Bayesian analysis of Box-Cox transformation model for multi-state progression-free survival data - Wang, Chunjie; Qi, Shunxin; Jiang, Jingjing (Journal of the Korean Statistical Society, 2025)
In this study, we address the inference problem associated with the Box-Cox transformation model when dealing with multi-state progression-free survival data. It is well-established that multi-state censoring data is frequently encountered in various medical scenarios, encompassing aspects such as progression times and mortality during multivariate events. Many existing methodologies for regression analysis are extended and developed under the assumption of a non-informative censoring mechanism. We employ a comprehensive class of semiparametric transformation models that encompass both proportional hazards and additional hazards models, specifically tailored to handle multi-state data where a relationship exists between different states. Our approach adopts Bayesian estimation for inference, utilizing a piecewise function to approximate the baseline hazard function. Furthermore, we develop a Bayesian framework with the Markov Chain Monte Carlo algorithm to estimate the unknown parameters and incorporate nonparametric procedures. To validate the effectiveness of our proposed methodology, we conduct simulations. And by incorporating frailty terms into the joint model, we propose the model in simulation 2 for comparison. Additionally, we apply our approach to analyze a dataset concerning Lung cancer cases.