Bayes analysis of the generalized gamma AFT models for left truncated and right censored data

Abstract

This article considers the Bayes analysis of generalized gamma accelerated failure time model and its two components Weibull and gamma when the given observations are left truncated and right censored. In order to perform the analysis, the paper proposes the use of an improved version of the Metropolis-Hastings algorithm, namely, the Metropolis-adjusted Langevin algorithm. Besides, the paper also checks the model compatibility and compares the considered models with its components using the Bayes factor computed on the basis of a recent methodology. A numerical illustration is provided based on a simulated as well as a real dataset. The real dataset consists of individuals infected with human immunodeficiency virus who are at the risk of acquired immunodeficiency syndrome and subsequent deaths. The numerical illustration is further extended to check the effect of different therapies including the highly active antiretroviral therapy on the lifetime of individuals.

Keywords:

• Generalized gamma distribution
• weibull distribution
• gamma distribution
• Langevin algorithm
• Metropolis-Hastings algorithm
• accelerated failure time model
• Bayes factor
• highly active antiretroviral therapy

Acknowledgments

The authors acknowledge their gratitude to the editor and the anonymous reviewers for providing their valuable and constructive suggestions that helped in improving the earlier version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.