Zetyra Bayesian Toolkit: A Comprehensive Suite of Validated Bayesian Calculators for Clinical Trial Design

The U.S. Food and Drug Administration’s January 12, 2026 draft guidance on the use of Bayesian methodology in clinical trials for drugs and biological products signals expanding regulatory acceptance of Bayesian approaches in clinical development. This companion white paper provides the mathematical formulations, validation results, and regulatory context for the six Bayesian modules implemented in the Zetyra Bayesian Toolkit. Modules Covered Prior Elicitation Quantile-matching methods, effective sample size (ESS) calibration, and prior informativeness classification across conjugate prior families (Beta–Binomial, Normal–Normal, Gamma–Poisson). Bayesian Borrowing from External Data Implementation of power priors, commensurate priors, and MAP estimation approaches for incorporating historical or external control data with adaptive discounting. Single-Arm Bayesian Trial Design Sample size determination and posterior decision thresholds for binary and continuous endpoints. Two-Arm Bayesian Trial Design Superiority and non-inferiority designs with extensions to survival endpoints using conjugate log-hazard frameworks. Bayesian Sequential Monitoring Stopping rules based on posterior probability and predictive probability criteria. Predictive Probability of Success (PPoS) Calculation of the probability that a trial will meet its success criterion given interim data, integrating over the posterior distribution of the treatment effect. Validation The Bayesian modules were evaluated using 248 automated validation tests, benchmarked against conjugate analytical solutions, published reference methods (Zhou & Ji, 2024), and parameter configurations derived from published clinical trials. All validation code and test cases are publicly available under an MIT license. Practical Guidance The white paper includes practical implementation guidance for Bayesian trial design, including: decision frameworks for prior–data conflict assessment a recommended five-prior sensitivity analysis panel consistent with regulatory expectations discussion of methodological limitations, including reliance on conjugate prior families, exchangeability assumptions for external-data borrowing, and assumptions regarding missing data This document serves as a companion to the Zetyra Technical White Paper (v2.0) and follows the structure commonly used in Bayesian clinical trial methodology texts (e.g., Berry, Carlin, Lee & Müller), while providing implementation-specific details on validation and regulatory considerations. Length: 47 pages covering Bayesian foundations, conjugate prior models, module methodologies, integrated workflow, validation framework, regulatory context, and limitations.