Estimation of accelerated hazards models based on case K informatively interval-censored failure time data

Abstract

The accelerated hazards model is one of the most commonly used models for regression analysis of failure time data and this is especially the case when, for example, the hazard functions may have monotonicity property. Correspondingly a large literature has been established for its estimation or inference when right-censored data are observed. Although several methods have also been developed for its inference based on interval-censored data, they apply only to limited situations or rely on some assumptions such as independent censoring. In this paper, we consider the situation where one observes case K interval-censored data, the type of failure time data that occur most in, for example, medical research such as clinical trials or periodical follow-up studies. For inference, we propose a sieve borrow-strength method and in particular, it allows for informative censoring. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The method is applied to a set of real data set arising from an AIDS clinical trial.

Keywords:

• Accelerated hazards model
• informative observation process
• case K interval-censored data
• sieve maximum likelihood
• Bernstein polynomials

Acknowledgments

The authors wish to thank the Editor, the Associate Editor and two reviewers for their many comments and suggestions that greatly improved the paper.

Disclosure statement

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

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China (No. 12071176), China Postdoctoral Science Foundation (No. 2021M700536), Outstanding Youth Fund Project of Jilin Natural Science Foundation (No. 20230101371JC), and Science and Technology Developing Plan of Jilin Province (Nos. 20200201258JC, 20190902012TC, 20190304129YY).