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Introduction to BayesianQDM

Source: vignettes/BayesianQDM.Rmd
BayesianQDM.Rmd

Overview

The BayesianQDM package provides comprehensive methods for Bayesian quantitative decision-making in clinical trials. This vignette demonstrates the basic functionality for both binary and continuous endpoints.

Decision Framework

The package implements a three-zone decision framework:

  • Go: Sufficient evidence to proceed (high posterior probability)
  • NoGo: Insufficient evidence (low posterior probability)
  • Gray: Inconclusive evidence (intermediate probability)

Binary Endpoints

Basic Example 

# Calculate decision probabilities for binary endpoint
result_binary <- 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_binary)
#>   pi1 pi2         Go      Gray      NoGo
#> 1 0.3 0.2 0.01578194 0.1810868 0.8031312
#> 2 0.5 0.2 0.21141006 0.4500322 0.3385577
#> 3 0.7 0.2 0.67440950 0.2761393 0.0494512

Posterior Probability 

# Calculate posterior probability
posterior_prob <- 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
)

cat("Posterior probability:", round(posterior_prob, 4))
#> Posterior probability: 0.3139

Continuous Endpoints

Basic Example 

# Calculate decision probabilities for continuous endpoint  
result_continuous <- pGNGsinglecontinuous(
  nsim = 50,  # Small nsim for vignette speed
  prob = 'posterior', 
  design = 'controlled', 
  prior = 'vague', 
  CalcMethod = 'WS',  # Fast method for vignette
  theta.TV = 1.5, theta.MAV = 0.5, theta.NULL = NULL,
  nMC = NULL, gamma1 = 0.8, gamma2 = 0.3,
  n1 = 12, n2 = 12, m1 = NULL, m2 = NULL,
  kappa01 = NULL, kappa02 = NULL, nu01 = NULL, nu02 = NULL,
  mu01 = NULL, mu02 = NULL, sigma01 = NULL, sigma02 = NULL,
  mu1 = 4.5, 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_continuous)
#>   mu1 mu2   Go Gray NoGo
#> 1 4.5   2 0.82 0.18    0

Comparing Calculation Methods 

# Compare NI and WS methods
prob_ni <- pPPsinglecontinuous(
  prob = 'posterior', design = 'controlled', prior = 'vague', CalcMethod = 'NI',
  theta0 = 1, n1 = 12, n2 = 12, bar.y1 = 3, bar.y2 = 1, s1 = 1.5, s2 = 1.2
)

prob_ws <- pPPsinglecontinuous(
  prob = 'posterior', design = 'controlled', prior = 'vague', CalcMethod = 'WS',
  theta0 = 1, n1 = 12, n2 = 12, bar.y1 = 3, bar.y2 = 1, s1 = 1.5, s2 = 1.2
)

cat("NI method:", round(prob_ni, 4), "\n")
#> NI method: 0.0503
cat("WS method:", round(prob_ws, 4), "\n")
#> WS method: 0.0429
cat("Difference:", round(abs(prob_ni - prob_ws), 4), "\n")
#> Difference: 0.0074

Study Designs

The package supports three study designs:

  1. Controlled Design: Standard two-arm randomized trial
  2. Uncontrolled Design: Single-arm with historical control
  3. External Control Design: Incorporating historical data through power priors

External Control Example 

# Binary endpoint with external control data
external_binary <- 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
)

cat("Posterior probability with external data:", round(external_binary, 4), "\n")
#> Posterior probability with external data: 0.3579

# Continuous endpoint with external control data
external_continuous <- pPPsinglecontinuous(
  prob = 'posterior',
  design = 'external',
  prior = 'vague',
  CalcMethod = 'WS',
  theta0 = 1.5,
  n1 = 20, n2 = 20,
  bar.y1 = 5.5, bar.y2 = 3.2,
  s1 = 2.1, s2 = 1.9,
  ne1 = NULL, ne2 = 40,
  alpha01 = NULL, alpha02 = 0.5,
  bar.ye1 = NULL, bar.ye2 = 3.0,
  se1 = NULL, se2 = 2.0
)

cat("Posterior probability with external control:", round(external_continuous, 4), "\n")
#> Posterior probability with external control: 0.0581

Next Steps

For more detailed examples and advanced usage:

References

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