Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling

• 成果类型: Article
• 署名作者: Xu, Gongjun; Sit, Tony; Wang, Lan; Huang, Chiung-Yu
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Michigan System; University of Michigan; Chinese University of Hong Kong; Johns Hopkins University; Johns Hopkins Medicine
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1222286
• 发表日期: 2017
• 页码: 1571-1586
• 关键词: semiparametric transformation models; case-cohort analysis; nonparametric-estimation; median regression; EFFICIENCY; bootstrap; density

摘要

Biased sampling occurs frequently in economics, epidemiology, and medical studies either by design or due to data collecting mechanism. Failing to take into account the sampling bias usually leads to incorrect inference. We propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes, including but not limited to the length-biased sampling, the case-cohort design, and variants thereof. We establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level. We also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality. We further propose a new resampling method for inference, which differs from alternative procedures in that it does not require to repeatedly solve estimating equations. It is proved that the resampling method consistently estimates the asymptotic covariance matrix. The unified framework proposed in this article provides researchers and practitioners a convenient tool for analyzing data collected from various designs. Simulation studies and applications to real datasets are presented for illustration. Supplementary materials for this article are available online.