Bayesian Survival Model based on Moment Characterization

TL;DR

This paper introduces a Bayesian survival analysis method based on moments, enabling estimation of non-linear functionals like medians and credible intervals, which are crucial in clinical settings.

Contribution

It summarizes and extends a hazard mixture model approach for approximate Bayesian inference on survival functions beyond posterior means.

Findings

Method allows estimation of medians and credible intervals.

Compared favorably to standard marginal methods in simulations.

Provides an R package 'momentify' for practical implementation.

Abstract

Bayesian nonparametric marginal methods are very popular since they lead to fairly easy implementation due to the formal marginalization of the infinite-dimensional parameter of the model. However, the straightforwardness of these methods also entails some limitations: they typically yield point estimates in the form of posterior expectations, but cannot be used to estimate non-linear functionals of the posterior distribution, such as median, mode or credible intervals. This is particularly relevant in survival analysis where non-linear functionals such as e.g. the median survival time, play a central role for clinicians and practitioners. The main goal of this paper is to summarize the methodology introduced in [Arbel et al., Comput. Stat. Data. An., 2015] for hazard mixture models in order to draw approximate Bayesian inference on survival functions that is not limited to the posterior mean. In addition, we propose a practical implementation of an R package called momentify designed for moment-based density approximation, and, by means of an extensive simulation study, we thoroughly compare the introduced methodology with standard marginal methods and empirical estimation.