A multivariate Polya tree model for meta-analysis with event-time distributions.

Area of Science:

• Statistics
• Biostatistics
• Bayesian Inference

Background:

• Meta-analysis of event-time data often requires flexible modeling of survival distributions.
• Existing methods may not adequately capture study-level covariate effects on survival outcomes.
• Nonparametric Bayesian approaches offer powerful tools for complex survival data.

Purpose of the Study:

• To develop a novel nonparametric Bayesian prior for joint event-time distributions in meta-analysis.
• To incorporate study-specific covariates to induce correlation between similar studies.
• To facilitate efficient posterior inference for meta-analysis of survival data.

Main Methods:

• Extension of the Polya tree (PT) prior to a multivariate PT model for multiple event-time distributions ($G_1, ..., G_n$).
• Introduction of a hierarchical prior using a Gaussian process on conditional splitting probabilities.
• The Gaussian process is indexed by study-specific covariates to model dependence structures.

Main Results:

• The proposed model establishes increased correlation for studies with similar characteristics.
• The construction allows for (conditionally) conjugate posterior updating.
• Enables inference using commonly reported summaries for event-time data.

Conclusions:

• The developed multivariate PT prior provides a flexible and computationally efficient Bayesian framework for meta-analysis of event-time data.
• The method effectively leverages study-specific covariates to improve modeling of treatment effects in cancer immunotherapy.
• This approach offers a robust alternative for synthesizing evidence from heterogeneous survival studies.