Accurate bootstrap confidence limits for the cumulative hazard and survivor functions under random censoring

• 成果类型: Article
• 署名作者: Strawderman, RL; Wells, MT
• 署名单位: University of Michigan System; University of Michigan; Cornell University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2965406
• 发表日期: 1997
• 页码: 1356-1374
• 关键词: edgeworth expansion; asymptotic expansions; random censorship; large sample; intervals; statistics; martingales; estimator; MODEL; time

摘要

In clinical trials and other settings, confidence intervals for survival probabilities at a fixed point in time are often required. Typically, such intervals are constructed on the cumulative hazard scale; the quantiles required for computing these intervals are generally obtained using a first-order normal theory approximation. The appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect. We demonstrate that significant improvement is possible for randomly censored data using the nonparametric bootstrap. In particular, using Edgeworth expansion, it is shown that the percentile-t and BCa bootstrap methodologies based on the studentized Nelson-Aalen estimator yield second-order-correct confidence limits for the cumulative hazard function at a fixed time point. An explicit formula for the correction term of the Edgeworth expansion is found. Easy-to-compute estimators for the components of the correction term are also found and lead to simple analytical corrections that avoid the need for resampling. Numerical results based on simulated data are given to support the theoretical results. The bootstrap is used to obtain confidence intervals for 1-year and median survival in a published Eastern Cooperative Oncology Group study of Taxol and non-small-cell lung cancer.