# Structured Simultaneous and Selective Inference for Grouped or Hierarchically Structured Data

### Description

Performs multiple corrections that take specific structure of hypotheses into account. The two procedures implemented are the Hierarchically FDR controlling procedure of Benjamini and Yekutieli and the Group Benjamini-Hochberg procedure of Hu, Zhou, and Zhao. The methods are applicable whenever information about hierarchical or group relationship between hypotheses can be ascertained before any data analysis.

### Details

Package: | structSSI |

Type: | Package |

Version: | 1.0 |

Date: | 2012-03-14 |

License: | GPL-2 |

This package implements two recently developed techniques in the field of selective and simultaneous inference (SSI). The first method is the Adaptive Groups Benjamini-Hochberg procedure of Hu, Zhou, and Zhao 2011. The second is the Hierarchical FDR Controlling Procedure of Benjamini and Yekutieli. Both methods attempt to employ apriori known information about the relationships between hypotheses in testing them and correcting for the multiple testing problem. These methods have been employed in genetics, QTL analysis, and clinical trials; more deatils about these applications can be read in the references stated below.

The Group Benjamini-Hochberg procedure is implemented in its adaptive
and oracle varieties through the functions `Adaptive.GBH`

and
`Oracle.GBH`

, respectively. The Hierarchical Procedure is
implemented in the function `hFDR.adjust`

and uses the class
`hypothesesTree`

to organize the information required for the
procedure. These functions describe the procedures in more
detail. Further, the references listed below present the derivations
and applications of these two procedures.

### Author(s)

Kris Sankaran

Maintainer: kriss1@stanford.edu

### References

Benjamini, Y, and Yekutieli, D. Hierarchical fdr testing of trees of hypotheses. 2002.

Hu, J.X., Zhao, H., and Zhou, H.H. False discovery rate control with groups. Journal of the American Statistical Association, volume 104, number 491. Pages 1215-1227. 2010.

Sankaran, K and Holmes, S. structSSI: Simultaneous and Selective Inference for Grouped or Hierarchically Structured Data. Journal of Statistical Software, 59(13), 1-21. 2014. http://jstatsoft.org/v59/i13/

Yekutieli, D. Hierarchical false discovery rate-controlling methodology. Journal of the American Statistical Association, 103(481):309-316, 2008.

### 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 | ```
## Example of using the Adaptive Benjamini-Hochberg Procedure.
set.seed(2249)
unadjp <- c(runif(40, 0, 0.001), runif(30, 0, 0.1), runif(130, 0, 1))
names(unadjp) <- paste("hyp", c(1:200))
groups <- c(sample(1:3, 200, replace = TRUE))
result <- Adaptive.GBH(unadjp, groups, method = "lsl", alpha = 0.05)
## Example of using the Hierarchical FDR controlling procedure.
library('igraph')
library('ape')
alternative.indices <- sample(1:49, 30)
unadj.p.values <- vector("numeric", length = 49)
unadj.p.values[alternative.indices] <- runif(30, 0, 0.01)
unadj.p.values[-alternative.indices] <- runif(19, 0, 1)
unadj.p.values[c(1:5)] <- runif(5, 0, 0.01)
names(unadj.p.values) <- paste("Hyp ", c(1:49))
tree <- as.igraph(rtree(25))
V(tree)$name <- names(unadj.p.values)
tree.el <- get.edgelist(tree)
hyp.tree <- hFDR.adjust(unadj.p.values, tree.el, 0.05)
plot(hyp.tree)
``` |

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