Compute conditional error rates — fCERCer • lrstat

Compute conditional error rates for the intersection hypotheses after the first stage of a two-stage multiple testing procedure.

fCERCer(
  stg1_p,
  wgtmat,
  family = NULL,
  corr = NULL,
  info_frac,
  stg1_bnd,
  stg2_bnd,
  nthreads = 0
)

Arguments

stg1_p: P-values for the elementary hypotheses in stage 1.
wgtmat: Weight matrix for the intersection hypotheses.
family: Family matrix indicating which hypotheses belong to which families. If NULL, all hypotheses are assumed to belong to the same family.
corr: Correlation matrix for the test statistics.
info_frac: Information fraction for the first stage.
stg1_bnd: Stage 1 bounds for the elementary hypotheses in each intersection hypothesis.
stg2_bnd: Stage 2 bounds for the elementary hypotheses in each intersection hypothesis.
nthreads: The number of threads to use in simulations (0 means the default RcppParallel behavior).

Value

A list containing:

stg1_elemhyp_r_idx: The 1-based indices of elementary hypotheses rejected in stage 1.
stg1_inthyp_nr_idx: The 1-based indices of intersection hypotheses not rejected in stage 1.
inthyp: The indicator matrix of those non-rejected intersection hypotheses.
CER: The conditional error rate for each non-rejected intersection hypothesis.

References

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

Author

Kaifeng Lu, kaifenglu@gmail.com

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)
bounds <- fCERStageBound(
  wgtmat, family, corr, alpha = 0.025,
  alpha1 = errorSpent(0.5, 0.025, "sfOF"),
  info_frac = 0.5, nthreads = 1)
fCERCer(stg1_p = c(0.00045, 0.0952, 0.0225, 0.1104),
        wgtmat, family, corr, info_frac = 0.5,
        bounds$stg1_bnd, bounds$stg2_bnd, nthreads = 1)
#> $stg1_elemhyp_r_idx
#> [1] 1
#> 
#> $stg1_inthyp_nr_idx
#> [1]  9 10 11 12 13 14 15
#> 
#> $inthyp
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    0    1    1    0
#> [3,]    0    1    0    1
#> [4,]    0    1    0    0
#> [5,]    0    0    1    1
#> [6,]    0    0    1    0
#> [7,]    0    0    0    1
#> 
#> $CER
#> [1] 0.11166977 0.11166977 0.07015762 0.07015762 0.14167454 0.21788372 0.05942589
#>