# Estimate FDR control variations for HFDR procedure 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 [REMOVE_ME]$$ FDR.est := \alpha * [\#\textit{discoveries} + \#\textit{families tested}] / [\textit{\#discoveries} + 1] [REMOVE_ME_2]$$ 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. ```r EstimatedHFDRControl(hyp.tree) ``` ## Arguments - `hyp.tree`: An object of class `HypothesesTree`, such as the result to a call of `hFDR.adjust`. ## Returns A list with the following elements, - **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. ## 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 $$ FDR.est := \alpha * [\#\textit{discoveries} + \#\textit{families tested}] / [\textit{\#discoveries} + 1] $$ 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. ## Details 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. https://jstatsoft.org/v59/i13/ ## Examples ```r 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) ```

EstimatedHFDRControl function