BayesianQDM

Overview

BayesianQDM is an R package that provides comprehensive methods for Bayesian quantitative decision-making in clinical trials. The package supports both binary and continuous endpoints with various study designs including controlled, uncontrolled, and external control designs.

Key Features

• Endpoint Types: Binary (response/non-response) and continuous (biomarker changes, scores)
• Study Designs: Controlled, uncontrolled, and external control designs
• Decision Framework: Go/NoGo/Gray zones for evidence-based decision making
• Calculation Methods: Multiple approaches optimized for accuracy and speed
• Prior Integration: Flexible prior specifications including power priors for external data

Decision Framework

The package implements a three-zone Bayesian decision framework:

• Go: Sufficient evidence to proceed to next phase (high posterior probability of efficacy)
• NoGo: Insufficient evidence to proceed (low posterior probability of efficacy)
  
• Gray: Inconclusive evidence (intermediate posterior probability requiring additional data)

For technical details about the methodology, please refer to Kang et al. (20XX).

Installation

You can install the development version of BayesianQDM from GitHub with:

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

Once submitted to CRAN, you will be able to install the stable version with:

install.packages("BayesianQDM")

Quick Start

Binary Endpoint Example

library(BayesianQDM)

# Calculate Go/NoGo/Gray probabilities for binary endpoint
result_binary <- BayesDecisionProbBinary(
  prob = 'posterior', design = 'controlled', 
  theta.TV = 0.3, theta.MAV = 0.1, theta.NULL = NULL,
  gamma1 = 0.8, gamma2 = 0.2,
  pi1 = c(0.2, 0.4, 0.6, 0.8), pi2 = rep(0.2, 4), 
  n1 = 20, n2 = 20,
  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_binary)

Continuous Endpoint Example

# Calculate Go/NoGo/Gray probabilities for continuous endpoint  
result_continuous <- BayesDecisionProbContinuous(
  nsim = 1000, prob = 'posterior', design = 'controlled', 
  prior = 'vague', CalcMethod = 'NI',
  theta.TV = 1.5, theta.MAV = 0.5, theta.NULL = NULL,
  nMC = NULL, nINLAsample = 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 = 3.0, mu2 = 1.2,
  sigma1 = 1.5, sigma2 = 1.5,
  r = NULL, ne1 = NULL, ne2 = NULL, alpha01 = NULL, alpha02 = NULL,
  seed = 123
)

print(result_continuous)

Documentation

📚 Comprehensive 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

• BayesDecisionProbBinary() - Go/NoGo/Gray probabilities for binary endpoints
• BayesDecisionProbContinuous() - Go/NoGo/Gray probabilities for continuous endpoints

Probability Calculation Functions

• BayesPostPredBinary() - Posterior/predictive probabilities for binary data
• BayesPostPredContinuous() - Posterior/predictive probabilities for continuous data

Distribution Functions

• pBetadiff(), pBetaBinomdiff() - Beta distribution differences
• pNIdifft(), pWSdifft(), pMCdifft() - t-distribution differences
  
• AppellsF1() - Appell’s hypergeometric function

Calculation Methods

For Continuous Endpoints

Method	Description	Use Case
NI	Numerical Integration	Most accurate, recommended for final analyses
WS	Welch-Satterthwaite	Fast approximation, good for simulations
MC	Monte Carlo	Flexible, handles complex scenarios
INLA	Integrated Nested Laplace Approximation	External data incorporation

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 <- pNIdifft(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 <- pWSdifft(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.

Uncontrolled Design

Single-arm study with comparison to historical control.

External Control Design

Incorporating historical data using power priors.

# External control example
external_result <- BayesPostPredBinary(
  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 = 30, ne2 = 30, ye1 = 15, ye2 = 6,  
  ae1 = 0.5, ae2 = 0.5  # Power prior weights
)

Visualization Example

library(dplyr)
library(tidyr) 
library(ggplot2)

# Create decision probability plot
results <- BayesDecisionProbBinary(
  prob = 'posterior', design = 'controlled',
  theta.TV = 0.3, theta.MAV = 0.1, theta.NULL = NULL,
  gamma1 = 0.8, gamma2 = 0.2,
  pi1 = seq(0.1, 0.9, by = 0.05), pi2 = rep(0.2, length(seq(0.1, 0.9, by = 0.05))),
  n1 = 20, n2 = 20, 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
) %>%
  mutate(theta = pi1 - pi2)

# Plot decision probabilities
results %>%
  pivot_longer(cols = c(Go, NoGo, Gray), names_to = 'Decision', values_to = 'Probability') %>%
  mutate(Decision = factor(Decision, levels = c('Go', 'Gray', 'NoGo'))) %>%
  ggplot(aes(x = theta, y = Probability)) +
  geom_line(aes(colour = Decision, linetype = Decision), linewidth = 1.2) +
  scale_color_manual(values = c('Go' = '#2E8B57', 'Gray' = '#808080', 'NoGo' = '#DC143C')) +
  theme_bw() +
  labs(title = 'Go/Gray/NoGo Decision Probabilities',
       x = 'Treatment Effect (π₁ - π₂)', y = 'Probability')

Prior Distributions

Binary Endpoints

• Beta priors: Beta(a, b) for response probabilities
• Common choices: Beta(0.5, 0.5) for Jeffreys prior, Beta(1, 1) for uniform

Continuous Endpoints

• Vague priors: Non-informative approach letting data drive conclusions
• Normal-Inverse-Chi-squared: Conjugate priors for incorporating prior knowledge
• Power priors: For external data incorporation with controlled borrowing

Advanced Features

Power Prior Integration

Control the degree of borrowing from external data:

# α = 0: No borrowing
# α = 1: Full borrowing  
# 0 < α < 1: Partial borrowing

alpha_values <- c(0, 0.5, 1.0)
comparison <- sapply(alpha_values, function(alpha) {
  BayesPostPredBinary(
    prob = 'posterior', design = 'external', theta0 = 0.2,
    n1 = 15, n2 = 15, y1 = 8, y2 = 6,
    a1 = 0.5, a2 = 0.5, b1 = 0.5, b2 = 0.5,
    m1 = NULL, m2 = NULL,
    ne1 = 20, ne2 = 20, ye1 = 10, ye2 = 4,
    ae1 = alpha, ae2 = alpha
  )
})

Operating Characteristics

Evaluate decision framework performance:

# Simulate trials across different scenarios
scenarios <- expand.grid(
  true_effect = c(0, 0.5, 1.0, 1.5, 2.0),
  sample_size = c(15, 25, 35)
)

# Calculate Go probabilities for each scenario
# (implementation details in vignettes)

Performance Considerations

• NI method: Most accurate but moderate computational cost
• WS method: Fast approximation suitable for simulations
• MC method: Flexible but computationally intensive (use larger nMC for precision)
• INLA method: Efficient for external data scenarios

For large simulation studies, consider: - Using WS method for screening - NI method for final analyses - Parallel processing for Monte Carlo approaches

Common Use Cases

Phase II Proof-of-Concept

• Objective: Determine if treatment shows efficacy signal
• Typical settings: θ_TV = 1.5 × MCID, γ₁ = 0.8

Dose-Finding Studies

• Objective: Select optimal dose for Phase III
• Considerations: Multiple comparisons, dose-response modeling

Biomarker-Driven Trials

• Objective: Evaluate treatment in biomarker-defined populations
• Challenges: Smaller samples, incorporation of biomarker information

Best Practices

Parameter Selection

• Thresholds: Align with clinical meaningfulness (e.g., MCID)
• Decision criteria: Balance Type I/II errors for study objectives
  
• Priors: Document rationale and conduct sensitivity analyses

Validation

• Operating characteristics: Evaluate across relevant scenarios
• Sensitivity analysis: Test robustness to assumptions
• Method comparison: Verify consistency across calculation approaches

Reporting

• Transparency: Report all inputs (priors, thresholds, methods)
• Uncertainty: Include credible intervals and sensitivity analyses
• Interpretation: Provide clinical context for decision probabilities

Integration with R Ecosystem

The package integrates seamlessly with: - tidyverse: Data manipulation and visualization workflows - ggplot2: Creating publication-quality decision probability plots - knitr/rmarkdown: Reproducible reporting and documentation

Citation

If you use BayesianQDM in your research, please cite:

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

References

Kang et al. (20XX). [Title]. [Journal].

License

This project is licensed under the MIT License - see the LICENSE.md file for details.

Support

• Documentation: See package vignettes and function help
• Issues: Report bugs or request features on GitHub
• Questions: Use GitHub Discussions for methodology questions

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