Variational bayesian inference for exponentiated weibullright-censored survnaldata - Abubakar, Jibril (2023)
The Weibull, log-logistic and log-normal distributions represent the heavy-tailed distributions that are often used in modelling time-to-event data. While the loglogistic and log-normal distributions are mainly used for modelling unimodal hazard functions, the Weibull distribution is well-known for modelling monotonic hazard rates. The commonly applied estimation technique for this class of model is the Maximum Likelihood Estimator (MLE). However, previous studies have established the inadequacy of this technique for the exponentiated class of models, such as the exponentiated-Weibull model. Thus, in this thesis, we revisited the parameter estimation for the exponentiated-Weibull model class by introducing a new Bayesian technique called Variational Bayes. We considered the case of accelerated failure time (AFT) exponentiated-Weibull regression model with covariates. The AFT model was developed using two comparative studies based on real-life Lung cancer and simulated datasets. The AFT model parameters were estimated using the MLE, Bayesian Metropolis-Hasting and Variational Bayes procedure. The data calibration results showed that the exponentiated Weibull regression adequately describes the time-toevent data. In addition, the Variational Bayesian procedure was found to be the most efficient among the three estimation techniques considered