A Bayesian transformation model for informative partly interval-censored data with covariates subject to measurement...

Linear transformation models are one of the commonly used models for regression analysis of failure time data due to their flexibility. Although the existing literature provides many methods for fitting transformation models with fixed covariates and non-informative censoring, extending these methods to scenarios with covariates subject to measurement error and informative censoring remains challenging. As pointed out in the literature, failure to account for covariate measurement errors or informative censoring may lead to estimation bias or misleading conclusions. Therefore, in this article, we consider a more complicated and general situation where both covariate measurement errors and informative censoring, or more especially informative partly interval censoring, exist. For this problem, we propose a new joint model for regression analysis of such data and present a general Bayesian estimation procedure that can handle both non-informative censoring and informative censoring, using I-splines to approximate unknown functions. To implement this method, we propose a flexible and stable Markov chain Monte Carlo (MCMC) algorithm through a four-stage data augmentation. This method is simple and easy to use. We conduct extensive simulation studies to compare the naive method with the Bayesian method, verifying the effectiveness of the Bayesian method. We also present a practical application to illustrate the proposed method.