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.

翻译：生存回归建模的贝叶斯推断在决策制定和外部数据借用方面具有诸多优势，但需要设定基线风险函数，这往往是一项具有挑战性的任务。我们提出一种无需指定该函数的替代方法。该方法结合伪观测值将删失数据转化为纵向数据，并利用广义矩方法（GMM）直接从生存函数估计感兴趣参数。GMM可视为当前用于频率学派伪观测值分析的广义估计方程（GEE）的扩展，并可通过伪似然函数推广至贝叶斯框架。我们评估了频率学派和贝叶斯GMM在分析伪观测值这一新情境中的表现。通过模拟双臂随机临床试验，将其性能与Cox模型、GEE及贝叶斯分段指数模型进行比较。频率学派和贝叶斯GMM在三种基准方法中均能提供有效推断且性能相近，仅在小样本量和高删失率情况下存在差异。为进行示例说明，我们对涉及尤因肉瘤患者的随机临床试验进行了三项事后疗效分析，结果与基准方法一致。通过风险比估计的简单应用，这些发现证实了基于伪观测值和广义矩方法的贝叶斯新方法的有效性，为贝叶斯生存分析中伪观测值的应用提供了新见解。