Accurate Bootstrap Confidence Limits for the Cumulative Hazard and Survivor Functions under Random Censoring

原文摘要

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 BC a 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.

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