Paper V5.1 Gaussian simulation
Main replications per primary/global-null configuration: 2000000 
Grid replications per non-primary effect: 10000000 
Seed (reproducibility record only): 20260722 
Runtime seconds: 1925.09 
K: 5  N per observed arm per stage: 100  rho: 0.5  alpha: 0.05 
Two-arm stage-2 Dunnett critical value: 1.916331945 

Main tables
 design             method primary_marginal_fwer conditional_power_arm1
   top1 closed_combination             0.0097660              0.6756566
   top1 selective_gaussian             0.0050870              0.7093815
   top1        stage2_only             0.0050885              0.5484150
   top2 closed_combination             0.0448535              0.5838599
   top2 selective_gaussian             0.0438770              0.6629210
   top2        stage2_only             0.0431905              0.4420899
 joint_power_arm1 boundary_null_conditional_fwer
        0.6024945                     0.09420985
        0.6325675                     0.04942882
        0.4890310                     0.04920182
        0.5679115                     0.04688466
        0.6448130                     0.04680867
        0.4300140                     0.04536550
 two_boundary_nulls_conditional_fwer
                                  NA
                                  NA
                                  NA
                          0.06774897
                          0.04709264
                          0.04721898
 harmful_arm_conditional_rejection_probability global_null_marginal_fwer
                                    0.07263400                 0.0499015
                                    0.03627983                 0.0501555
                                    0.03734543                 0.0498625
                                    0.03409088                 0.0437280
                                    0.03150609                 0.0469820
                                    0.03363120                 0.0498405
 boundary_stratum_probability harmful_arm_selection_probability
                    0.0881065                         0.0201765
                    0.0881065                         0.0201765
                    0.0881065                         0.0201765
                    0.7764160                         0.2077535
                    0.7764160                         0.2077535
                    0.7764160                         0.2077535

Validation
                                      check
                      Dunnett interpolation
                      Dunnett interpolation
                      Dunnett interpolation
                      Dunnett interpolation
             Two-arm Dunnett critical value
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
 Singleton boundary conditional calibration
                              Marginal FWER
                              Marginal FWER
                              Marginal FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
                 Selection-conditional FWER
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
         Marginal/conditional decomposition
                                      detail     estimate    target
                                 dimension 2 5.443493e-09 0.0000000
                                 dimension 3 3.638741e-09 0.0000000
                                 dimension 4 6.030368e-09 0.0000000
                                 dimension 5 6.477206e-09 0.0000000
              shared-control correlation 0.5 9.500000e-01 0.9500000
         theta1_0.25 top1 closed_combination 9.766000e-03 0.0500000
         theta1_0.25 top1 selective_gaussian 5.087000e-03 0.0500000
                theta1_0.25 top1 stage2_only 5.088500e-03 0.0500000
        theta1_0.25 selective_gaussian arm 2 4.873072e-02 0.0500000
               theta1_0.25 stage2_only arm 2 4.910479e-02 0.0500000
        theta1_0.25 selective_gaussian arm 3 5.059863e-02 0.0500000
               theta1_0.25 stage2_only arm 3 4.911695e-02 0.0500000
        theta1_0.25 selective_gaussian arm 4 4.895796e-02 0.0500000
               theta1_0.25 stage2_only arm 4 4.938398e-02 0.0500000
         theta1_0.25 top2 closed_combination 4.485350e-02 0.0500000
         theta1_0.25 top2 selective_gaussian 4.387700e-02 0.0500000
                theta1_0.25 top2 stage2_only 4.319050e-02 0.0500000
         global_null top1 closed_combination 4.990150e-02 0.0500000
         global_null top1 selective_gaussian 5.015550e-02 0.0500000
                global_null top1 stage2_only 4.986250e-02 0.0500000
        global_null selective_gaussian arm 1 5.100942e-02 0.0500000
               global_null stage2_only arm 1 5.033564e-02 0.0500000
        global_null selective_gaussian arm 2 5.003546e-02 0.0500000
               global_null stage2_only arm 2 4.960599e-02 0.0500000
        global_null selective_gaussian arm 3 5.011880e-02 0.0500000
               global_null stage2_only arm 3 4.974233e-02 0.0500000
        global_null selective_gaussian arm 4 4.987039e-02 0.0500000
               global_null stage2_only arm 4 4.995038e-02 0.0500000
        global_null selective_gaussian arm 5 4.974444e-02 0.0500000
               global_null stage2_only arm 5 4.967929e-02 0.0500000
         global_null top2 closed_combination 4.372800e-02 0.0500000
         global_null top2 selective_gaussian 4.698200e-02 0.0500000
                global_null top2 stage2_only 4.984050e-02 0.0500000
   theta1_0.25 top1 selective_gaussian set 1 0.000000e+00 0.0500000
          theta1_0.25 top1 stage2_only set 1 0.000000e+00 0.0500000
   theta1_0.25 top1 selective_gaussian set 2 4.873072e-02 0.0500000
          theta1_0.25 top1 stage2_only set 2 4.910479e-02 0.0500000
   theta1_0.25 top1 selective_gaussian set 3 5.059863e-02 0.0500000
          theta1_0.25 top1 stage2_only set 3 4.911695e-02 0.0500000
   theta1_0.25 top1 selective_gaussian set 4 4.895796e-02 0.0500000
          theta1_0.25 top1 stage2_only set 4 4.938398e-02 0.0500000
   theta1_0.25 top1 selective_gaussian set 5 3.627983e-02 0.0500000
          theta1_0.25 top1 stage2_only set 5 3.734543e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 1-2 4.644904e-02 0.0500000
        theta1_0.25 top2 stage2_only set 1-2 4.555717e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 1-3 4.718525e-02 0.0500000
        theta1_0.25 top2 stage2_only set 1-3 4.531775e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 1-4 4.679069e-02 0.0500000
        theta1_0.25 top2 stage2_only set 1-4 4.522192e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 1-5 3.224919e-02 0.0500000
        theta1_0.25 top2 stage2_only set 1-5 3.425919e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 2-3 4.976326e-02 0.0500000
        theta1_0.25 top2 stage2_only set 2-3 5.024640e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 2-4 4.646805e-02 0.0500000
        theta1_0.25 top2 stage2_only set 2-4 4.918494e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 2-5 3.873612e-02 0.0500000
        theta1_0.25 top2 stage2_only set 2-5 4.375992e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 3-4 4.512126e-02 0.0500000
        theta1_0.25 top2 stage2_only set 3-4 4.230118e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 3-5 3.970837e-02 0.0500000
        theta1_0.25 top2 stage2_only set 3-5 4.283296e-02 0.0500000
 theta1_0.25 top2 selective_gaussian set 4-5 4.142395e-02 0.0500000
        theta1_0.25 top2 stage2_only set 4-5 4.310680e-02 0.0500000
   global_null top1 selective_gaussian set 1 5.100942e-02 0.0500000
          global_null top1 stage2_only set 1 5.033564e-02 0.0500000
   global_null top1 selective_gaussian set 2 5.003546e-02 0.0500000
          global_null top1 stage2_only set 2 4.960599e-02 0.0500000
   global_null top1 selective_gaussian set 3 5.011880e-02 0.0500000
          global_null top1 stage2_only set 3 4.974233e-02 0.0500000
   global_null top1 selective_gaussian set 4 4.987039e-02 0.0500000
          global_null top1 stage2_only set 4 4.995038e-02 0.0500000
   global_null top1 selective_gaussian set 5 4.974444e-02 0.0500000
          global_null top1 stage2_only set 5 4.967929e-02 0.0500000
 global_null top2 selective_gaussian set 1-2 4.715482e-02 0.0500000
        global_null top2 stage2_only set 1-2 4.997669e-02 0.0500000
 global_null top2 selective_gaussian set 1-3 4.702901e-02 0.0500000
        global_null top2 stage2_only set 1-3 4.928824e-02 0.0500000
 global_null top2 selective_gaussian set 1-4 4.746779e-02 0.0500000
        global_null top2 stage2_only set 1-4 4.997503e-02 0.0500000
 global_null top2 selective_gaussian set 1-5 4.699310e-02 0.0500000
        global_null top2 stage2_only set 1-5 4.995935e-02 0.0500000
 global_null top2 selective_gaussian set 2-3 4.692271e-02 0.0500000
        global_null top2 stage2_only set 2-3 5.022551e-02 0.0500000
 global_null top2 selective_gaussian set 2-4 4.742174e-02 0.0500000
        global_null top2 stage2_only set 2-4 4.934410e-02 0.0500000
 global_null top2 selective_gaussian set 2-5 4.551705e-02 0.0500000
        global_null top2 stage2_only set 2-5 4.994225e-02 0.0500000
 global_null top2 selective_gaussian set 3-4 4.705841e-02 0.0500000
        global_null top2 stage2_only set 3-4 5.006310e-02 0.0500000
 global_null top2 selective_gaussian set 3-5 4.656217e-02 0.0500000
        global_null top2 stage2_only set 3-5 4.938019e-02 0.0500000
 global_null top2 selective_gaussian set 4-5 4.769218e-02 0.0500000
        global_null top2 stage2_only set 4-5 5.025337e-02 0.0500000
         theta1_0.25 top1 closed_combination 9.766000e-03 0.0097660
         theta1_0.25 top1 selective_gaussian 5.087000e-03 0.0050870
                theta1_0.25 top1 stage2_only 5.088500e-03 0.0050885
         theta1_0.25 top2 closed_combination 4.485350e-02 0.0448535
         theta1_0.25 top2 selective_gaussian 4.387700e-02 0.0438770
                theta1_0.25 top2 stage2_only 4.319050e-02 0.0431905
         global_null top1 closed_combination 4.990150e-02 0.0499015
         global_null top1 selective_gaussian 5.015550e-02 0.0501555
                global_null top1 stage2_only 4.986250e-02 0.0498625
         global_null top2 closed_combination 4.372800e-02 0.0437280
         global_null top2 selective_gaussian 4.698200e-02 0.0469820
                global_null top2 stage2_only 4.984050e-02 0.0498405
         mcse                                rule passed
 0.000000e+00                    absolute <= 2e-7   TRUE
 0.000000e+00                    absolute <= 2e-7   TRUE
 0.000000e+00                    absolute <= 2e-7   TRUE
 0.000000e+00                    absolute <= 2e-7   TRUE
 0.000000e+00                   absolute <= 1e-10   TRUE
 6.953641e-05 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 5.030468e-05 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 5.031206e-05 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.878028e-04         absolute <= 6 MCSE + 0.0003   TRUE
 8.910285e-04         absolute <= 6 MCSE + 0.0003   TRUE
 9.045080e-04         absolute <= 6 MCSE + 0.0003   TRUE
 8.918613e-04         absolute <= 6 MCSE + 0.0003   TRUE
 8.907490e-04         absolute <= 6 MCSE + 0.0003   TRUE
 8.944158e-04         absolute <= 6 MCSE + 0.0003   TRUE
 1.463586e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.448306e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.437447e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.539665e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.543372e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.539094e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.482083e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.460237e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.445034e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.430993e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.445210e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.432926e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.441533e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.444146e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.441444e-04         absolute <= 6 MCSE + 0.0003   TRUE
 3.439308e-04         absolute <= 6 MCSE + 0.0003   TRUE
 1.445958e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.496240e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.538773e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 0.000000e+00 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 0.000000e+00 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.878028e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.910285e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 9.045080e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.918613e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.907490e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 8.944158e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 9.308296e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 9.438784e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.927263e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.900379e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.945100e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.889058e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.935455e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.888200e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.819687e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.903211e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.137574e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.147379e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.037423e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.093151e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.218726e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.352047e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.012495e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 1.951465e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.228095e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.310330e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.267200e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 2.310763e-03 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.482083e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.460237e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.445034e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.430993e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.445210e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.432926e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.441533e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.444146e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.441444e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 3.439308e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.745573e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.878264e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.732972e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.839576e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.752100e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.869567e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.741051e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.880778e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.723541e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.878480e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.743115e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.833413e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.660858e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.870839e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.738881e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.880117e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.709717e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.842970e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.766485e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 4.886214e-04 estimate <= alpha + 6 MCSE + 0.0003   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE
 0.000000e+00                   absolute <= 1e-12   TRUE

R session
R version 4.6.1 (2026-06-24)
Platform: aarch64-apple-darwin24.6.0
Running under: macOS Sequoia 15.3.2

Matrix products: default
BLAS:   /opt/homebrew/Cellar/openblas/0.3.33/lib/libopenblasp-r0.3.33.dylib 
LAPACK: /opt/homebrew/Cellar/r/4.6.1/lib/R/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US/en_US/en_US/C/en_US/en_US

time zone: Europe/London
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
[1] compiler_4.6.1
