In Survival Analysis, the observed lifetimes often correspond to individuals for which the event occurs within a specific calendar time interval. With such interval sampling, the lifetimes are doubly truncated at values determined by the birth dates and the sampling interval. This double truncation may induce a systematic bias in estimation, so specific corrections are needed. A relevant target in Survival Analysis is the hazard rate function, which represents the instantaneous probability for the event of interest. In this work we introduce a flexible estimation approach for the hazard rate under double truncation. Specifically, a kernel smoother is considered, in both a fully nonparametric setting and a semiparametric setting in which the incidence process fits a given parametric model. Properties of the kernel smoothers are investigated both theoretically and through simulations. In particular, an asymptotic expression of the mean integrated squared error is derived, leading to a data-driven bandwidth for the estimators. The relevance of the semiparametric approach is emphasized, in that it is generally more accurate and, importantly, it avoids the potential issues of nonexistence or nonuniqueness of the fully nonparametric estimator. Applications to the age of diagnosis of Acute Coronary Syndrome (ACS) and AIDS incubation times are included.

翻译：在《生存分析》中,观察到的寿命期通常与在特定日历时间间隔内发生事件的个人相对应,在这种间隔抽样中,根据出生日期和抽样间隔确定的价值,寿命的寿命加倍缩短。这种双重缩短可能会在估计中引起系统的偏差,因此需要进行具体的纠正。在《生存分析》中,一个相关的目标是危险率函数,它代表了发生感兴趣的事件的瞬间概率。在这项工作中,我们采用了一种在双轨脱轨情况下危险率的灵活估计方法。具体地说,在完全非对称的设置和事件过程适合特定参数模型的半对称设置中,考虑到一个内螺旋滑动的考虑。从理论上和通过模拟对内核滑动器的属性进行调查。特别是,得出了平均综合正方差的不稳态表达方式,为估计者提供了一种数据驱动的带宽。在这项工作中,半对称方法的相关性得到了强调,因为这种方法一般更加准确,而且重要的是,它避免了在完全不与艾滋病综合的诊断期中可能存在的或非对准的问题。