A general approach to the predictability issue in survival analysis with applications

• 成果类型: Article
• 署名作者: Mammen, Enno; Nielsen, Jens Perch
• 署名单位: University of Mannheim; City St Georges, University of London
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm062
• 发表日期: 2007
• 页码: 873892
• 关键词: bias reduction method; counting-processes; hazard estimation; large sample; regression; MODEL; markers

摘要

Very often in survival analysis one has to study martingale integrals where the integrand is not predictable and where the counting process theory of martingales is not directly applicable, as for example in nonparametric and semiparametric applications where the integrand is based on a pilot estimate. We call this the predictability issue in survival analysis. The problem has been resolved by approximations of the integrand by predictable functions which have been justified by ad hoc procedures. We present a general approach to the solution of this problem. The usefulness of the approach is shown in three applications. In particular, we argue that earlier ad hoc procedures do not work in higher-dimensional smoothing problems in survival analysis.