In the context of right-censored and interval-censored data we develop asymptotic formulas to compute pseudo-observations for the survival function and the Restricted Mean Survival Time (RMST). Those formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right-censored data, Von Mises expansions of the Kaplan-Meier estimator are used to derive the pseudo-observations. For interval censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo-observations is derived involving the Hessian matrix and the score vector of the density. The formula is illustrated on the piecewise-constant hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated on Monte-Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for large dataset.

翻译：在右检查和间隔审查数据方面,我们开发了用于计算生存功能和限制平均生存时间的假观察的零星公式。这些公式以原始估计值为基础,并不涉及计算千斤顶估计值。关于右检查数据,使用卡普兰-米耶估计值的Von Mises扩展法来得出伪观察。关于间隔审查数据,正在研究生存功能的参数模型的一般类别。模拟模型的默认表示法涉及赫斯矩阵和密度的分数矢量。该公式用笔一致危害模型来说明。拟议的估计值非常精确,即使是小样本尺寸的,如蒙特-卡洛模拟和真实数据所示。我们还研究计算时间的增益,与原始的杰克尼法方法相比,这对大数据设置可能很重要。