Variational Bayesian Inference for Exponentiated Weibull Right Censored Survival Data

Abstract

The exponential, Weibull, log-logistic and lognormal distributions represent the class of light and heavy-tailed distributions that are often used in modelling time-to-event data. The exponential distribution is often applied if the hazard is constant, while the log-logistic and lognormal distributions are mainly used for modelling unimodal hazard functions. The Weibull distribution is on the other hand well-known for modelling monotonic hazard rates. Recently, in practice, survival data often exhibit both monotone and non-monotone hazards. This gap has necessitated the introduction of Exponentiated Weibull Distribution (EWD) that can accommodate both monotonic and non-monotonic hazard functions. It also has the strength of adapting unimodal functions with bathtub shape. Estimating the parameter of EWD distribution poses another problem as the flexibility calls for the introduction of an additional parameter. Parameter estimation using the maximum likelihood approach has no closed-form solution, and thus, approximation techniques such as Newton-Raphson is often used. Therefore, in this paper, we introduce another estimation technique called Variational Bayesian (VB) approach. We considered the case of the accelerated failure time (AFT) regression model with covariates. The AFT model was developed using two comparative studies based on real-life and simulated data sets. The results from the experiments reveal that the Variational Bayesian (VB) approach is better than the competing Metropolis-Hasting Algorithm and the reference maximum likelihood estimates.