bayprior

Structured Bayesian prior elicitation, conflict diagnostics, and regulatory reporting.

Overview

bayprior is an advanced interactive R package and Shiny application designed for biostatisticians and clinical researchers to implement Bayesian Prior Elicitation, Conflict Diagnostics, and Sensitivity Analysis for clinical trials.

bayprior focuses on a specific stage of the Bayesian trial workflow: how do you construct, validate, and justify your prior to a regulator? It brings structured elicitation, prior-data conflict diagnostics, and regulatory report generation together in one integrated workflow. The FDA’s 2026 draft guidance on Bayesian methods makes this a growing area of focus.

bayprior enables users to:

• Elicit structured priors — SHELF-style quantile matching, moment matching, and the interactive roulette method across Beta, Normal, Gamma, Log-Normal, Exponential, and Weibull families.
• Aggregate expert opinions — Linear or logarithmic pooling of multiple expert priors with pairwise Bhattacharyya agreement diagnostics and cross-family compatibility validation.
• Derive priors from historical trials — Meta-analytic-predictive (MAP) priors from a random-effects meta-analysis, with an explicit prior on between-trial heterogeneity.
• Diagnose prior-data conflict — Box’s p-value (Normal approximation or exact prior predictive), S-value, surprise index, KL divergence, Bhattacharyya overlap, and multivariate Mahalanobis distance, supporting binary, continuous, Poisson/count, and survival data types.
• Quantify sensitivity — Posterior conclusions evaluated across hyperparameter grids via tornado plots and influence heatmaps, with independent data entry.
• Build robust priors — Sceptical, robust mixture, and calibrated power priors for regulatory sensitivity analyses.
• Generate regulatory reports — Self-contained HTML, PDF, or Word (.docx) prior justification reports rendered via Quarto.

Features and Modules

Core Methodology

Prior Elicitation

Three structured elicitation approaches are implemented. Quantile matching fits a parametric distribution to expert-specified probability-value pairs via numerical optimisation. Moment matching derives hyperparameters analytically from an expert-supplied mean and SD. The SHELF roulette method (Oakley & O’Hagan, 2010) lets the expert allocate chips across histogram bins, fitting a parametric family to the chip allocation in real time.

All three methods support six distribution families:

MAP Prior (Historical Data)

The meta-analytic-predictive (MAP) approach (Schmidli et al., 2014) derives an informative prior directly from multiple historical trials via a random-effects meta-analysis, with an explicit prior on the between-trial heterogeneity parameter tau – how much heterogeneity is assumed among historical trials directly affects how much borrowing is justified, so map_prior() requires this to be stated rather than left as an unstated default (see ?resolve_tau_prior for outcome-specific defaults). It returns an ordinary prior object that can be used directly, or passed into robust_prior() for an additional vague-mixture component.

y/se per historical trial can be supplied directly, or derived from raw trial-level summary statistics via the optional convenience function historical_effect_sizes(), a thin wrapper around metafor::escalc() (metafor is Suggests-only and not required to use map_prior() itself).

Prior-Data Conflict Diagnostics

Conflict detection follows Box (1980). Complementary metrics are computed:

• Prior predictive p-value — tests whether observed data is plausible under the prior predictive distribution.
• S-value (surprisal, bits) — -log2(p): an exploratory companion to the p-value above, not a thresholded decision rule, since prior-data conflict checks are typically not powered for a binary accept/reject call.
• Surprise index — standardised distance between prior mean and observed data.
• Bhattacharyya overlap — distributional overlap between prior and normalised likelihood.
• KL divergence — information-theoretic distance from prior to likelihood.

By default the Box p-value uses a Normal approximation to the prior and the likelihood. prior_conflict(..., exact = TRUE) instead uses the exact prior predictive distribution where one has a closed form: Beta-Binomial (Beta prior, binary data) and Gamma-Poisson / Negative Binomial (Gamma prior, Poisson or survival data). Other combinations fall back to the Normal approximation with a message, and $box_pvalue_method reports which was used.

Four data types are supported:

Sensitivity Analysis

The sensitivity module is fully independent of conflict diagnostics — users can enter observed data directly without running conflict diagnostics first. Results are visualised as tornado plots and influence heatmaps. A dedicated sensitivity_cri() function tracks credible interval width specifically — a key regulatory quantity.

Robust and Power Priors

The robust mixture prior (Schmidli et al., 2014) mixes the informative prior with a vague Normal component. The sceptical prior (Spiegelhalter & Freedman, 1994) is centred at the null treatment effect. The power prior (Ibrahim & Chen, 2000) down-weights historical data by delta in (0, 1], calibrated to achieve a target Bayes Factor.

Shiny application

run_app() launches the full workflow as an interactive app (also available as a live demo). The Welcome page shows the analytical workflow, tracks which steps you have completed, and can load a synthetic Phase II example (TRIAL-001) so you can try the conflict check straight away.

Installation

PDF reports require Quarto CLI and a LaTeX installation:

install.packages("tinytex")
tinytex::install_tinytex()

Quick Start

library(bayprior)

# Elicit a Beta prior
prior <- elicit_beta(mean = 0.35, sd = 0.10, method = "moments",
                     label = "Response rate", expert_id = "Expert_1")
plot(prior)

# Pool two experts
e1  <- elicit_beta(mean = 0.30, sd = 0.10, method = "moments", expert_id = "E1")
e2  <- elicit_beta(mean = 0.42, sd = 0.12, method = "moments", expert_id = "E2")
agg <- aggregate_experts(list(E1 = e1, E2 = e2), weights = c(0.6, 0.4))

# Conflict diagnostics (add exact = TRUE for the exact prior predictive p-value)
cd <- prior_conflict(prior, list(type = "binary", x = 18, n = 40))
print(cd)

# Derive a MAP prior from historical trials (log-odds scale)
hist_prior <- map_prior(
  y  = qlogis(c(0.28, 0.35, 0.31)),   # historical response rates, as log-odds
  se = c(0.30, 0.26, 0.34),           # their standard errors
  outcome_type = "single_arm_log_odds"
)
plot(hist_prior)

# Sensitivity analysis
sa <- sensitivity_grid(
  prior,
  data_summary = list(type = "binary", x = 18, n = 40),
  param_grid   = list(alpha = seq(1, 8, 0.5), beta = seq(2, 20, 1)),
  target       = c("posterior_mean", "prob_efficacy"),
  threshold    = 0.30
)
plot_tornado(sa)

# Robust and sceptical priors
rob  <- robust_prior(prior, vague_weight = 0.20)
scep <- sceptical_prior(null_value = 0.20, family = "beta",
                        strength = "moderate")

# Generate regulatory report
prior_report(
  prior           = prior,
  conflict        = cd,
  sensitivity     = sa,
  robust_prior    = rob,
  sceptical_prior = scep,
  output_format   = "html",
  trial_name      = "TRIAL-001",
  sponsor         = "Example Pharma Ltd",
  author          = "N.P., Biostatistician"
)

# Launch the Shiny app
run_app()

Vignettes

browseVignettes("bayprior")

Documentation

Full documentation — vignettes, changelog, and cheat sheet. Function help is available in R via help(package = "bayprior") or ?bayprior.

Code of Conduct

Please note that the bayprior project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

References

• O’Hagan, A. et al. (2006). Uncertain Judgements: Eliciting Experts’ Probabilities. Wiley.
• Box, G. E. P. (1980). Sampling and Bayes’ inference in scientific modelling and robustness. JRSS-A, 143, 383-430.
• Greenland, S. (2023). Divergence versus decision P-values: A distinction worth making in theory and keeping in practice. Scandinavian Journal of Statistics, 50(1), 54-88.
• Oakley, J. E. & O’Hagan, A. (2010). SHELF: the Sheffield Elicitation Framework. University of Sheffield.
• Schmidli, H. et al. (2014). Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 70, 1023-1032.
• Neuenschwander, B., Capkun-Niggli, G., Branson, M. & Spiegelhalter, D. J. (2010). Summarizing historical information on controls in clinical trials. Clinical Trials, 7(1), 5-18.
• Roever, C., Bender, R., Dias, S., Schmid, C. H., Schmidli, H., Sturtz, S., Weber, S. & Friede, T. (2021). On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis. Research Synthesis Methods, 12(4), 448-474.
• Ibrahim, J. G. & Chen, M.-H. (2000). Power prior distributions for regression models. Statistical Science, 15, 46-60.
• Spiegelhalter, D. J., Freedman, L. S. & Parmar, M. K. B. (1994). Bayesian approaches to randomized trials. JRSS-A, 157, 357-416.
• U.S. Food and Drug Administration (2026). Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products (Draft Guidance for Industry).