# Significance Analysis of Function and Expression

### Description

Performs a significance analysis of function and expression (SAFE) for a gene expression experiment and a set of functional categories specified by the user. SAFE is a two-stage resampling-based method that can be applied to a 2-sample, paired, multi-class, simple linear and right-censored linear regression models. Other experimental designs can also be accommodated through user-defined functions.

### Usage

1 2 3 4 5 6 7 | ```
safe(X.mat, y.vec, C.mat = NULL, Z.mat = NULL,
method = "permutation", platform = NULL,
annotate = NULL, min.size = 2, max.size = Inf,
by.gene = FALSE, local = "default", global = "default",
args.local = NULL, args.global = list(one.sided = FALSE),
Pi.mat = NULL, error = "FDR.BH", parallel=FALSE, alpha = NA,
epsilon = 10^(-10), print.it = TRUE, ...)
``` |

### Arguments

`X.mat` |
A matrix or data.frame of expression data of size m by n where each row corresponds to a gene feature and each column to a sample. Data should be properly normalized and cannot contain missing values. |

`y.vec` |
A numeric, integer or character vector of length n containing the response of interest. For examples of the acceptable forms |

`C.mat` |
A matrix containing the gene category assignments. Each column represents a category and should be named accordingly. For each column, values of 1 ( |

`Z.mat` |
A data.frame of size n by p, with p covariates as numeric or factors. |

`method` |
Type of hypothesis test can be specified as "permutation", "bootstrap.t", and "bootstrap.q". "express" calls the dependent package |

`platform` |
If |

`annotate` |
If |

`min.size` |
Optional minimum category size in building |

`max.size` |
Optional maximum category size in building |

`by.gene` |
Logical argument (default = |

`local` |
Specifies the gene-specific statistic from the following options: "t.Student", "t.Welch", and "t.paired", for 2-sample designs, "f.ANOVA" for 1-way ANOVAs, and "t.LM" for simple linear regressions. "default" will choose between "t.Student", "f.ANOVA", and "t.LM" based on the form of |

`global` |
Specifies the global statistic for a gene categories. By default, the Wilcoxon rank sum ("Wilcoxon") is used. Else, a Fisher's Exact test statistic ("Fisher"), a Pearson's chi-squared type statistic ("Pearson") or t-statistic for average difference ("AveDiff") is available. User-defined global statistics can also be implemented. |

`args.local` |
An optional list to be passed to user-defined local statistics that require additional arguments. By default |

`args.global` |
An optional list to be passed to global statistics that require additional arguments. For two-sided local statistics, |

`Pi.mat` |
Either an integer, or a matrix or data.frame containing the permutations. See |

`error` |
Specifies the method for computing error rate estimates. By default, Benjamini-Hochberg step down ("FDR.BH") FDR estimates are computed. A Bonferroni ("FWER.Bonf") and Holm's step-up ("FWER.Holm") adjustment can also be specified. Under permutation, "FDR.YB" computes the Yekutieli-Benjamini FDR estimate, and "FWER.WY" computes the Westfall-Young FWER estimate. The user can also specify "none" if no error rates are desired. |

`parallel` |
Logical argument (default = |

`alpha` |
The threshold for significant results to return. By default, alpha will be 0.05 for nominal p-values ( |

`epsilon` |
Numeric argument sets the minimum difference for ranking local and global statistics, correcting a numerical precision issue when computing empirical p-values in small data sets (n < 15). The default value is 10^(-10). |

`print.it` |
Logical argument (default = |

`...` |
Allows arguments from version 2.0 to be ignored. |

### Details

`safe`

utilizes a general framework for testing differential expression across gene categories that allows it to be used in various experimental designs. Through structured resampling of the data, `safe`

accounts for the unknown correlation among genes, and enables proper estimation of error rates when testing multiple categories. `safe`

also provides statistics and empirical p-values for the gene-specific differential expression.

### Value

The function returns an object of class `SAFE`

. See help for `SAFE-class`

for more details.

### Author(s)

William T. Barry: bbarry@jimmy.harvard.edu

### References

W. T. Barry, A. B. Nobel and F.A. Wright, 2005, *Significance Analysis of functional categories in gene expression studies: a structured permutation approach*, *Bioinformatics* **21**(9) 1943–1949.

See also the vignette included with this package.

### See Also

`safeplot`

, `safe.toptable`

, `gene.results`

, `getCmatrix`

, `getPImatrix`

.

### Examples

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 | ```
## Simulate a dataset with 1000 genes and 20 arrays in a 2-sample design.
## The top 100 genes will be differentially expressed at varying levels
g.alt <- 100
g.null <- 900
n <- 20
data<-matrix(rnorm(n*(g.alt+g.null)),g.alt+g.null,n)
data[1:g.alt,1:(n/2)] <- data[1:g.alt,1:(n/2)] +
seq(2,2/g.alt,length=g.alt)
dimnames(data) <- list(c(paste("Alt",1:g.alt),
paste("Null",1:g.null)),
paste("Array",1:n))
## A treatment vector
trt <- rep(c("Trt","Ctr"),each=n/2)
## 2 alt. categories and 18 null categories of size 50
C.matrix <- kronecker(diag(20),rep(1,50))
dimnames(C.matrix) <- list(dimnames(data)[[1]],
c(paste("TrueCat",1:2),paste("NullCat",1:18)))
dim(C.matrix)
results <- safe(data,trt,C.mat = C.matrix,Pi.mat = 100)
results
## SAFE-plot made for the first category
if (interactive()) {
safeplot(results,"TrueCat 1")
}
``` |

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