# Estimate FDR control variations for HFDR procedure

### Description

This function estimates two types of HFDR control appropriate for trees of hypotheses. If the BH procedure is applied at level alpha within each of the tree families, this is defined as

FDR.est := α * [\#\textit{discoveries} + \#\textit{families tested}] / [\textit{\#discoveries} + 1]

where a discovery is defined as an adjusted p value below alpha within the entire tree or at the tips for tree and tips FDR, respectively.

### Usage

 1 EstimatedHFDRControl(hyp.tree) 

### Arguments

 hyp.tree An object of class HypothesesTree, such as the result to a call of hFDR.adjust.

### Value

 tree The estimated full-tree FDR. tip The estimated outer-nodes FDR. n.families.tested The number of families of hypotheses tested by the HFDR procedure. n.tree.discoveries The number of discoveries over the whole tree. n.tip.discoveries The number of discoveries among the tree tips.

Kris Sankaran

### References

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

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

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/

hypothesesTree-class hFDR.adjust

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 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) EstimatedHFDRControl(hyp.tree) 

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