AI 中文总结
本文针对右删失下固定时间点的两条生存函数比较问题，将单样本Greenwood方差调整纳入delta法两样本应用，扩展BPCP融合区间为中p版本，经模拟发现BPCP融合可保证全场景覆盖率，中p版本覆盖率最接近名义，还提供了bpcp R包函数。
AI 中文摘要
针对存在右删失时固定时间点的两条生存曲线比较问题，标准方法采用渐近方法，基于两个Kaplan-Meier估计量，搭配Greenwood方差估计量及利用delta法进行变换。由于Kaplan-Meier估计值为0或1、样本量较小或删失程度较重，相关估计量的置信区间可能失效或出现覆盖率不足的情况。尽管已有学者针对单个样本提出了Greenwood方差的调整方案，但这些调整尚未被纳入delta法的两样本应用中；本文不仅将这类调整纳入该应用，还针对Kaplan-Meier估计值为0或1的情况提供了修正方案。现有一种名为beta乘积置信程序（BPCP）融合（melding）的非渐近替代方法，无论样本量大小，其置信区间至少具有名义覆盖率。无删失时，该问题简化为比较两个独立二项分布，BPCP融合方法得到的p值与Fisher精确检验的p值等价，且能为治疗比较估计量提供相容的置信区间；不过，这种融合可能非常保守。本文将BPCP融合区间扩展为包含中p版本，该版本旨在实现更接近名义的覆盖率，虽无法保证所有情况的覆盖率。本文主要通过数值方法或模拟研究这些现有方法及对它们的微小修正，结果显示仅BPCP融合方法能在所有研究场景中保证覆盖率，其中p版本通常具有最接近名义的覆盖率。本文在bpcp R包中提供了对应的R函数。
英文摘要
For comparing two survival curves at a fixed timepoint with right censoring, a standard method uses asymptotic methods on two Kaplan-Meier estimators with Greenwood variance estimators and transformations using the delta method. Confidence intervals on associated estimands can either breakdown or undercover due to Kaplan-Meier estimates of zero or one, small sample sizes, or heavy censoring. Although others have proposed adjustments to the Greenwood variance for a single sample, these adjustments have not been incorporated into the two-sample application of the delta method and we do that here as well as provide modifications when Kaplan-Meier estimates are zero or one. An alternative non-asymptotic existing method called melding on the beta product confidence procedure (BPCP) appears to have at least nominal coverage regardless of the sample size. Without censoring the problem reduces to comparing two independent binomials and melding on the BPCP gives p-values equivalent to Fisher's exact test p-values and further gives compatible confidence intervals for treatment comparison estimands; however, the melding can be very conservative. In this paper, we expand the melding on the BPCP intervals to include mid-p versions, which are designed to achieve coverage closer to nominal without guaranteeing coverage for all cases. We study these existing methods and our minor modifications of them primarily by numerical methods or simulation. Results suggest only the melding on the BPCP can guarantee coverage in all studied scenarios, and the mid-p version most often has closest to nominal coverage. We provide R functions in the bpcp R package.
Comments68 pages, 47 figures (main paper first 20 pages, the rest is supplementary material)
