Bayesian analysis of the Box-Cox transformation model based on left-truncated and right-censored data

Abstract

In this paper, we discuss the inference problem about the Box-Cox transformation model when one faces left-truncated and right-censored data, which often occur in studies, for example, involving the cross-sectional sampling scheme. It is well-known that the Box-Cox transformation model includes many commonly used models as special cases such as the proportional hazards model and the additive hazards model. For inference, a Bayesian estimation approach is proposed and in the method, the piecewise function is used to approximate the baseline hazards function. Also the conditional marginal prior, whose marginal part is free of any constraints, is employed to deal with many computational challenges caused by the constraints on the parameters, and a MCMC sampling procedure is developed. A simulation study is conducted to assess the finite sample performance of the proposed method and indicates that it works well for practical situations. We apply the approach to a set of data arising from a retirement center.

Keywords:

• Left-truncated and right-censored data
• additive hazards model
• proportional hazards model
• Bayesian
• MCMC sampling

2010 Mathematics Subject Classifications:

• 62N02
• 62N01

Acknowledgments

We would like to thank the editor for their significant guidance. Also, we would like to thank the anonymous reviewers for orienting us toward important references and for helping in improving this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of the first author was supported by grants from the National Natural Science Foundation of China (11671054). This work of the corresponding author was partly supported by the National Natural Science Foundation of China Grant No. 11901054 and the Mathematics Tianyuan Foundation of NSFC (11926340, 11926341).