Bayesian Survival Model based on Moment Characterization

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.