# Bayesian significance test for discriminating between survival distributions

## TL;DR

This paper evaluates the Fully Bayesian Significance Test (FBST) for selecting the best survival distribution among lognormal, gamma, and Weibull by using a mixture model and applying it to both simulated and real patient data.

## Contribution

It introduces a Bayesian mixture model with reparametrized distributions for survival analysis and applies FBST to discriminate among competing survival distributions.

## Key findings

- FBST effectively distinguishes between survival distributions in simulations.
- The mixture model provides clear posterior weights indicating the most suitable distribution.
- Application to real patient data demonstrates practical utility in medical survival analysis.

## Abstract

An evaluation of FBST, Fully Bayesian Significance Test, restricted to survival models is the main objective of the present paper. A Survival distribution should be chosen among the tree celebrated ones, lognormal, gamma, and Weibull. For this discrimination, a linear mixture of the three distributions, for which the mixture weights are defined by a Dirichlet distribution of order three, is an important tool: the FBST is used to test the hypotheses defined on the mixture weights space. Another feature of the paper is that all three distributions are reparametrized in that all the six parameters - two for each distribution - are written as functions of the mean and the variance of the population been studied. Note that the three distributions share the same two parameters in the mixture model. The mixture density has then four parameters, the same two for the three discriminating densities and two for the mixture weights. Some numerical results from simulations with some right-censored data are considered. The lognormal-gamma-Weibull model is also applied to a real study with dataset being composed by patient's survival times of patients in the end-stage of chronic kidney failure subjected to hemodialysis procedures; data from Rio de Janeiro hospitals. The posterior density of the weights indicates an order of the mixture weights and the FBST is used for discriminating between the three survival distributions. Keywords: Model choice; Separate Models; Survival distributions; Mixture model; Significance test; FBST