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 The FDA’s 2026 draft guidance on Bayesian methods makes this a growing area of focus.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.
• Diagnose prior-data conflict — Box’s p-value, surprise index, 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:

Prior-Data Conflict Diagnostics

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

• Prior predictive p-value — tests whether observed data is plausible under the prior predictive distribution.
• 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.

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.

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
cd <- prior_conflict(prior, list(type = "binary", x = 18, n = 40))
print(cd)

# 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, function reference, changelog, and cheat sheet.

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.
• 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.
• 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).