A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data

ABSTRACT

Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are available online.

KEYWORDS:

• Bernstein polynomial
• Efficient estimation
• Frailty model
• Semiparametric transformation model
• Sieve estimation

Supplementary Materials

In the supplementary materials, Section 1 includes some additional simulation results and Section 2 includes the two lemmas used in the proof of Theorem 1, their proofs, and the more detailed proof of Theorem 3.

Acknowledgments

The authors thank the editor, Dr. Nicholas P. Jewell, the associate editor, and two reviewers for their many helpful and insightful comments and suggestions.

Funding

This research was supported in part by a grant from the National Science Foundation of China to Hu and a grant from the National Institutes of Health to Sun.