This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

中文翻译：

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基于部分秩排序集样本的生存分析中的改进的Kaplan-Meier估计器。

这项研究提出了一种新颖的方法，使用部分排序集（PROS）抽样设计中的排序观察结果，研究了随机审查时间下生存概率的非参数估计，并将其用于血液系统疾病研究。PROS采样设计在医学，社会科学和生态学中有许多应用，在这些领域中，精确测量采样单位非常昂贵；但是，可以通过使用判断等级或可用的伴随信息来订购采样单位。通用估计方法不适用于样本来自基于等级的抽样设计的情况，因为抽样单位不满足相同分布的假设。我们在PROS采样设计下得出Kaplan-Meier（KM）估计量的渐近分布。最后，我们通过一些模拟研究比较了建议估算器的性能，并将建议的方法应用于实际数据集。结果表明，在基于秩的抽样设计下，拟议的估计量优于简单随机样本（SRS）中的估计量。