  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.
