# Bayesian generalized method of moments applied to pseudo-observations in survival analysis

## TL;DR

This paper introduces a new Bayesian method for survival analysis that avoids specifying the baseline hazard function by using pseudo-observations and generalized method of moments.

## Contribution

The novelty is a Bayesian GMM approach for survival analysis using pseudo-observations without requiring baseline hazard specification.

## Key findings

- Bayesian and frequentist GMMs provided valid inferences comparable to benchmark methods in most scenarios.
- Performance was similar to Cox, GEE, and Bayesian piecewise exponential models except for small samples and high censoring.
- Post-hoc analyses on Ewing Sarcoma trials confirmed the method's effectiveness in estimating hazard ratios.

## Abstract

Bayesian inference for survival regression modeling offers numerous advantages, especially for decision-making and external data borrowing, but demands the specification of the baseline hazard function, which may be a challenging task. We propose an alternative approach that does not need the specification of this function. Our approach combines pseudo-observations to convert censored data into longitudinal data with the generalized method of moments (GMM) to estimate the parameters of interest from the survival function directly. GMM may be viewed as an extension of the generalized estimating equations (GEE) currently used for frequentist pseudo-observations analysis and can be extended to the Bayesian framework using a pseudo-likelihood function. We assessed the behavior of the frequentist and Bayesian GMM in the new context of analyzing pseudo-observations. We compared their performances to the Cox, GEE, and Bayesian piecewise exponential models through a simulation study of two-arm randomized clinical trials. Frequentist and Bayesian GMMs gave valid inferences with similar performances compared to the three benchmark methods, except for small sample sizes and high censoring rates. For illustration, three post-hoc efficacy analyses were performed on randomized clinical trials involving patients with Ewing Sarcoma, producing results similar to those of the benchmark methods. Through a simple application of estimating hazard ratios, these findings confirm the effectiveness of this new Bayesian approach based on pseudo-observations and the generalized method of moments. This offers new insights on using pseudo-observations for Bayesian survival analysis.

The online version contains supplementary material available at 10.1007/s10985-025-09670-1.