Local partial likelihood estimation in proportional hazards regression

• 成果类型: Article
• 署名作者: Chen, Songnian; Zhou, Lingzhi
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001299
• 发表日期: 2007
• 页码: 888-916
• 关键词: model; EFFICIENCY

摘要

Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661-1690] considered the estimation of the risk function psi(x) in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function Psi(x(2)) - Psi(x(1)) for any location normalization point x(1). The main novelty in our approach is that we select observations in shrinking neighborhoods of both x(1) and x(2) when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661-1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out.