  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 Methods 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
Equation (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 GMM 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.
