Proper Closed Testing Procedure for Hierarchical Hypotheses

This implements a valid closed testing procedure following Goeman's methodology that ensures proper FWER control by testing all intersection hypotheses.

Usage

closed_testing_procedure(node_dat, tracker, alpha = 0.05, method = "simes")

Arguments

node_dat

Data table with node information including p-values and hierarchy

tracker

Node tracker object with tree structure

alpha

Overall Type I error rate

method

Method for combining p-values in intersections ("simes", "fisher", "min")

Value

Updated node_dat with valid rejection decisions

References

Goeman, J. J., & Solari, A. (2011). Multiple testing for exploratory research. Statistical science, 26(4), 584-597.

Goeman, J. J., & Finos, L. (2012). The inheritance procedure: multiple testing of tree-structured hypotheses. Statistical Applications in Genetics and Molecular Biology, 11(1).

Examples

if (FALSE) { # \dontrun{
# Load example data and run find_blocks with closed testing
data(example_dat, package = "manytestsr")
library(data.table)
library(dplyr)

# Prepare data
idat <- as.data.table(example_dat)
bdat <- idat %>%
  group_by(blockF) %>%
  summarize(
    nb = n(),
    pb = mean(trt),
    hwt = (nb / nrow(idat)) * (pb * (1 - pb)),
    .groups = "drop"
  ) %>%
  as.data.table()

# Run find_blocks with closed testing procedure
results_closed <- find_blocks(
  idat = idat,
  bdat = bdat,
  blockid = "blockF",
  splitfn = splitCluster,
  pfn = pIndepDist,
  fmla = Y1 ~ trtF | blockF,
  splitby = "hwt",
  parallel = "no",
  use_closed_testing = TRUE,
  closed_testing_method = "simes", # Goeman & Solari recommend Simes
  thealpha = 0.05,
  maxtest = 20
)

# Compare with traditional approach
results_traditional <- find_blocks(
  idat = idat,
  bdat = bdat,
  blockid = "blockF",
  splitfn = splitCluster,
  pfn = pIndepDist,
  fmla = Y1 ~ trtF | blockF,
  splitby = "hwt",
  parallel = "no",
  use_closed_testing = FALSE,
  thealpha = 0.05,
  maxtest = 20
)

# Examine closed testing results
if ("closed_testing_reject" %in% names(results_closed$node_dat)) {
  closed_rejections <- results_closed$node_dat[
    closed_testing_reject == TRUE,
    .(nodenum, p, closed_testing_reject)
  ]
  cat("Closed testing rejections:\n")
  print(closed_rejections)
}

# Traditional rejections for comparison
traditional_detections <- report_detections(results_traditional$bdat, fwer = TRUE)
cat("Traditional FWER rejections:", sum(traditional_detections$hit, na.rm = TRUE), "\n")
} # }