Analysis of Unobserved Heterogeneity via Accelerated Failure Time Models Under Bayesian and Classical Approaches

TL;DR

This paper compares Bayesian and classical Accelerated Failure Time models for unobserved heterogeneity in survival data, highlighting their differences, advantages, and performance through real data examples.

Contribution

It provides a comparative analysis of Bayesian mixture models and classical frailty models for unobserved heterogeneity in AFT models, including practical insights.

Findings

Inverse-Gaussian mixture distribution outperforms other models

Classical frailty estimates tend to be underestimated

Bayesian and classical estimates show notable differences

Abstract

This paper deals with unobserved heterogeneity in the survival dataset through Accelerated Failure Time (AFT) models under both frameworks--Bayesian and classical. The Bayesian approach of dealing with unobserved heterogeneity has recently been discussed in Vallejos and Steel (2017), where mixture models are used to diminish the effect that anomalous observations or some kinds of covariates which are not included in the survival models. The frailty models also deal with this kind of unobserved variability under classical framework and have been used by practitioners as alternative to Bayesian. We discussed both approaches of dealing with unobserved heterogeneity with their pros and cons when a family of rate mixtures of Weibul distributions and a set of random effect distributions were used under Bayesian and classical approaches respectively. We investigated how much the classical estimates differ with the Bayesian estimates, although the paradigm of estimation methods are different. Two real data examples--a bone marrow transplants data and a kidney infection data have been used to illustrate the performances of the methods. In both situations, it is observed that the use of an Inverse-Gaussian mixture distribution outperforms the other possibilities. It is also noticed that the estimates of the frailty models are generally somewhat underestimated by comparing with the estimates of their counterpart.