# Nonparametric inference for linear models in Gene-Set-Enrichment Analysis (GSEA)

### Description

Provides permutation-based p-values for a main effect at the gene-set
level, potentially adjusting for the effect of other variables via a
linear model. This is a generalization and upgrade of `gseattperm`

.

### Usage

1 |

### Arguments

`eSet` |
An |

`formula` |
An object of class |

`mat` |
A 0/1 incidence matrix with each row representing a gene set and each column representing a gene. A 1 indicates membership of a gene in a gene set. |

`nperm` |
Number of permutations used to simulate the reference null distribution. |

`na.rm` |
Should missing observations be ignored? (passed on to |

`pooled` |
Should variance be pooled across all genes?
(passed on to |

`detailed` |
Would you like a detailed output, or just the p-values? Defaults to FALSE for back-compatibility. |

`...` |
Additional parameters passed on to |

### Details

If a formula is provided, the permutation test permutes sample (i.e. column) labels, so essentially the effect is compared with the null distribution of effects for *each particular gene-set separately*. This neutralizes the impact of intra-sample correlations. If the formula contains two or more covariates, the effect of interest must be the first one in the formula. This effect's covariate values are permuted within each subgroup defined by identical values on all other covariates. This means, that the other covariates *must* be discrete, otherwise the analysis is meaningless. The effect of interest is the only one that can be continuous.

If a formula is *not* provided, a row-permutation test is performed on average expression levels. This test examines whether each gene-set is differentially expressed (on the average), compared with a permutation baseline of random gene-sets of the same size.

The p-values have now been corrected to reflect the accepted statistical approach, i.e. that the observed data is considered part of the permutation distribution under the null. Hence, p-values of zero are impossible from now on. This is hard-coded.

### Value

If `detailed=FALSE`

, A matrix with the same number of rows as `mat`

and two columns,
"Lower" and "Upper". The "Lower" ("Upper") column gives
the probability of seeing a t-statistic smaller or equal (larger or equal) to the
observed. If 'mat' had row names, so will the output.

If `detailed=TRUE`

, A list with components:

`pvalues` |
The above-mentioned, two-column p-value matrix. |

`lmfit` |
The |

`stats` |
The observed statistics generated via the true model; i.e., the ones for which the p-values are calculated. |

`perms` |
The full matrix of permutation statistics, of dimension nrow( |

### Warnings

1. Inference is *only* for the first term in the model. If you want inference for more terms, re-run the function on the same model, changing order of terms each time.

2. To repeat: the adjusting covariates (all terms except the first) have to be discrete. Adding a continuous covariate with unique values for most samples, may result in an infinite loop. However, you *can* put a continuous covariate as your first term.

### Note

This function is a generic template for GSEA permutation tests. The
particular type of GSEA statistic used is determined by `GSNormalize`

, which is called by this function. Permutations are generated via repeated calls to `lmPerGene`

.

### Author(s)

Assaf Oron

### See Also

`gseattperm`

,`GSNormalize`

, `lmPerGene`

. The
`GlobalAncova`

package provides a generic
$F$-test for model selection, while `gsealmPerm`

can be
used as a Wald test for the addition of a single covariate to the model.

### 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 32 33 | ```
data(sample.ExpressionSet)
### Generating random pseudo-gene-sets
fauxGS=matrix(sample(c(0,1),size=50000,replace=TRUE,prob=c(.9,.1)),nrow=100)
### inference for sex: sex is first term
sexPvals=gsealmPerm(sample.ExpressionSet,~sex+type,mat=fauxGS,nperm=40)
### inference for type: type is first term
typePvals=gsealmPerm(sample.ExpressionSet,~type+sex,mat=fauxGS,nperm=40,removeShift=TRUE)
### plotting the p-values; note that the effect direction depends upon
### factor level order (defaults to alphabetical)
layout(t(1:2))
### Sex p-values are center-heavy, typical when the effect is dominated
### by another effect
hist(sexPvals[,2],10,main="Sex Effect p-values",xlab="p-values for Male minus Female",xlim=c(0,1))
### The dominating effect is type, where there is a baseline shift in
### favor of controls
hist(typePvals[,1],10,main="Type Effect p-values",xlab="p-values for Case minus Control",xlim=c(0,1))
############
### Modeling type again - and now we add a baseline-shift removal (the 'removeShift' argument passed on to 'GSNormalize')
typePvals1=gsealmPerm(sample.ExpressionSet,~type+sex,mat=fauxGS,nperm=40,removeShift=TRUE)
### Modeling type again - and now the shift removal is by mean instead
### of the default median
typePvals2=gsealmPerm(sample.ExpressionSet,~type+sex,mat=fauxGS,nperm=40,removeShift=TRUE,removeStat=mean)
### Now notice the differences between the 3 versions! This is a weird
### dataset indeed; it's also important to undrestand which research
### question you are trying to answer :)
hist(typePvals1[,1],10,main="Type Effect p-values",xlab="p-values for Case minus Control",xlim=c(0,1))
hist(typePvals2[,1],10,main="Type Effect p-values",xlab="p-values for Case minus Control",xlim=c(0,1))
``` |

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