We devise a new method to produce smooth estimates of baseline survival and hazard functions for incomplete data observed subject to interval‐censoring, that can in principle be viewed as being nonparametric. The key idea is to start from the nonparametric maximum likelihood estimate, and to then construct an empirical moment generating function for the underlying data generating mechanism, which is subsequently inverted via a saddlepoint approximation in order to obtain smooth distributional estimates. Unlike the typical spline‐based and other semiparametric methods that have thus far been devised for the same purpose, the proposed approach is unencumbered by the choice of tuning parameters. Simulation studies show that in terms of integrated squared error, the method is very close in performance to the parametric gold standard, and should generally be preferred over the well‐established spline‐based approach implemented in R package logspline. The methodology is illustrated on some publicly available real datasets, and its implications and limitations are discussed.

中文翻译：

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在区间删失下产生平稳生存和危险函数的经验鞍点近似方法。

我们设计了一种新的方法，可以对在间隔检查的情况下观察到的不完整数据进行基线生存率和危害函数的平滑估计，这在原则上可以视为非参数。关键思想是从非参数最大似然估计开始，然后为基础数据生成机制构造一个经验矩生成函数，随后通过鞍点近似对其进行倒置以获得平滑的分布估计。与迄今为止为相同目的设计的典型的基于样条曲线的方法和其他半参数方法不同，建议的方法不受调整参数的选择的束缚。仿真研究表明，就积分平方误差而言，该方法的性能非常接近参数金标准，logspline。在一些可公开获得的真实数据集上说明了该方法，并讨论了其含义和局限性。