# A Bayesian hierarchical meta-analytic method for modelling surrogate relationships that vary across treatment classes using aggregate data

## TL;DR

This paper introduces Bayesian hierarchical meta-analytic methods to model surrogate relationships across treatment classes, enabling information sharing and improved estimation when data are limited within classes.

## Contribution

The paper proposes two novel Bayesian meta-analytic approaches that allow for full or partial borrowing of information across treatment classes to better evaluate surrogate endpoints.

## Key findings

- Methods improve estimation precision of surrogate relationships.
- Hierarchical models outperform subgroup analysis in simulations.
- Application to colorectal cancer data demonstrated practical utility.

## Abstract

Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final clinical outcome and to predict clinical benefit or harm. Such endpoints are assessed for their predictive value of clinical benefit by investigating the surrogate relationship between treatment effects on the surrogate and final outcomes using meta-analytic methods. When surrogate relationships vary across treatment classes, such validation may fail due to limited data within each treatment class. In this paper, two alternative Bayesian meta-analytic methods are introduced which allow for borrowing of information from other treatment classes when exploring the surrogacy in a particular class. The first approach extends a standard model for the evaluation of surrogate endpoints to a hierarchical meta-analysis model assuming full exchangeability of surrogate relationships across all the treatment classes, thus facilitating borrowing of information across the classes. The second method is able to relax this assumption by allowing for partial exchangeability of surrogate relationships across treatment classes to avoid excessive borrowing of information from distinctly different classes. We carried out a simulation study to assess the proposed methods in nine data scenarios and compared them with subgroup analysis using the standard model within each treatment class. We also applied the methods to an illustrative example in colorectal cancer which led to obtaining the parameters describing the surrogate relationships with higher precision.