We propose a Bayesian method for deriving the distribution of restricted mean survival time (RMST) using posterior samples, which accounts for covariates and heterogeneity among clusters based on a parametric model for survival time. We derive an explicit RMST equation by devising an integral of the survival function, allowing for the calculation of not only the mean and credible interval but also the mode, median, and probability of exceeding a certain value. Additionally, We propose two methods: one using random effects to account for heterogeneity among clusters and another utilizing frailty. We developed custom Stan code for the exponential, Weibull, log-normal frailty, and log-logistic models, as they cannot be processed using the brm functions in R. We evaluate our proposed methods through computer simulations and analyze real data from the eight Empowered Action Group states in India to confirm consistent results across states after adjusting for cluster differences. In conclusion, we derived explicit RMST formulas for parametric models and their distributions, enabling the calculation of the mean, median, mode, and credible interval. Our simulations confirmed the robustness of the proposed methods, and using the shrinkage effect allowed for more accurate results for each cluster.

翻译：我们提出了一种基于参数化生存时间模型的贝叶斯方法，该方法利用后验样本推导受限平均生存时间的分布，同时考虑协变量和群组间的异质性。通过设计生存函数的积分形式，我们推导出显式的受限平均生存时间方程，使得不仅能够计算均值和可信区间，还能计算众数、中位数以及超过特定阈值的概率。此外，我们提出了两种方法：一种采用随机效应处理群组间的异质性，另一种利用脆弱性模型。针对指数分布、威布尔分布、对数正态脆弱性模型以及对数逻辑分布，我们开发了定制的Stan代码，因为这些模型无法通过R语言中的brm函数进行处理。我们通过计算机模拟评估了所提出的方法，并分析了印度八个赋权行动组邦的实际数据，以验证在调整群组差异后各邦结果的一致性。综上所述，我们推导了参数化模型的显式受限平均生存时间公式及其分布，从而能够计算均值、中位数、众数和可信区间。模拟实验证实了所提方法的稳健性，且利用收缩效应能够为每个群组获得更精确的结果。