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 0.051%.

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 0.38%.

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 0.0016.

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 0.46%.

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 \(\text{RD}_1 = 0\). 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 4.5.2 (2025-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Debian GNU/Linux forky/sid

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_US.UTF-8    LC_NUMERIC=C            LC_TIME=C              
 [4] LC_COLLATE=en_US.UTF-8  LC_MONETARY=C           LC_MESSAGES=en_US.UTF-8
 [7] LC_PAPER=C              LC_NAME=C               LC_ADDRESS=C           
[10] LC_TELEPHONE=C          LC_MEASUREMENT=C        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] RARtrials_0.0.2 pins_1.4.1      brar_0.1        SimDesign_2.23 

loaded via a namespace (and not attached):
 [1] jsonlite_2.0.0      future.apply_1.20.1 dplyr_1.2.0        
 [4] compiler_4.5.2      brio_1.1.5          tidyselect_1.2.1   
 [7] clipr_0.8.0         parallel_4.5.2      globals_0.19.0     
[10] yaml_2.3.12         R6_2.6.1            generics_0.1.4     
[13] curl_7.0.0          rbibutils_2.4.1     future_1.69.0      
[16] tibble_3.3.1        pillar_1.11.1       R.utils_2.13.0     
[19] rlang_1.1.7         testthat_3.3.2      fs_1.6.6           
[22] audio_0.1-12        otel_0.2.0          cli_3.6.5          
[25] magrittr_2.0.4      progressr_0.18.0    Rdpack_2.6.6       
[28] class_7.3-23        digest_0.6.39       pbapply_1.7-4      
[31] beepr_2.0           rappdirs_0.3.4      lifecycle_1.0.5    
[34] R.methodsS3_1.8.2   R.oo_1.27.1         vctrs_0.7.1        
[37] proxy_0.4-29        glue_1.8.0          listenv_0.10.0     
[40] sessioninfo_1.2.3   codetools_0.2-20    parallelly_1.46.1  
[43] e1071_1.7-17        httr_1.4.8          purrr_1.2.1        
[46] tools_4.5.2         pkgconfig_2.0.3    
─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.5.2 (2025-10-31)
 os       Debian GNU/Linux forky/sid
 system   x86_64, linux-gnu
 ui       X11
 language en_US:en
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       Europe/Zurich
 date     2026-02-21
 pandoc   3.8.3 @ /usr/bin/pandoc
 quarto   NA

─ Packages ───────────────────────────────────────────────────────────────────
 package      * version date (UTC) lib source
 audio          0.1-12  2025-12-15 [1] CRAN (R 4.5.2)
 beepr          2.0     2024-07-06 [1] CRAN (R 4.5.2)
 brar         * 0.1     2026-02-16 [1] local (/home/spawel/simulation-brar/brar/package/out/brar_0.1.tar.gz)
 brio           1.1.5   2024-04-24 [1] CRAN (R 4.5.2)
 class          7.3-23  2025-01-01 [3] CRAN (R 4.5.2)
 cli            3.6.5   2025-04-23 [1] CRAN (R 4.5.2)
 clipr          0.8.0   2022-02-22 [1] CRAN (R 4.5.2)
 codetools      0.2-20  2024-03-31 [3] CRAN (R 4.5.2)
 curl           7.0.0   2025-08-19 [1] CRAN (R 4.5.2)
 digest         0.6.39  2025-11-19 [1] CRAN (R 4.5.2)
 dplyr          1.2.0   2026-02-03 [1] CRAN (R 4.5.2)
 e1071          1.7-17  2025-12-18 [1] CRAN (R 4.5.2)
 fs             1.6.6   2025-04-12 [1] CRAN (R 4.5.2)
 future         1.69.0  2026-01-16 [1] CRAN (R 4.5.2)
 future.apply   1.20.1  2025-12-09 [1] CRAN (R 4.5.2)
 generics       0.1.4   2025-05-09 [1] CRAN (R 4.5.2)
 globals        0.19.0  2026-02-02 [1] CRAN (R 4.5.2)
 glue           1.8.0   2024-09-30 [1] CRAN (R 4.5.2)
 httr           1.4.8   2026-02-13 [1] CRAN (R 4.5.2)
 jsonlite       2.0.0   2025-03-27 [1] CRAN (R 4.5.2)
 lifecycle      1.0.5   2026-01-08 [1] CRAN (R 4.5.2)
 listenv        0.10.0  2025-11-02 [1] CRAN (R 4.5.2)
 magrittr       2.0.4   2025-09-12 [1] CRAN (R 4.5.2)
 otel           0.2.0   2025-08-29 [1] CRAN (R 4.5.2)
 parallelly     1.46.1  2026-01-08 [1] CRAN (R 4.5.2)
 pbapply        1.7-4   2025-07-20 [1] CRAN (R 4.5.2)
 pillar         1.11.1  2025-09-17 [1] CRAN (R 4.5.2)
 pins         * 1.4.1   2025-04-30 [1] CRAN (R 4.5.2)
 pkgconfig      2.0.3   2019-09-22 [1] CRAN (R 4.5.2)
 progressr      0.18.0  2025-11-06 [1] CRAN (R 4.5.2)
 proxy          0.4-29  2025-12-29 [1] CRAN (R 4.5.2)
 purrr          1.2.1   2026-01-09 [1] CRAN (R 4.5.2)
 R.methodsS3    1.8.2   2022-06-13 [1] CRAN (R 4.5.2)
 R.oo           1.27.1  2025-05-02 [1] CRAN (R 4.5.2)
 R.utils        2.13.0  2025-02-24 [1] CRAN (R 4.5.2)
 R6             2.6.1   2025-02-15 [1] CRAN (R 4.5.2)
 rappdirs       0.3.4   2026-01-17 [1] CRAN (R 4.5.2)
 RARtrials    * 0.0.2   2025-04-03 [1] CRAN (R 4.5.2)
 rbibutils      2.4.1   2026-01-21 [1] CRAN (R 4.5.2)
 Rdpack         2.6.6   2026-02-08 [1] CRAN (R 4.5.2)
 rlang          1.1.7   2026-01-09 [1] CRAN (R 4.5.2)
 sessioninfo    1.2.3   2025-02-05 [1] CRAN (R 4.5.2)
 SimDesign    * 2.23    2026-02-10 [1] CRAN (R 4.5.2)
 testthat       3.3.2   2026-01-11 [1] CRAN (R 4.5.2)
 tibble         3.3.1   2026-01-11 [1] CRAN (R 4.5.2)
 tidyselect     1.2.1   2024-03-11 [1] CRAN (R 4.5.2)
 vctrs          0.7.1   2026-01-23 [1] CRAN (R 4.5.2)
 yaml           2.3.12  2025-12-10 [1] CRAN (R 4.5.2)

 [1] /home/spawel/lib/R
 [2] /usr/local/lib/R/site-library
 [3] /usr/local/lib/R/library
 * ── Packages attached to the search path.

──────────────────────────────────────────────────────────────────────────────