Mean rate of successes (i.e., the number of successes in a study divided by its sample size averaged over all simulations). The maximum MCSE is 0.047%.

Rate of allocations to treatment group 1 averaged across simulations. Treatment group 1 is the ‘best’ treatment group in all conditions apart from the conditions with \(\text{RD}_1 = \theta_1 - \theta_C = 0\), where the remaining treatments are the most benefitial. The maximum MCSE is 0.27%.

Mean difference in sample size between treatment group 1 and average sample size in remaining groups (control and other treatments). Error bars indicate 2.5% and 97.5% quantiles.

Proportion of simulations with more than 10% of the sample size randomized to other groups than treatment group 1. The maximum MCSE is 0.5%.

Mean proportion of randomization probabilities either less than 0.1 or greater than 0.9. The maximum MCSE is 0.33%.

Empirical bias of the estimate of the risk difference \(\text{RD}_1\) between the first treatment group and the control group. The maximum MCSE is 0.0013.

Empirical coverage of the 95% Wald confidence interval for the risk difference \(\text{RD}_1\) between the first treatment group and the control group. The maximum MCSE is 0.38%.

Empirical type I error rate of the Wald test of \(\text{RD}_1 = 0\). Error bars denote MCSEs (Monte Carlo Standard Errors).

Empirical power of the Wald test of $ ext{RD}_1 = 0$. The maximum MCSE is 0.5%.

Mean convergence
Mean convergence rate within a study averaged across simulations.

Below information on the computational environment from the server where the simulation study was run.

R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Debian GNU/Linux 13 (trixie)

Matrix products: default
BLAS:   /usr/local/lib/R/lib/libRblas.so 
LAPACK: /usr/local/lib/R/lib/libRlapack.so;  LAPACK version 3.12.1

locale:
 [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=de_CH.UTF-8        LC_COLLATE=en_GB.UTF-8    
 [5] LC_MONETARY=de_CH.UTF-8    LC_MESSAGES=en_GB.UTF-8   
 [7] LC_PAPER=de_CH.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=de_CH.UTF-8 LC_IDENTIFICATION=C       

time zone: Europe/Zurich
tzcode source: system (glibc)

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

other attached packages:
[1] brar_0.1         SimDesign_2.20.0

loaded via a namespace (and not attached):
 [1] vctrs_0.6.5         progressr_0.15.1    cli_3.6.3          
 [4] rlang_1.1.5         generics_0.1.3      glue_1.8.0         
 [7] future.apply_1.20.0 listenv_0.9.1       brio_1.1.5         
[10] tibble_3.2.1        lifecycle_1.0.4     beepr_2.0          
[13] compiler_4.5.0      dplyr_1.1.4         codetools_0.2-20   
[16] sessioninfo_1.2.3   testthat_3.2.1.1    pkgconfig_2.0.3    
[19] pbapply_1.7-2       future_1.67.0       R.oo_1.27.1        
[22] R.utils_2.13.0      digest_0.6.35       R6_2.5.1           
[25] tidyselect_1.2.1    pillar_1.10.1       parallelly_1.45.1  
[28] parallel_4.5.0      magrittr_2.0.3      R.methodsS3_1.8.2  
[31] tools_4.5.0         globals_0.18.0      audio_0.1-11       
─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.5.0 (2025-04-11)
 os       Debian GNU/Linux 13 (trixie)
 system   x86_64, linux-gnu
 ui       X11
 language (EN)
 collate  en_GB.UTF-8
 ctype    en_GB.UTF-8
 tz       Europe/Zurich
 date     2025-08-24
 pandoc   NA
 quarto   NA

─ Packages ───────────────────────────────────────────────────────────────────
 package      * version date (UTC) lib source
 audio          0.1-11  2023-08-18 [1] CRAN (R 4.5.0)
 beepr          2.0     2024-07-06 [1] CRAN (R 4.5.0)
 brar         * 0.1     2025-08-22 [1] local (/home/spawel/simulation-brar/brar/package/out/brar_0.1.tar.gz)
 brio           1.1.5   2024-04-24 [1] CRAN (R 4.4.0)
 cli            3.6.3   2024-06-21 [1] CRAN (R 4.4.0)
 codetools      0.2-20  2024-03-31 [2] CRAN (R 4.5.0)
 digest         0.6.35  2024-03-11 [1] CRAN (R 4.3.3)
 dplyr          1.1.4   2023-11-17 [1] CRAN (R 4.3.3)
 future         1.67.0  2025-07-29 [1] CRAN (R 4.5.0)
 future.apply   1.20.0  2025-06-06 [1] CRAN (R 4.5.0)
 generics       0.1.3   2022-07-05 [1] CRAN (R 4.3.3)
 globals        0.18.0  2025-05-08 [1] CRAN (R 4.5.0)
 glue           1.8.0   2024-09-30 [1] CRAN (R 4.4.1)
 lifecycle      1.0.4   2023-11-07 [1] CRAN (R 4.3.3)
 listenv        0.9.1   2024-01-29 [1] CRAN (R 4.5.0)
 magrittr       2.0.3   2022-03-30 [1] CRAN (R 4.3.3)
 parallelly     1.45.1  2025-07-24 [1] CRAN (R 4.5.0)
 pbapply        1.7-2   2023-06-27 [1] CRAN (R 4.3.3)
 pillar         1.10.1  2025-01-07 [1] CRAN (R 4.4.1)
 pkgconfig      2.0.3   2019-09-22 [1] CRAN (R 4.3.3)
 progressr      0.15.1  2024-11-22 [1] CRAN (R 4.5.0)
 R.methodsS3    1.8.2   2022-06-13 [1] CRAN (R 4.5.0)
 R.oo           1.27.1  2025-05-02 [1] CRAN (R 4.5.0)
 R.utils        2.13.0  2025-02-24 [1] CRAN (R 4.5.0)
 R6             2.5.1   2021-08-19 [1] CRAN (R 4.3.3)
 rlang          1.1.5   2025-01-17 [1] CRAN (R 4.4.1)
 sessioninfo    1.2.3   2025-02-05 [1] CRAN (R 4.5.0)
 SimDesign    * 2.20.0  2025-07-16 [1] CRAN (R 4.5.0)
 testthat       3.2.1.1 2024-04-14 [1] CRAN (R 4.4.0)
 tibble         3.2.1   2023-03-20 [1] CRAN (R 4.3.3)
 tidyselect     1.2.1   2024-03-11 [1] CRAN (R 4.3.3)
 vctrs          0.6.5   2023-12-01 [1] CRAN (R 4.3.3)

 [1] /home/spawel/lib/R
 [2] /usr/local/lib/R/library

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