# Oracle Group Benjamini-Hochberg Correction Performs the Group Benjamini-Hochberg procedure when the true proportion of null hypotheses is known within each group. The procedure is applicable whenever group structure about the relationship between different hypotheses is known before testing begins. The idea is to control the FDR within each group and to use the proportion of null hypotheses present within each group to make the testing procedure within that group either more or less conservative -- this is in fact the idea behind all adaptive multiple testing procedures. The Oracle GBH method can also be used when we would like to use the Adaptive GBH procedure but with estimates of proportions of true null hypotheses within groups that are not made directly available through the `Adaptive.GBH` function -- in this case those estimates can be input as the argument `pi.groups` in the this function `Oracle.GBH`. ```r Oracle.GBH(unadj.p, group.index, pi.groups, alpha = 0.05) ``` ## Arguments - `unadj.p`: A vector of the unadjusted p-values resulting from a multiple testing experiment. - `group.index`: A vector of the same length as the vector of unadjusted p-values, where a "G" in the jth coordinate indicates that the jth unadjusted p-values in `unadj.p` belongs to group "G". This code can be either a factor giving group names, or a numeric index. - `pi.groups`: A vector of the known proportions of true null hypotheses within each of the groups. This vector should be named so that each element of the `group.index` vector correspond to one of the names of the `pi.groups` vector. - `alpha`: The level that we are attempting to control the FDR at. ## Returns An object of class `GBH`, which provides the adjusted p-values. ## Details 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. https://jstatsoft.org/v59/i13/ ## Examples ```r # A very simple example, with only 5 hypotheses. unadjp <- c(0.002, 0.1, 0.001, 0.01, 0.4) names(unadjp) <- paste("hyp", 1:5) groups <- c(1, 2, 1, 2, 2) # Say we know goup 1 has pi_0,1 = 0.3 and pi_0,2 = 0.9 pi.groups <- c("1" = 0.3, "2" = 0.9) Oracle.GBH(unadjp, groups, pi.groups) # An example where we use an external pi0 estimation routine unadjp.2 <- c(runif(500, 0, 0.01), runif(1500, 0, 1)) names(unadjp.2) <- paste("hyp", 1:2000) groups.2 <- c(sample(1:2, 2000, replace = TRUE)) pi.groups <- c("1" = NA, "2" = NA) for(i in 1:2){ pi.groups[i] <- estimate.pi0(unadjp.2[which(groups.2 == i)], method = "storey") } result <- Oracle.GBH(unadjp.2, groups.2, pi.groups, 0.05) result@pi0 result@p.vals ```

Oracle.GBH function