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

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.