BayesianQDM • BayesianQDM

Overview

BayesianQDM provides a comprehensive framework for Bayesian Quantitative Decision-Making in clinical trials. The package enables researchers to make Go/NoGo/Gray decisions using posterior and predictive probabilities for both binary and continuous endpoints.

Key Features

✅ Multiple Study Designs: Controlled, uncontrolled, and external control designs
📊 Flexible Endpoints: Support for both binary and continuous outcomes
🔢 Multiple Calculation Methods: For continuous endpoints (Numerical Integration, Monte Carlo, Welch-Satterthwaite)
🎯 Three-Zone Decision Framework: Go/NoGo/Gray probability calculation
📈 Power Priors: Incorporation of historical/external data

Installation

From CRAN

install.packages("BayesianQDM")

Development Version

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

Quick Start

Binary Endpoint Example

library(BayesianQDM)

# Calculate Go/NoGo/Gray probabilities for binary endpoint
result <- pGNGsinglebinary(
  prob = 'posterior', 
  design = 'controlled',
  theta.TV = 0.3, theta.MAV = 0.1, theta.NULL = NULL,
  gamma1 = 0.8, gamma2 = 0.2,
  pi1 = c(0.3, 0.5, 0.7), 
  pi2 = rep(0.2, 3),
  n1 = 15, n2 = 15,
  a1 = 0.5, a2 = 0.5, b1 = 0.5, b2 = 0.5,
  z = NULL, m1 = NULL, m2 = NULL,
  ne1 = NULL, ne2 = NULL, ye1 = NULL, ye2 = NULL, ae1 = NULL, ae2 = NULL
)

print(result)

Continuous Endpoint Example

# Calculate Go/NoGo/Gray probabilities for continuous endpoint
result <- pGNGsinglecontinuous(
  nsim = 100, 
  prob = 'posterior', 
  design = 'controlled', 
  prior = 'vague', 
  CalcMethod = 'NI',
  theta.TV = 1.5, theta.MAV = 0.5, theta.NULL = NULL,
  nMC = NULL, gamma1 = 0.8, gamma2 = 0.3,
  n1 = 15, n2 = 15, m1 = NULL, m2 = NULL,
  kappa01 = NULL, kappa02 = NULL, nu01 = NULL, nu02 = NULL,
  mu01 = NULL, mu02 = NULL, sigma01 = NULL, sigma02 = NULL,
  mu1 = 4.0, mu2 = 2.0, sigma1 = 1.5, sigma2 = 1.3,
  r = NULL, ne1 = NULL, ne2 = NULL, alpha01 = NULL, alpha02 = NULL,
  bar.ye1 = NULL, bar.ye2 = NULL, se1 = NULL, se2 = NULL,
  seed = 123
)

print(result)

Documentation

📚 Vignettes

The package includes detailed vignettes with practical examples:

Introduction to BayesianQDM: Overview and quick start guide
Binary Endpoints: Detailed examples for binary outcome analysis
Continuous Endpoints: Comprehensive guide for continuous outcome analysis

📖 Function Documentation

Full Reference: Complete function documentation with examples

🌐 Package Website

Visit our pkgdown website for: - Interactive documentation - Downloadable examples - Method comparisons - Best practice guides

Local Access

Access vignettes locally after installation:

# View available vignettes
vignette(package = "BayesianQDM")

# Open specific vignettes
vignette("BayesianQDM")
vignette("binary-endpoints", package = "BayesianQDM")  
vignette("continuous-endpoints", package = "BayesianQDM")

Core Functions

Decision Making Functions

pGNGsinglebinary() - Go/NoGo/Gray probabilities for binary endpoints
pGNGsinglecontinuous() - Go/NoGo/Gray probabilities for continuous endpoints

Probability Calculation Functions

pPPsinglebinary() - Posterior/predictive probabilities for binary endpoints
pPPsinglecontinuous() - Posterior/predictive probabilities for continuous endpoints

Distribution Functions

p2betadiff() - CDF for difference of two beta distributions
p2betabinomdiff() - Beta-binomial posterior predictive probability
pNI2tdiff() - Numerical integration for t-distribution differences
pMC2tdiff() - Monte Carlo for t-distribution differences
pWS2tdiff() - Welch-Satterthwaite approximation for t-distribution differences
d2betadiff() - Density function for difference of two beta distributions

Utility Functions

AppellsF1() - Appell’s hypergeometric function F1

Study Designs

Controlled Design

Standard randomized controlled trials with treatment and control groups.

Uncontrolled Design

Single-arm studies using historical controls with beta priors (binary) or informative priors (continuous).

External Control Design

Incorporating historical/external data through power priors for enhanced decision making. For binary endpoints, use ne1, ne2, ye1, ye2, ae1, ae2 parameters. For continuous endpoints, use ne1, ne2, alpha01, alpha02, bar.ye1, bar.ye2, se1, se2 parameters.

Calculation Methods

For Continuous Endpoints

Method	Description	Use Case
NI	Numerical Integration	Most accurate, recommended for final analyses
WS	Welch-Satterthwaite	Fast approximation for unequal variances
MC	Monte Carlo	Flexible simulation-based approach

Method Comparison Example

# Compare calculation methods
mu1 <- 3.5; mu2 <- 1.8; sd1 <- 1.3; sd2 <- 1.1; nu1 <- 14; nu2 <- 16

# Numerical integration (exact)
prob_ni <- pNI2tdiff(q = 1.5, mu.t1 = mu1, mu.t2 = mu2, 
                     sd.t1 = sd1, sd.t2 = sd2, nu.t1 = nu1, nu.t2 = nu2)

# Welch-Satterthwaite approximation (fast)  
prob_ws <- pWS2tdiff(q = 1.5, mu.t1 = mu1, mu.t2 = mu2, 
                     sd.t1 = sd1, sd.t2 = sd2, nu.t1 = nu1, nu.t2 = nu2)

cat("NI:", round(prob_ni, 4), "WS:", round(prob_ws, 4), 
    "Diff:", round(abs(prob_ni - prob_ws), 4))

Study Design Examples

Controlled Design

Standard two-arm randomized controlled trial.

# Binary endpoint
result <- pPPsinglebinary(
  prob = 'posterior', 
  design = 'controlled', 
  theta0 = 0.15,
  n1 = 12, n2 = 15, y1 = 7, y2 = 5, 
  a1 = 0.5, a2 = 0.5, b1 = 0.5, b2 = 0.5,
  m1 = NULL, m2 = NULL,
  ne1 = NULL, ne2 = NULL, ye1 = NULL, ye2 = NULL, ae1 = NULL, ae2 = NULL
)

Uncontrolled Design

Single-arm study with historical control assumption.

result <- pPPsinglebinary(
  prob = 'posterior', 
  design = 'uncontrolled', 
  theta0 = 0.15,
  n1 = 20, n2 = 20, y1 = 12, y2 = 3.5,
  a1 = 0.5, a2 = 0.5, b1 = 0.5, b2 = 0.5,
  m1 = NULL, m2 = NULL,
  ne1 = NULL, ne2 = NULL, ye1 = NULL, ye2 = NULL, ae1 = NULL, ae2 = NULL
)

External Control Design

Incorporating historical data using power priors.

result <- pPPsinglebinary(
  prob = 'posterior', 
  design = 'external', 
  theta0 = 0.15,
  n1 = 20, n2 = 20, y1 = 12, y2 = 8,
  a1 = 0.5, a2 = 0.5, b1 = 0.5, b2 = 0.5,
  m1 = NULL, m2 = NULL,
  ne1 = 15, ne2 = 25, ye1 = 9, ye2 = 10, ae1 = 0.5, ae2 = 0.5
)

References

For theoretical background and methodology details, please refer to the package vignettes and function documentation.

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 (>= 3).

Authors

Gosuke Homma
Yusuke Yamaguchi

Issues and Contributions

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