Likelihood approaches for the invariant density ratio model with biased-sampling data

• 成果类型: Article
• 署名作者: Shen, Yu; Ning, Jing; Qin, Jing
• 署名单位: University of Texas System; UTMD Anderson Cancer Center; National Institutes of Health (NIH) - USA; NIH National Institute of Allergy & Infectious Diseases (NIAID)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass008
• 发表日期: 2012
• 页码: 363378
• 关键词: semiparametric regression; Empirical Likelihood; survival

摘要

The full likelihood approach in statistical analysis is regarded as the most efficient means for estimation and inference. For complex length-biased failure time data, computational algorithms and theoretical properties are not readily available, especially when a likelihood function involves infinite-dimensional parameters. Relying on the invariance property of length-biased failure time data under the semiparametric density ratio model, we present two likelihood approaches for the estimation and assessment of the difference between two survival distributions. The most efficient maximum likelihood estimators are obtained by the em algorithm and profile likelihood. We also provide a simple numerical method for estimation and inference based on conditional likelihood, which can be generalized to k-arm settings. Unlike conventional survival data, the mean of the population failure times can be consistently estimated given right-censored length-biased data under mild regularity conditions. To check the semiparametric density ratio model assumption, we use a test statistic based on the area between two survival distributions. Simulation studies confirm that the full likelihood estimators are more efficient than the conditional likelihood estimators. We analyse an epidemiological study to illustrate the proposed methods.