Prior Specifications in ‘rctbayespower’ • rctbayespower

Setup:

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# Set CRAN mirror
options(repos = c(CRAN = "https://cloud.r-project.org/"))

# Check and install required packages
packages <- c("dplyr", "kableExtra", "pander")
install.packages(setdiff(packages, rownames(installed.packages())))
invisible(lapply(packages, require, character.only = TRUE))
library(rctbayespower)

# Set number of cores and simulations:
n_cores <- parallel::detectCores() - 2
n_sims <- 500

The rctbayespower package uses two types of priors: estimation priors (for Bayesian model fitting) and design priors (for integrating effect size uncertainty). This vignette demonstrates their impact on power analysis through two focused examples.

1 Example 1: Different Estimation Priors

Estimation priors affect how treatment effects are estimated during Bayesian model fitting. Here we compare default priors versus informative priors.

Ancova model with two arms is used to illustrate the impact of different priors on power analysis results. We will compare uninformative and sceptical priors.

Let’s first define the sample size for our analysis:

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sample_size <- 100

1.1 Analysis of Medium Effect of Cohen’s d = 0.5

1.1.1 Analysis with uninformative priors

Uninformative, locally flat prior on treatment effect: \[d \sim \mathcal{N}(0,100)\]

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# Create ANCOVA model with uninformative priors
uninformative_model <- build_model_ancova_cont_2arms(
  prior_treatment = brms::set_prior("normal(0, 100)", class = "b"),
  prior_covariate = brms::set_prior("normal(0, 100)", class = "b", coef = "covariate"),
  prior_intercept = brms::set_prior("normal(0, 100)", class = "Intercept"),
  prior_sigma = brms::set_prior("normal(0, 100)", class = "sigma", lb = 0),
  link_sigma = "identity"
)

Compiling the brms model ...
Model compilation done!

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# Create design
uninformative_design <- build_design(
  model = uninformative_model,
  target_params = "b_arm2",
  n_interim_analyses = 0,
  thresholds_success = 0.3,
  thresholds_futility = 0.1,
  p_sig_success = 0.95,
  p_sig_futility = 0.5
)

# Create conditions
uninformative_conditions <- build_conditions(
  design = uninformative_design,
  condition_values = list(
    n_total = sample_size
  ),
  static_values = list(
    b_arm_treat = 0.5, # Medium effect
    b_covariate = 0 # No covariate effect
  )
)

# Run power analysis
uninformative_analysis <- rctbayespower::power_analysis(
  conditions = uninformative_conditions,
  n_sims = n_sims,
  n_cores = n_cores,
  verbose = FALSE
)

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res_uninformative <- uninformative_analysis@summarized_results|>
  select(
    n_total,
    median,
    sd,
    prob_success,
    power_success,
    prob_futility,
    power_futility
  ) |>
  dplyr::mutate(Prior = "uninformative", .before = everything())

res_uninformative |> 
  kableExtra::kable(digits = 3, format = "html")

Prior	n_total	median	sd	prob_success	power_success	prob_futility	power_futility
uninformative	100	0.509	0.205	0.765	0.262	0.077	0.018

Analysis with Informative Prior

Informative, sceptical prior on treatment effect:

\[d \sim \mathcal{t_3}(0,1)\]

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# Create ANCOVA model with informative/sceptical priors
informative_model <- build_model_ancova_cont_2arms(
  prior_treatment = brms::set_prior("student_t(3, 0, 2)", class = "b"),
  prior_covariate = brms::set_prior("student_t(3, 0, 2)", class = "b", coef = "covariate"),
  prior_intercept = brms::set_prior("student_t(3, 0, 2)", class = "Intercept"),
  prior_sigma = brms::set_prior("student_t(3, 0, 2)", class = "sigma", lb = 0),
  link_sigma = "identity"
)

Compiling the brms model ...
Model compilation done!

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# Create design (same as uninformative)
informative_design <- build_design(
  model = informative_model,
  target_params = "b_arm2",
  n_interim_analyses = 0,
  thresholds_success = 0.3,
  thresholds_futility = 0.1,
  p_sig_success = 0.975,
  p_sig_futility = 0.5
)

# Create conditions
informative_conditions <- build_conditions(
  design = informative_design,
  condition_values = list(n_total = sample_size),
  static_values = list(
    b_arm_treat = 0.5, # Medium effect
    b_covariate = 0 # No covariate effect
  )
)

# Run power analysis
informative_analysis <- power_analysis(
  conditions = informative_conditions,
  n_sims = n_sims,
  n_cores = n_cores,
  verbose = FALSE
)

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res_informative <- informative_analysis@summarized_results|>
  select(
    n_total,
    median,
    sd,
    prob_success,
    power_success,
    prob_futility,
    power_futility
  ) |>
  dplyr::mutate(Prior = "informative", .before = everything())

res_informative |> 
  kableExtra::kable(digits = 3, format = "html")

Prior	n_total	median	sd	prob_success	power_success	prob_futility	power_futility
informative	100	0.478	0.203	0.733	0.142	0.095	0.026

Comparing the results of the two analyses:

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estimation_comparison <- 
  rbind(
    res_uninformative,
    res_informative
  ) 

estimation_comparison|>
  # round the numeric columns for better readability
  kableExtra::kable(digits = 3)

Prior	n_total	median	sd	prob_success	power_success	prob_futility	power_futility
uninformative	100	0.509	0.205	0.765	0.262	0.077	0.018
informative	100	0.478	0.203	0.733	0.142	0.095	0.026

1.2 Alpha Error Rate

To evaluate the alpha error rate (false positive rate) for both prior configurations, we need to run the power analysis under the null hypothesis (effect size = 0) and examine how often we incorrectly conclude for success. This tells us how well our Bayesian decision framework controls Type I error. Luckily, the rctbayespower package allows us to reuse the same model and design configurations, only changing the effect size to zero.

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# Create design (same as uninformative)
alpha_uninformative_design <- build_design(
  model = uninformative_model,
  target_params = "b_arm2",
  n_interim_analyses = 0,
  thresholds_success = 0,
  thresholds_futility = 0,
  p_sig_success = 0.95,
  p_sig_futility = 0.5
)

alpha_uninformative_conditions <- build_conditions(
  design = alpha_uninformative_design,
  condition_values = list(n_total = sample_size),
  static_values = list(
    b_arm_treat = 0, # Null hypothesis: no effect
    b_covariate = 0 # No covariate effect
  )
)

alpha_uninformative <- power_analysis(
  conditions = alpha_uninformative_conditions,
  n_sims = n_sims,
  n_cores = n_cores,
  verbose = FALSE
)

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alpha_informative_design <- build_design(
  model = informative_model,
  target_params = "b_arm2",
  n_interim_analyses = 0,
  thresholds_success = 0,
  thresholds_futility = 0,
  p_sig_success = 0.95,
  p_sig_futility = 0.5
)

alpha_informative_conditions <- build_conditions(
  design = alpha_informative_design,
  condition_values = list(n_total = sample_size),
  static_values = list(
    b_arm_treat = 0, # Null hypothesis: no effect
    b_covariate = 0 # No covariate effect
  )
)

alpha_informative <- power_analysis(
  conditions = alpha_informative_conditions,
  n_sims = n_sims,
  n_cores = n_cores,
  verbose = TRUE
)


=== Power Analysis ===
Conditions:
# A tibble: 1 × 2
  id_cond n_total
    <int>   <dbl>
1       1     100

Conditions to test: 1
Simulations per condition: 500
Total simulations: 500

Functions exported from package namespace

Combined results dimensions: 500 18
Column names: parameter, threshold_success, threshold_futility, success_prob, futility_prob, power_success, power_futility, median, mad, mean, sd, rhat, ess_bulk, ess_tail, id_sim, id_cond, converged, error

Total analysis time: 1.46 minutes

Comparing the alpha error rates:

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res_alpha <- 
  rbind(
    alpha_uninformative@summarized_results |>
      select(
        n_total,
        prob_success,
        power_success
      ) |>
      dplyr::mutate(Prior = "uninformative", .before = everything()),
    alpha_informative@summarized_results |>
      select(
        n_total,
        prob_success,
        power_success,
      ) |>
      dplyr::mutate(Prior = "informative", .before = everything())
  ) |> 
  dplyr::rename(
    
    alpha = power_success,
    "p(d > 0)" = prob_success,
  )

res_alpha |> 
  kableExtra::kable(digits = 3, format = "html")

Prior	n_total	p(d > 0)	alpha
uninformative	100	0.501	0.052
informative	100	0.525	0.050

Using a sceptical prior reduces the probability of falsely concluding success when there is no true effect, thus controlling the alpha error rate more effectively than the uninformative priors.

2 Example 2: Design Priors

Coming soon …

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pander::pander(sessionInfo())

R version 4.5.1 (2025-06-13 ucrt)

Platform: x86_64-w64-mingw32/x64

locale: LC_COLLATE=German_Germany.utf8, LC_CTYPE=German_Germany.utf8, LC_MONETARY=German_Germany.utf8, LC_NUMERIC=C and LC_TIME=German_Germany.utf8

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: rctbayespower(v.0.0.0.9000), pander(v.0.6.6), kableExtra(v.1.4.0) and dplyr(v.1.1.4)

loaded via a namespace (and not attached): gtable(v.0.3.6), tensorA(v.0.36.2.1), QuickJSR(v.1.8.1), xfun(v.0.53), ggplot2(v.4.0.0), htmlwidgets(v.1.6.4), processx(v.3.8.6), inline(v.0.3.21), lattice(v.0.22-7), callr(v.3.7.6), ps(v.1.9.1), vctrs(v.0.6.5), tools(v.4.5.1), generics(v.0.1.4), stats4(v.4.5.1), parallel(v.4.5.1), tibble(v.3.3.0), pkgconfig(v.2.0.3), brms(v.2.23.0), Matrix(v.1.7-4), data.table(v.1.17.8), checkmate(v.2.3.3), RColorBrewer(v.1.1-3), S7(v.0.2.0), distributional(v.0.5.0), RcppParallel(v.5.1.11-1), lifecycle(v.1.0.4), compiler(v.4.5.1), farver(v.2.1.2), stringr(v.1.5.2), textshaping(v.1.0.4), Brobdingnag(v.1.2-9), codetools(v.0.2-20), htmltools(v.0.5.8.1), bayesplot(v.1.14.0), yaml(v.2.3.10), lazyeval(v.0.2.2), plotly(v.4.11.0), pillar(v.1.11.1), tidyr(v.1.3.1), StanHeaders(v.2.32.10), bridgesampling(v.1.1-2), abind(v.1.4-8), nlme(v.3.1-168), posterior(v.1.6.1), rstan(v.2.32.7), tidyselect(v.1.2.1), digest(v.0.6.37), mvtnorm(v.1.3-3), stringi(v.1.8.7), purrr(v.1.0.4), fastmap(v.1.2.0), grid(v.4.5.1), cli(v.3.6.5), magrittr(v.2.0.3), loo(v.2.8.0), pkgbuild(v.1.4.8), withr(v.3.0.2), scales(v.1.4.0), backports(v.1.5.0), rmarkdown(v.2.30), httr(v.1.4.7), matrixStats(v.1.5.0), gridExtra(v.2.3), pbapply(v.1.7-4), coda(v.0.19-4.1), evaluate(v.1.0.5), knitr(v.1.50), pwr(v.1.3-0), viridisLite(v.0.4.2), rstantools(v.2.5.0), rlang(v.1.1.6), Rcpp(v.1.1.0), glue(v.1.8.0), xml2(v.1.4.0), svglite(v.2.2.2), rstudioapi(v.0.17.1), jsonlite(v.2.0.0), R6(v.2.6.1) and systemfonts(v.1.3.1)