Bayesian Borrowing for Single Arm Studies

Analysis Parameters

Historical Data

Historical Responders:

Historical Total Sample Size:

Current Study Data

Current Study Responders:

Current Study Total Sample Size:

Prior Parameters

Prior Alpha (Beta Distribution):

Prior Beta (Beta Distribution):

Borrowing Parameters

Borrowing Weight:

Borrowing Method:

Analysis Options

Credible Interval Level:

MCMC Samples:

Analysis Results

Welcome to Bayesian Borrowing Analysis

Configure your parameters on the left and click 'Run Analysis' to begin.

Analysis Summary

Posterior Statistics

Prior and Posterior Distributions

Borrowing Impact Analysis

Click 'Compare All Methods' to see how different borrowing methods compare.

Comparison Across Borrowing Methods

Method Comparison Visualization

Borrowing Methods Overview

Power Prior

Direct control over the effective sample size from historical data. Most straightforward approach.

Commensurate Prior

Uses precision parameter to weight historical information based on similarity to current data.

Hierarchical Model

Assumes exchangeability between studies through common hyperpriors.

Meta-Analytic Predictive

Conservative approach that accounts for uncertainty in historical estimates.

User Guide

Getting Started

This application performs Bayesian borrowing analysis for single-arm clinical trials focusing on single proportion (responder rate) estimation.

Input Parameters

Historical Data: Enter the number of responders and total sample size from your historical study.
Current Study Data: Enter the number of responders and total sample size from your current study.
Prior Parameters: Specify the Beta distribution parameters for your prior belief.
Borrowing Weight: Control how much historical information to borrow (0 = no borrowing, 1 = full borrowing).
Method: Choose from four different Bayesian borrowing approaches.

Borrowing Methods

Power Prior: Raises the historical likelihood to a power determined by the borrowing weight. Most transparent method.
Commensurate Prior: Uses a precision parameter to weight historical data based on compatibility with current data.
Hierarchical Model: Assumes studies are exchangeable with common hyperpriors.
Meta-Analytic Predictive: Conservative approach that propagates uncertainty from historical data.

Interpreting Results

Posterior Mean: The expected value of the response rate given all data.
Credible Intervals: Bayesian confidence intervals for the response rate.
Effective Sample Size: The equivalent sample size contributed by historical borrowing.
Method Comparison: Shows how different borrowing approaches affect your conclusions.

Example Analysis

The default values provide a working example:

Historical study: 15/50 responders (30% response rate)
Current study: 8/25 responders (32% response rate)
Non-informative prior: Beta(1,1)
Moderate borrowing: weight = 0.5

Best Practices

Start with the default example to understand the interface
Compare multiple methods to assess sensitivity
Consider the clinical context when choosing borrowing weights
Validate results with domain experts