All numerical results in the book are produced by R code that the reader can run. Nearly all of the computation lives in a companion R package, bayestrials, and the chapters call it in short chunks and draw the figures with ggplot2. This appendix describes how to install the package, how it is organized, a worked example, how to reproduce the results, the companion online lab, and the established software that practitioners use for trial design.
The book was built with R 4.5.2. The package declares R 4.1 as its minimum version; it is version 0.1.0, it exports 200 functions, it passes R CMD check, and its tests run under testthat. The source is in the bayestrials/ directory of the book repository. From a clone of the repository it installs with
R CMD INSTALL bayestrialsor, directly from its GitHub repository (https://github.com/VadimSokolov/bayestrials), with the line below.
remotes::install_github("VadimSokolov/bayestrials")The chapters also use ggplot2 for figures, and the package imports only stats and parallel, with mvtnorm and the other packages it can use listed under Suggests. Quarto renders the book through knitr, and each chapter begins with a hidden setup chunk that loads bayestrials and ggplot2.
Functions are named in snake_case, and the prefix tells the reader which part of the book the function belongs to. Arguments follow one convention throughout (see Section A.2): alpha is the one-sided type I error, theta an effect, p0 and p1 response rates, n a number of patients or events, nsim the number of simulated trials, and seed an optional random seed. Functions return numbers, named vectors, data frames or named lists. They never print or plot.
bayestrials.
| Family | What it does | Where used |
|---|---|---|
Core posterior and gs_ |
Beta-binomial and normal posteriors (beta_post, prob_superior, normal_update), effective sample size (ess_beta, ess_normal), group sequential boundaries and crossing probabilities (gs_boundary, gs_spending_boundary, gs_crossing_prob, gs_tolls) |
Chapter 6, Chapter 8, Chapter 11 |
Basics and assign_ |
Permutation test, binary z test, simple, block, stratified and minimization randomization (assign_*), covariate imbalance, small simulations of two-arm trials |
Chapter 4, Chapter 5 |
| Evidence | Bayes factors, minimum Bayes factor, false positive risk, the Bayesian bar | Chapter 7 |
n_ and power |
Sample size for binary, continuous and time-to-event endpoints (n_fixed, n_binary, n_continuous, n_md), power, assurance, number of events |
Chapter 9 |
oc_ |
Simulation of Bayesian designs with interim looks, calibration of the threshold to a type I error target, operating characteristics tables (oc_simulate, oc_calibrate, oc_summarize) |
Chapter 14 |
pp_ |
Predictive probability of success, conditional power, backward induction | Chapter 15 |
rar_ |
Response-adaptive randomization, Thompson sampling, allocation probabilities | Chapter 16 |
dose_ |
3+3, CRM, BOIN, isotonic regression, dose-finding simulation | Chapter 17 |
borrow_ |
Power priors, meta-analytic-predictive and robust priors, basket posteriors, borrowing decision tables | Chapter 19 |
platform_ |
Shared control, correlation between arms, false positive counts, time trends | Chapter 20 |
mult_ and shrink_ |
Bonferroni, Holm, Hochberg and graphical procedures, empirical Bayes shrinkage and posterior probabilities | Chapter 10 |
ev_ |
E-values, test martingales, mixtures, betting paths | Chapter 12 |
select_ |
The reconstruction of the SELECT trial: log Bayes factor, look table, event timing, simulation | Chapter 21 |
The package also contains four datasets: ulcer (the four-operation ulcer trial of Chapter 10), select_design (the design of the SELECT trial, Chapter 21), ctgov_counts and ctgov_bayesian_records (counts and records of registered trials that mention Bayesian methods, retrieved from ClinicalTrials.gov). Each function has a help page with an example that runs in under a second, and the files bayestrials/data-raw/map-*.md map the book’s earlier Python functions to their R replacements.
The example calibrates a two-arm Bayesian design with three looks, at 100, 200 and 300 patients per arm and a control response rate of 0.30. The success rule is that the posterior probability of superiority exceeds a threshold \(c\) at any look. oc_calibrate chooses the smallest \(c\) that keeps the type I error at 0.025 under the null, and then the same threshold is applied to the alternative of a response rate of 0.45.
library(bayestrials)
looks <- c(100, 200, 300)
sim0 <- oc_simulate(p0 = 0.3, p1 = 0.3, looks = looks, nsim = 20000, seed = 1)
c_star <- oc_calibrate(sim0, alpha = 0.025)
sim0v <- oc_simulate(p0 = 0.3, p1 = 0.3, looks = looks, nsim = 20000, seed = 3)
sim1 <- oc_simulate(p0 = 0.3, p1 = 0.45, looks = looks, nsim = 20000, seed = 2)
oc0 <- oc_summarize(sim0, c_star); oc0v <- oc_summarize(sim0v, c_star); oc1 <- oc_summarize(sim1, c_star)The script gives a calibrated threshold of \(c =\) 0.989. The rejection proportion in the calibration run, 0.0246, is the calibration target and not an error assessment. On a fresh null run with another seed the type I error is 0.0234 and the expected total sample size is 594 (the maximum is 600). Under the alternative the power is 0.943 and the expected total sample size is 346, because the trial stops early at the first look that crosses the threshold. These numbers are Monte Carlo estimates from 20,000 trials; the seed makes them repeatable and a different seed gives values that differ in the third decimal place. A full validation would repeat the fresh null run across the prespecified nuisance grid. Chapter 14 explains how to report the Monte Carlo error.
Every simulation either calls set.seed() in the chunk or passes seed = to the package function, so the seed is visible next to the result. Functions draw random numbers from R’s global generator after the seed is set, so a chunk is repeatable but its results depend on the order of the random calls inside it. Monte Carlo results are reported with their Monte Carlo error (Chapter 14). Quarto’s freeze mechanism (freeze: auto in _quarto.yml) stores the computed output of each chapter, so a rebuild reuses stored results unless the source of that chapter has changed, and the slow simulation chunks are also knitr-cached with the cache keyed to a checksum of the installed package. To regenerate a result after the package changes, reinstall it, delete the chapter’s directory under _freeze/ and its knitr cache directory, and render the chapter again. The R version and the installed package versions can be recorded with sessionInfo(), and the authors recommend that a reader who needs exact reproduction record them for their own protocol.
An interactive tutorial accompanies the book at https://nytel.ai/testing/. It runs in the browser and has modules that match the chapters, where the reader predicts an outcome and then checks it. The Bayesian trial simulator at https://nytel.ai/testing/14-simulator.html lets the reader set a design (arms, prior, thresholds, interim looks) and see simulated operating characteristics, in the spirit of the simulation report discussed in Chapter 14. The full open simulator at https://nytel.ai/testing/14-studio.html is a free tool in the style of commercial design software such as FACTS: it handles several doses, adaptive allocation, scenarios and operating characteristics tables, and is the place to explore a design before writing code. Chapters that have a matching module end with a “Try it in the lab” callout.
The following tools are in wide use. The descriptions are brief and cover only the purpose of each tool; consult each tool’s documentation for current features and versions. The R packages below are on CRAN, except bcrm, which CRAN archived on 8 May 2026. On the machine where the book was built, rpact 4.4.0, gsDesign 3.11.0, BOIN 2.7.2, brms 2.23.0 and rstan 2.32.7 were installed; the other tools were not checked.
rpact (R package). Confirmatory adaptive design: group sequential designs, sample size reassessment and combination tests, with simulation.
gsDesign (R package). Group sequential design, including spending functions and boundaries, and power and sample size calculation. A reader can compare its boundaries with gs_boundary and gs_spending_boundary (Chapter 11).
RBesT (R package). Bayesian evidence synthesis tools: construction of meta-analytic-predictive priors, robustification, and operating characteristics for designs that use historical data. Relevant to Chapter 19.
SampleSizeProportions and SampleSizeMeans (R packages, by Joseph and Bélisle). Bayesian sample size criteria (ALC, ACC, WOC) for proportions and means. The lupus example of Section 9.2.5.1 uses SampleSizeProportions 1.1.3.
BOIN (R package). Design and simulation of Bayesian optimal interval phase I dose-finding trials. Relevant to Chapter 17.
trialr (R package). Bayesian clinical trial designs fitted with Stan, including dose-finding and phase II designs.
adaptr (R package). Simulation of Bayesian adaptive multi-arm trials, with response-adaptive randomization, early stopping and calibration of the stopping rules, summarized as operating characteristics. It is the closest open R counterpart to the simulation part of bayestrials for multi-arm designs.
bcrm (R package; archived on CRAN on 8 May 2026, so it no longer installs from CRAN by default). Bayesian continual reassessment method for dose finding. Relevant to Chapter 17.
Stan and brms. Stan is a probabilistic programming language for Bayesian inference by Hamiltonian Monte Carlo. brms is an R package that fits multilevel models through Stan with a formula interface. Both are used to fit analysis models when conjugate formulas are not available.
FACTS (Berry Consultants). Commercial software for designing and simulating Bayesian adaptive trials, including dose finding, response-adaptive randomization and platform designs. Simulation output of this kind is what regulators ask for in a CID meeting (Chapter 3).
East Horizon (Cytel). Commercial software for the design, simulation and monitoring of fixed, group sequential and adaptive trials. It belongs to the same family as the East product line from the same company.