lrstat (version 0.3.3)

fCERRej: Determine stage 2 rejections from conditional error rates

Description

Determine the elementary hypotheses rejected after stage 2 using adapted stage 2 bounds and cumulative p-values.

Usage

fCERRej(cum_p, stg1_elemhyp_r_idx, stg2_elemhyp_idx, stg2_inthyp, stg2_bnd_new)

Value

A logical vector containing:

• One value for each elementary hypothesis, indicating whether it is rejected after stage 2.

• Values are ordered by the elementary-hypothesis indices of the original procedure.

Arguments

cum_p

Cumulative p-values for the elementary hypotheses in stage 2.

stg1_elemhyp_r_idx

Indices of the elementary hypotheses rejected in stage 1.

stg2_elemhyp_idx

Indices of the elementary hypotheses in stage 2.

stg2_inthyp

Indicator matrix of the intersection hypotheses in stage 2.

stg2_bnd_new

New stage 2 bounds for the elementary hypotheses in each intersection hypothesis.

Author

Kaifeng Lu,

References

Cyrus Mehta, Ajoy Mukhopadhyay, and Martin Posch. Graph Based, Adaptive, Multiarm, Multiple Endpoint, Two-Stage Designs. Statistics in Medicine. 2025.

Examples

initial_weights <- c(0.5, 0.5, 0, 0)
transition_matrix <- matrix(c(0, 0.5, 0.5, 0,
                              0.5, 0, 0, 0.5,
                              0, 1, 0, 0,
                              1, 0, 0, 0),
                            nrow = 4, byrow = TRUE)
wgtmat <- fwgtmat(initial_weights, transition_matrix)
family <- matrix(c(1, 1, 0, 0,
                   0, 0, 1, 1), nrow = 2, byrow = TRUE)
corr <- matrix(c(1, 0.5, NA, NA,
                 0.5, 1, NA, NA,
                 NA, NA, 1, 0.5,
                 NA, NA, 0.5, 1),
               nrow = 4, byrow = TRUE)
stage1_pvalues <- c(0.00045, 0.0952, 0.0225, 0.1104)
bounds <- fCERStageBound(
  wgtmat, family, corr, alpha = 0.025,
  alpha1 = errorSpent(0.5, 0.025, "sfOF"),
  info_frac = 0.5, nthreads = 1)
conditional_error_rates <- fCERCer(
  stage1_pvalues, wgtmat, family, corr, info_frac = 0.5,
  bounds$stg1_bnd, bounds$stg2_bnd, nthreads = 1)
stage2_weight_matrix <- fwgtmat(
  w = c(0.5, 0.5),
  G = matrix(c(0, 1, 1, 0), 2, 2, byrow = TRUE))
adapted_bounds <- fCERNewBound(
  stage1_pvalues, wgtmat, family, corr,
  conditional_error_rates$stg1_inthyp_nr_idx,
  conditional_error_rates$CER,
  stg2_elemhyp_idx = c(2, 4), stage2_weight_matrix,
  info_frac_new = 0.4, nthreads = 1)
stage2_cumulative_pvalues <-
  1 - pnorm(sqrt(0.4) * qnorm(1 - c(0.0952, 0.1104)) +
              sqrt(1 - 0.4) * qnorm(1 - c(0.0299, 0.0586)))
fCERRej(stage2_cumulative_pvalues,
        conditional_error_rates$stg1_elemhyp_r_idx,
        stg2_elemhyp_idx = c(2, 4),
        adapted_bounds$inthyp, adapted_bounds$stg2_bnd_new)