Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients

Abstract

The log-normal, log-logistic and Weibull distributions are commonly utilized to model survival data. Unimodal (or non-monotone) failure rate functions are modeled using the log-normal and the log-logistic families, whereas monotone failure rate functions are modeled using the Weibull family. The growing availability of survival data with a variety of features encourages statisticians to propose more flexible parametric models that can accommodate both monotone (increasing or decreasing), and non-monotone (unimodal or bathtub) failure rate functions. One such model is the generalized log-logistic distribution which not only accommodates unimodal failure rates but also allows for a monotone and non-monotone failure rate functions. This distribution has shown to have a lot of potential in univariate analysis of survival data. However, many studies are primarily concerned with determining the link between survival time and one or more explanatory variables. This leads to the study of hazard-based regression models in survival and reliability analysis, which can be formulated in a variety of ways. One such method concerns formulating hazard-based regression models for the accelerated failure time (AFT) family of continuous probability distributions. The log-logistic, Weibull and log-normal distributions are the most widely utilized this framework. In this paper, we show that the generalized log-logistic distribution is closed under the accelerated failure time framework. We then formulate an accelerated failure time model based on the generalized log-logistic distribution. Furthermore, we show parameter estimation for the model using Bayesian and frequentist approaches. An extensive simulation study is conducted to illustrate the inferential properties of the proposed model, more specifically, the tendency to recover the baseline hazard shapes, parameter estimation, as well as the effect of censoring proportions on inference. The simulation results demonstrate that the generalized log-logistic accelerated failure time model can be capable of modeling survival data with various hazard rate shapes. Finally, a real-life survival data relating to larynx-cancer patients was used.