Effects of Censoring on the Validity of Confidence Intervals
删失对置信区间有效性的影响AI 解读 ↓
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删失对置信区间有效性的影响
- 研究问题
- 当真实生存分布偏离指数分布时，增加删失是否会改善基于指数最大似然估计构造的生存分位数置信区间覆盖率？
- 方法与思路
- 作者研究分位数估计的一致渐近正态条件，推导局部替代下的覆盖率，并分析极端删失、最不利偏离及反例。
- 材料陈述的贡献
- 摘要称偏离与删失分布无关时，特定极限下覆盖率趋于指数模型的预期水平；偏离依赖删失时则存在反例。
- 阅读关注点
- 应核对一致渐近正态性的条件、局部替代与删失极限如何配合，以及理论覆盖率和删失Weibull模拟的比较。
- 阅读边界
- 索引摘要未注明稿件版本，不能推断刊本变化；所述改善依赖特定渐近设定，不能据此认为增加删失普遍提高推断有效性。
原文摘要
This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds asymptotically in the case of complete censoring, first conditions are found under which the exponential maximum likelihood estimate of a percentile is asymptotically normal uniformly in F, where F is an arbitrary survival distribution function. Then, the asymptotic coverage probability of the exponential-based interval is found for a percentile of a local alternative to the exponential distribution. If the censoring distribution converges weakly to point mass at 0, and if the departure from exponentiality is independent of the censoring distribution, then the asymptotic coverage probability converges to the expected coverage probability under exponentiality. The least favorable direction of departure from exponentiality is found, and it is shown by counterexample that in the limiting case of complete censoring, if the departure from exponentiality depends on the censoring distribution as it does in the least favorable case, then the asymptotic coverage probability does not necessarily converge to the expected coverage probability under exponentiality. Finally, the results of this article are applied to uniformly censored Weibull alternatives, and the asymptotic-theory coverage probabilities are compared with simulated coverage probabilities.