcat.stat` returns a vector containing a shrinkage estimate of the “CAT score” for each variable/gene.

The corresponding `shrinkcat.fun` functions return a function that computes the cat score when applied to a data matrix (this is very useful for simulations).

The scale factor in the ”shrinkage CAT” statistic is computed from the estimated frequencies (to use the standard empirical scale factor set `lambda.freqs=0`).

Author(s)

Verena Zuber and Korbinian Strimmer (http://strimmerlab.org).

References

Zuber, V., and K. Strimmer. 2009. Gene ranking and biomarker discovery under correlation. Bioinformatics 25: 2700-2707. http://dx.doi.org/10.1093/bioinformatics/btp460.

`catscore`, `shrinkt.stat`, `cst.stat`, `lait.stat`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76``` ```# load st library library("st") # prostate data set data(singh2002) X = singh2002\$x L = singh2002\$y dim(X) # 102 6033 length(L) # 102 # shrinkage cat statistic score = shrinkcat.stat(X, L) idx = order(score^2, decreasing=TRUE) idx[1:10] # 610 364 1720 3647 3375 332 3282 3991 1557 914 # compute q-values and local false discovery rates library("fdrtool") fdr.out = fdrtool(as.vector(score)) sum(fdr.out\$qval < 0.05) sum(fdr.out\$lfdr < 0.2) # compared with: # shrinkage t statistic score = shrinkt.stat(X, L) idx = order(score^2, decreasing=TRUE) idx[1:10] # 610 1720 3940 914 364 332 3647 4331 579 1068 # shrinkage CAT score with zero correlation among predictors # is the same as shrinkage t score2 = shrinkcat.stat(X, L, lambda=1) sum((score2-score)^2) # Student t statistic score = studentt.stat(X, L) idx = order(score^2, decreasing=TRUE) idx[1:10] # 610 1720 364 332 914 3940 4546 1068 579 4331 # shrinkage CAT score with zero correlation and no shrinkage # is the same as student t score2 = shrinkcat.stat(X, L, lambda=1, lambda.var=0, lambda.freqs=0, verbose=FALSE) sum((score2-score)^2) # difference of means ("Fold Change") score = diffmean.stat(X, L) idx = order(abs(score), decreasing=TRUE) idx[1:10] # 735 610 694 298 698 292 739 3940 702 721 ## paired CAT score # we drop two cancer cases to make samples size equal in # the two groups to allow to compute paired statistic X = X[1:100,] L = L[1:100] sum(L=="cancer") # 50 sum(L=="healthy") # 50 # paired shrinkage CAT score scat.paired = shrinkcat.stat(X, L, paired=TRUE) # for zero correlation the paired shrinkage CAT score # reduces to the paired shrinkage t score score = shrinkt.stat(X, L, paired=TRUE, verbose=FALSE) score2 = shrinkcat.stat(X, L, lambda=1, paired=TRUE, verbose=FALSE) sum((score-score2)^2) ```