# Implementation of five SAM test statistics in the SAM procedure

### Description

The function calculates SAM test statistics from permutations for the five test statistics (the global likelihood test, Williams, Marcus, M, and the modified M).

### Usage

1 | ```
Isoqqstat(x, y, fudge, niter)
``` |

### Arguments

`x` |
indicates the dose levels |

`y` |
gene expression for all genes |

`fudge` |
the fudge factor value to be used in the SAM test statistics: either fudge="pooled" then it is calculated by the function, or fudge="none" then no fudge factor is used |

`niter` |
number of permutations used in the SAM procedure |

### Value

A list with components

`aa1` |
the matrix of the observed test statistic values using the likelihood ratio test with 4 columns: the first column contains the observed test statistic values sorted in ascending order, the second contains the mean expected test statistic values obtained from permutations, the third column contains the difference between the first and the second column, and the last column gives the ranking of the genes in ascending order. |

`to1` |
the matrix of the test statistic values from permutations using the likelihood ratio test: each column of the matrix corresponds to the sorted test statistic from each permutation in an ascending order. |

`aa2` |
the matrix of the observed test statistic values using Williams' test with 4 columns: the first column is the sorted observed test statistic values in an ascending order, the second is the mean expected test statistic values obtained from permutations, the third column is the difference between the first and the second column, and the last column is the rankings of the genes in an ascending order. |

`to2` |
the matrix of the test statistic values from permutations using Williams' test: each column of the matrix corresponds to the sorted test statistic from each permutation in an ascending order. |

`aa3` |
the matrix of the observed test statistic values using Marcus' test with 4 columns: the first column is the sorted observed test statistic values in an ascending order, the second is the mean expected test statistic values obtained from permutations, the third column is the difference between the first and the second column, and the last column is the rankings of the genes in an ascending order. |

`to3` |
the matrix of the test statistic values from permutations using Marcus' test: each column of the matrix corresponds to the sorted test statistic from each permutation in an ascending order. |

`aa4` |
the matrix of the observed test statistic values using the M test with 4 columns: the first column is the sorted observed test statistic values in an ascending order, the second is the mean expected test statistic values obtained from permutations, the third column is the difference between the first and the second column, and the last column is the rankings of the genes in an ascending order. |

`to4` |
the matrix of the test statistic values from permutations using the M test: each column of the matrix corresponds to the sorted test statistic from each permutation in an ascending order. |

`aa5` |
the matrix of the observed test statistic values using the modified M test with 4 columns: the first column is the sorted observed test statistic values in an ascending order, the second is the mean expected test statistic values obtained from permutations, the third column is the difference between the first and the second column, and the last column is the rankings of the genes in an ascending order. |

`to5` |
the matrix of the test statistic values from permutations using the modified M test: each column of the matrix corresponds to the sorted test statistic from each permutation in an ascending order. |

### Note

This function calculates the SAM test statistics to be used in the SAM procedure for the five test statistics. To use the SAM procedure, the number of genes in the data set is preferably larger than 500.

### Author(s)

Lin et al.

### References

Lin D., Shkedy Z., Yekutieli D., Amaratunga D., and Bijnens, L. (editors). (2012) Modeling Dose-response Microarray Data in Early Drug Development Experiments Using R. Springer.

IsoGene: An R Package for Analyzing Dose-response Studies in Microarray Experiments, Pramana S., Lin D., Haldermans P., Shkedy Z., Verbeke T., De Bondt A., Talloen W., Goehlmann H., Bijnens L. 2010, R Journal 2/1.

### See Also

`isoreg`

, `Isoallfdr`

, `IsoGenemSAM`

`Isoqval`

,`IsoTestSAM`

,`IsoSAMPlot`

### Examples

1 2 3 4 5 6 7 8 | ```
set.seed(1234)
x <- c(rep(1,3),rep(2,3),rep(3,3))
y1 <- matrix(rnorm(4500, 1,1),500,9) ## 500 genes with no trends
y2 <- matrix(c(rnorm(1500, 1,1),rnorm(1500,2,1),
rnorm(1500,3,1)),500,9) ## 500 genes with increasing trends
y <- data.frame(rbind(y1, y2)) ##y needs to be a data frame
qqstat <- Isoqqstat(x, y, fudge="pooled", niter = 50)
``` |