Shrinkage priors for isotonic probability vectors and binary data modeling, with applications to dose-response...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Medical Physics

Background:

• Modeling dose-response and dose-toxicity curves is crucial for clinical trial design.
• Bayesian isotonic regression is used for binary outcomes with ordered predictors.
• Existing Dirichlet/gamma priors face numerical instability issues.

Purpose of the Study:

• To develop a numerically stable horseshoe-based prior for Bayesian isotonic regression.
• To model monotonically non-decreasing dose-response relationships.
• To improve estimation efficiency in dose-finding studies.

Main Methods:

• Developed a novel horseshoe-based prior for Bayesian isotonic regression.
• Analyzed numerical stability compared to Dirichlet/gamma priors using mathematical and simulation arguments.
• Applied the prior to model radiation-induced lung toxicity in cancer patients.

Main Results:

• The proposed horseshoe-based prior demonstrates superior numerical stability over Dirichlet/gamma priors.
• The horseshoe prior leads to more efficient estimation of the true dose-response curve.
• The method was successfully applied to predict lung toxicity as a function of radiation dose.

Conclusions:

• The horseshoe-based prior offers a more stable and efficient alternative for Bayesian isotonic regression in dose-response modeling.
• This methodology is suitable for designing dose-finding studies and other related contexts.
• The R package `isotonicBayes` implements this advanced Bayesian approach.