Generalized Topp-Leone-Weibull AFT Modelling: A Bayesian Analysis with MCMC Tools using R and Stan

Abstract

The generalized Topp-Leone-Weibull (GTL-W) distribution is a generalization of Weibull distribution which is obtained by using generalized Topp-Leone (GTL) distribution as a generator and considering Weibull distribution as a baseline distribution. Weibull distribution is a widely used survival model that has monotone- increasing or decreasing hazard. But it cannot accommodate bathtub shaped and unimodal shaped hazards. As a survival model, GTL-W distribution is more flexible than the Weibull distribution to accommodate different types of hazards. The present study aims at fitting GTL-W model as an accelerated failure time (AFT) model to censored survival data under Bayesian setting using R and Stan languages. The GTL-W AFT model is compared with its sub-model and the baseline model. The Bayesian model selection criteria LOOIC and WAIC are applied to select the best model.

Comparison of Random Survival Forest with Accelerated Failure Time-Weibull Model for Bridge Deck Deterioration

“…To compare RSF with traditional deterioration models, a Weibull distribution-based accelerated failure time model is chosen as a benchmark, which is commonly used in the infrastructure deterioration analysis ( 3, 33 ). The AFT-Weibull model can take any bathtub shape distribution as the basic deterioration function and, therefore, is proved to be more appropriate than other distribution-based models.…”

“…Here, 80% of the data is used to estimate the model and the remaining 20% of the data is used to test the model performance. Both censored data and uncensored data are incorporated by the PDF and CDF, respectively, in the likelihood function ( 33 ). The model is estimated with a Python package lifeline ( 34 ), and the parameters are estimated using the maximum likelihood estimation approach.…”

A New Power Topp–Leone distribution with applications to engineering and industry data

“…This modification is a novelty in the literature. The following are some prominent instances of such families: Poisson-G [ 1 ], Odd Fréchet-G [ 2 ], Truncated inverse Kumaraswamy-G [ 3 ], New Power of Topp-Leone-G [ 4 ], Introduction to the generalized Topp-Leone family [ 5 ], Garhy-G [ 6 ], Inverse-Lomax power [ 7 ], Half-Logistic-G type II [ 8 ], Topp-Leone Inverse Lomax [ 9 ], Topp-Leone-Weibull [ 10 ], temporal distribution [ 11 ], Topp-Leone distribution, estimation [ 12 ], Topp-Leone family of distributions and some of its application on real data and some of its statsistical properties [ 13 ], moments of order statistics of Topp-Leone distribution [ 14 ] Fréchet Topp-Leone-G [ 15 ], Topp-Leone G transmuted [ 16 ], new insights on goodness-of-fit tests [ 17 ], a generalized Birnbaum-Saunders distribution [ 18 ], efficient reliability estimation in two-parameter exponential distributions [ 19 ], the Marshall-Olkin extended generalized Rayleigh distribution [ 20 ], tests to determine whether or not the Rayleigh distribution is a good fit [ 21 ], Bayesian analysis [ 22 , 23 ] is also of big interest in our study.…”

The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data

“…Modifications to remove the assumption of "proportional hazards (PH)" are discussed in Cox's original paper [1]. Many efforts have been made to increase the adaptability of hazard-based regression models using flexible functions for both the baseline hazard and the inclusion of time-dependent parameters, primarily using modified probability distributions [2][3][4][5].…”