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 infinitedimensional 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 functional of the posterior distribution, such as median, mode or credible intervals. This is particularly relevant in survival analysis where non-linear functionals such as 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, Lijoi and Nipoti, Comput. Stat. Data. Anal. 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. By means of an extensive simulation study, we thoroughly compare the introduced methodology with standard marginal methods and empirical estimation.