Regression analysis of case II interval-censored data with auxiliary covariates

Abstract

The effect of some exposures on a survival time is often of interest in many epidemiological and biomedical studies. Due to budget constraints or technical difficulties, some exposures of interest may not be measured for the whole study cohort but only available in a subset of them. While the exposure of interest is not fully observed, there could exist an auxiliary covariate related to it that is cheaper or more convenient to observe. Given such situations, statistical methods that take advantage of existing auxiliary information about an expensive exposure variable are desirable in practice. Such methods should improve the study efficiency and increase the statistical power for a definite quantities of assays. In this paper, we discusses regression analysis of case II interval-censored data with continuous auxiliary covariates. An estimator of regression parameters was proposed by maximizing the estimated partial likelihood function which makes use of the available auxiliary information. Asymptotic properties of the resulting estimator are established. An extensive simulation study was conducted to assess the finite sample performance of the proposed method. The proposed method was also illustrated through an application to a HIV-1 infection example.

Keywords:

• Auxiliary covariates
• interval-censored data
• partial likelihood function
• validation sample

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62N02

Acknowledgments

The authors gratefully acknowledge many helpful and useful comments and suggestions of the Associate Editor and the two reviewers that led to a great improvement of the paper.

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China (11471252 and 11571263), the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University) of Ministry of Education, the National Statistical Science Research Project of China (2018380).