BayesianQDM

Overview

BayesianQDM provides a comprehensive framework for Bayesian Quantitative Decision-Making in clinical trials. The package enables researchers to compute posterior probabilities, posterior predictive probabilities, and Go/NoGo/Gray decision probabilities for both single and two-endpoint analyses with binary and continuous outcomes. The package also provides functions to find optimal Go/NoGo thresholds that satisfy user-specified operating characteristic criteria.

Key Features

• Single and Two Endpoints: Supports single binary, single continuous, two binary, and two continuous endpoint analyses
• Multiple Study Designs: Controlled, uncontrolled (hypothetical control), and external designs
• Flexible Prior Specification: Vague (Jeffreys) priors and conjugate priors (Beta, Normal-Inverse-Chi-squared, Normal-Inverse-Wishart, Dirichlet)
• Power Priors: Exact conjugate representation for incorporating historical or external data without MCMC
• Multiple Calculation Methods: Numerical integration (NI), Monte Carlo simulation (MC), and Moment-Matching approximation (MM) for continuous endpoints
• Three-Zone Decision Framework: Go/NoGo/Gray probability calculation with user-defined thresholds (TV and MAV)
• Optimal Threshold Search: Grid-search functions to find Go/NoGo thresholds satisfying target operating characteristics

Installation

From CRAN

install.packages("BayesianQDM")

Development Version

# install.packages("devtools")
devtools::install_github("gosukehommaEX/BayesianQDM")

Core Functions

Posterior / Posterior Predictive Probability Functions

Function	Description
pbayespostpred1bin()	Posterior or predictive probability for a single binary endpoint
pbayespostpred1cont()	Posterior or predictive probability for a single continuous endpoint
pbayespostpred2bin()	Joint region probabilities for two binary endpoints
pbayespostpred2cont()	Joint region probabilities for two continuous endpoints

Decision Probability Functions

Function	Description
pbayesdecisionprob1bin()	Go/NoGo/Gray probabilities for a single binary endpoint
pbayesdecisionprob1cont()	Go/NoGo/Gray probabilities for a single continuous endpoint
pbayesdecisionprob2bin()	Go/NoGo/Gray probabilities for two binary endpoints
pbayesdecisionprob2cont()	Go/NoGo/Gray probabilities for two continuous endpoints

Optimal Threshold Search Functions

Function	Description
getgamma1bin()	Find optimal Go/NoGo thresholds for a single binary endpoint
getgamma1cont()	Find optimal Go/NoGo thresholds for a single continuous endpoint
getgamma2bin()	Find optimal Go/NoGo thresholds for two binary endpoints
getgamma2cont()	Find optimal Go/NoGo thresholds for two continuous endpoints

S3 Methods

Function	Description
print.pbayesdecisionprob1bin()	Print method for pbayesdecisionprob1bin objects
print.pbayesdecisionprob1cont()	Print method for pbayesdecisionprob1cont objects
print.pbayesdecisionprob2bin()	Print method for pbayesdecisionprob2bin objects
print.pbayesdecisionprob2cont()	Print method for pbayesdecisionprob2cont objects
plot.pbayesdecisionprob1bin()	Plot method for pbayesdecisionprob1bin objects
plot.pbayesdecisionprob1cont()	Plot method for pbayesdecisionprob1cont objects
plot.pbayesdecisionprob2bin()	Plot method for pbayesdecisionprob2bin objects
plot.pbayesdecisionprob2cont()	Plot method for pbayesdecisionprob2cont objects
plot.getgamma1bin()	Plot method for getgamma1bin objects
plot.getgamma1cont()	Plot method for getgamma1cont objects
plot.getgamma2bin()	Plot method for getgamma2bin objects
plot.getgamma2cont()	Plot method for getgamma2cont objects

Distribution and Utility Functions

Function	Description
pbetadiff()	CDF for the difference of two independent Beta distributions
pbetabinomdiff()	Beta-binomial posterior predictive probability
ptdiff_NI()	CDF for the difference of two t-distributions via numerical integration
ptdiff_MC()	CDF for the difference of two t-distributions via Monte Carlo simulation
ptdiff_MM()	CDF for the difference of two t-distributions via Moment-Matching approximation
rdirichlet()	Random sampler for the Dirichlet distribution
getjointbin()	Joint binary probability from marginals and correlation
allmultinom()	Enumerate all multinomial outcome combinations

Study Designs

Controlled Design

Standard randomised controlled trials with concurrent treatment and control groups.

Uncontrolled Design

Single-arm studies using a hypothetical control distribution specified through prior parameters or a variance scaling factor.

External Design

Incorporates historical or external control and/or treatment data through power priors using exact conjugate representations, enabling efficient Bayesian computation without MCMC sampling.

Statistical Methods for Continuous Endpoints

For single continuous endpoints, three methods are available for computing the CDF of the difference between two independent t-distributions:

• NI (Numerical Integration): Exact computation via adaptive quadrature (stats::integrate)
• MC (Monte Carlo): Simulation-based estimation; supports vectorised batch processing
• MM (Moment-Matching): Closed-form approximation by matching the first two even moments of the difference distribution to a single t-distribution; fully vectorised and recommended for large-scale simulation studies

For two continuous endpoints, MC and MM methods are available for computing joint rectangular region probabilities under a bivariate t-distribution approximation.

Optimal Threshold Search

The getgamma family of functions finds optimal Go threshold $\gamma_go$ and NoGo threshold $\gamma_nogo$ by grid search, given user-specified target operating characteristics (e.g., Pr(Go) and Pr(NoGo) under specified true parameter scenarios). The search follows a two-stage precompute-then-sweep strategy for computational efficiency.

Documentation

Vignettes

The package includes detailed vignettes with practical examples:

Getting Started

• Overview of BayesianQDM - Framework overview and key concepts

Single Endpoint Analysis

• Single Binary Endpoint - Binary endpoint analysis with Go/NoGo/Gray decisions
• Single Continuous Endpoint - Continuous endpoint analysis with multiple computation methods

Two Endpoint Analysis

• Two Binary Endpoints - Joint analysis of two binary endpoints
• Two Continuous Endpoints - Joint analysis of two continuous endpoints

Access vignettes locally after installation:

vignette(package = "BayesianQDM")
vignette("overview", package = "BayesianQDM")
vignette("single-binary", package = "BayesianQDM")
vignette("single-continuous", package = "BayesianQDM")
vignette("two-binary", package = "BayesianQDM")
vignette("two-continuous", package = "BayesianQDM")

Package Website

Visit the pkgdown website for interactive documentation and the full function reference.

Citation

To cite BayesianQDM in publications, please use:

Homma, G., Yamaguchi, Y. (2025). BayesianQDM: Bayesian Quantitative
Decision-Making Framework for Binary and Continuous Endpoints.
R package version 0.1.0.

License

This package is licensed under GPL (>= 2).

Authors

• Gosuke Homma (maintainer)
• Yusuke Yamaguchi

Issues and Contributions

To report bugs or request features, please visit our GitHub repository.