Bayesian Parametric Methods for Deriving Distribution of Restricted Mean Survival Time

TL;DR

This paper introduces a Bayesian approach to estimate the distribution of restricted mean survival time (RMST) incorporating covariates and heterogeneity, with explicit formulas and custom models validated through simulations and real data analysis.

Contribution

It develops explicit RMST formulas for parametric survival models and introduces methods to account for heterogeneity using random effects and frailty, implemented in custom Stan code.

Findings

Methods are robust in simulations

Accurate cluster-specific results via shrinkage

Consistent results across Indian states after adjustment

Abstract

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.