This work was motivated by observational studies in pregnancy with spontaneous abortion (SAB) as outcome. Clearly some women experience the SAB event but the rest do not. In addition, the data are left truncated due to the way pregnant women are recruited into these studies. For those women who do experience SAB, their exact event times are sometimes unknown. Finally, a small percentage of the women are lost to follow-up during their pregnancy. All these give rise to data that are left truncated, partly interval and right-censored, and with a clearly defined cured portion. We consider the non-mixture Cox regression cure rate model and adopt the semiparametric spline-based sieve maximum likelihood approach to analyze such data. Using modern empirical process theory we show that both the parametric and the nonparametric parts of the sieve estimator are consistent, and we establish the asymptotic normality for both parts. Simulation studies are conducted to establish the finite sample performance. Finally, we apply our method to a database of observational studies on spontaneous abortion.

中文翻译：

---

具有部分间隔删减和左截断数据的治愈模型下的半参数筛查最大似然估计，用于自然流产。

这项工作是受妊娠中以自然流产（SAB）为结果的观察性研究的推动。显然，有些女性会经历SAB事件，而其他女性则没有。此外，由于招募孕妇参加这些研究的方式，数据被截断了。对于确实经历过SAB的女性，她们的确切活动时间有时是未知的。最后，一小部分妇女在怀孕期间迷失了随访。所有这些都会导致数据被截短，部分间隔和右删失，并具有明确定义的固化部分。我们考虑非混合Cox回归治愈率模型，并采用基于半参数样条的筛网最大似然法来分析此类数据。使用现代经验过程理论，我们证明了筛估计器的参数部分和非参数部分都是一致的，并且我们为这两个部分建立了渐近正态性。进行仿真研究以建立有限的样本性能。最后，我们将我们的方法应用于自然流产的观察性研究数据库。