Nonparametric estimation of the survival function for either incident or prevalent cohort failure time data, exclusively, has been well studied in the literature; the Kaplan‐Meier (KM) estimator is routinely used for right‐censored incident cohort failure time data, whereas a modified form of the KM estimator, sometimes referred to as the Tsai–Jewell–Wang (TJW) estimator, is the default estimator used for prevalent cohort data with follow‐up. Often, failure time data comprise observations from a combination of incident and prevalent cohorts. In this note, we justify the use of the TJW estimator for a combined sample of incident and prevalent cohort data with follow‐up. We suggest how the TJW estimator forms the basis for density estimation and hypothesis testing problems, when incident and prevalent cohorts are combined.

中文翻译：

---

关于标准非参数最大似然估计量对组合事件和流行队列数据的适用性的注释

文献中已经很好地研究了事件或流行队列失效时间数据的生存函数的非参数估计。Kaplan-Meier（KM）估计器通常用于右删失的事件队列失败时间数据，而KM估计器的修改形式（有时称为Tsai-Jewell-Wang（TJW）估计器）是默认使用的估计器追踪人群数据。故障时间数据通常包括来自突发事件和流行队列的组合的观察结果。在本说明中，我们证明使用TJW估算器对事件和流行队列数据的合并样本进行跟踪。我们建议结合事件和流行队列时，TJW估计器如何构成密度估计和假设检验问题的基础。