Anderson J R, Bernstein L, Pike M C
Biometrics. 1982 Jun;38(2):407-16.
For survival probabilities with censored data, Rothman (1978, Journal of Chronic Diseases 31, 557-560) has recommended the use of quadratic confidence limits based on the assumption that the product of the 'effective' sample size at time t and the life-table estimate of the survival probability past time t follows a binomial distribution. This paper shows that the proposed confidence limits are asymptotically correct for continuous survival data. These intervals, as well as those based on the arcsine transformation, the logit transformation and the log(--log) transformation, are compared by simulation to those based on Greenwood's formula--the usual method of interval estimation in life-table analysis. With large amounts of data, the alternatives to the Greenwood method all produce acceptable intervals. On the basis of overall performance, the intervals suggested by Rothman are preferred for smaller samples. Any of these methods may be used to generate confidence sets for the median survival time or for any other quantile.
对于含有删失数据的生存概率，罗斯曼（1978年，《慢性病杂志》第31卷，557 - 560页）建议使用基于以下假设的二次置信限：时间t处的“有效”样本量与时间t之后生存概率的生命表估计值之积服从二项分布。本文表明，对于连续生存数据，所提出的置信限在渐近意义上是正确的。通过模拟将这些区间以及基于反正弦变换、对数it变换和对数（-对数）变换的区间与基于格林伍德公式的区间进行比较——格林伍德公式是生命表分析中常用的区间估计方法。对于大量数据，格林伍德方法的替代方法都能产生可接受的区间。基于整体性能，对于较小样本，罗斯曼建议的区间更受青睐。这些方法中的任何一种都可用于生成中位生存时间或任何其他分位数的置信集。
