E-value Based Sequential Testing

Implementation of e-value methodology for sequential hypothesis testing following the framework of Ramdas et al. This provides anytime-valid inference with optional stopping and flexible error control.

Usage

evalue_sequential_test(
  data,
  formula,
  blocks,
  alpha = 0.05,
  wealth_rule = "kelly",
  stopping_rule = "wealth_threshold"
)

Arguments

data

Individual-level data

formula

Test formula

blocks

Block identifiers

alpha

Type I error rate

wealth_rule

Wealth accumulation rule ("kelly", "fixed", "adaptive")

stopping_rule

Early stopping rule ("never", "wealth_threshold", "e_threshold")

Value

E-value based test results

References

Ramdas, A., Grünwald, P., Vovk, V., & Shafer, G. (2023). Game-theoretic statistics and safe anytime-valid inference. Statistical Science, 38(4), 576-601.

Examples

if (FALSE) { # \dontrun{
# Load example data for e-value testing with find_blocks
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 e-value methodology (experimental)
# Note: This provides anytime-valid inference
results_evalues <- find_blocks(
  idat = idat,
  bdat = bdat,
  blockid = "blockF",
  splitfn = splitCluster,
  pfn = pOneway,
  fmla = Y1 ~ trtF | blockF,
  splitby = "hwt",
  parallel = "no",
  use_evalues = TRUE,
  evalue_wealth_rule = "kelly", # Ramdas recommends Kelly betting
  thealpha = 0.05,
  maxtest = 15
)

# Direct use of e-value sequential testing
evalue_results <- evalue_sequential_test(
  data = idat,
  formula = Y1 ~ trtF,
  blocks = idat$blockF,
  alpha = 0.05,
  wealth_rule = "kelly",
  stopping_rule = "wealth_threshold"
)

# Examine e-value results
cat("E-value sequential testing results:\n")
cat("Final wealth:", evalue_results$final_wealth, "\n")
cat("Total rejections:", evalue_results$total_rejections, "\n")
cat("Stopped early:", evalue_results$stopped_early, "\n")

# Plot wealth accumulation over time
if (requireNamespace("ggplot2", quietly = TRUE)) {
  library(ggplot2)
  wealth_plot <- ggplot(
    evalue_results$results,
    aes(x = seq_along(block_id), y = wealth)
  ) +
    geom_line() +
    geom_hline(yintercept = 1 / 0.05, linetype = "dashed", color = "red") +
    labs(
      x = "Sequential Test Number", y = "Wealth",
      title = "E-value Wealth Accumulation",
      subtitle = "Red line shows rejection threshold (1/alpha)"
    )
  print(wealth_plot)
}

# Compare e-values with traditional p-values
comparison_data <- data.frame(
  test = seq_along(evalue_results$results$e_value),
  e_value = evalue_results$results$e_value,
  p_value = evalue_results$results$p_value,
  wealth = evalue_results$results$wealth
)

cat("E-value vs P-value comparison (first 5 tests):\n")
print(head(comparison_data, 5))
} # }