Restricted mean survival times for comparing grouped survival data: a Bayesian nonparametric approach

TL;DR

This paper introduces a Bayesian nonparametric method for comparing survival data using restricted mean survival times, providing a flexible framework with closed-form expressions for posterior analysis.

Contribution

It extends univariate neutral to the right processes to a multivariate setting, enabling Bayesian comparison of survival functions via RMSTs.

Findings

Provides closed-form expressions for prior and posterior moments of RMSTs.

Enables approximation of posterior distributions of RMSTs for group comparisons.

Facilitates analysis of time-to-event data in treatment effect studies.

Abstract

Comparing survival experiences of different groups of data is an important issue in several applied problems. A typical example is where one wishes to investigate treatment effects. Here we propose a new Bayesian approach based on restricted mean survival times (RMST). A nonparametric prior is specified for the underlying survival functions: this extends the standard univariate neutral to the right processes to a multivariate setting and induces a prior for the RMST's. We rely on a representation as exponential functionals of compound subordinators to determine closed form expressions of prior and posterior mixed moments of RMST's. These results are used to approximate functionals of the posterior distribution of RMST's and are essential for comparing time--to--event data arising from different samples.