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. Theoretical results that justify the use of pseudo-observations in regression are also derived. 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：针对右删失和区间删失数据，我们开发了生存函数及限制性平均生存时间（RMST）伪观测值的渐近计算公式。这些公式基于原始估计量，无需计算刀切估计量。对于右删失数据，利用Kaplan-Meier估计量的Von Mises展开来推导伪观测值；对于区间删失数据，则研究了一类参数化生存函数模型，通过Hessian矩阵和得分向量导出伪观测值的渐近表示。我们还推导了支持伪观测值在回归中应用的理论依据。以分段常数风险模型为例展示了RMST伪观测值的计算公式。蒙特卡洛模拟和实际数据验证表明，即使在小样本情形下，所提近似方法仍具有极高的准确性。相较于原始刀切法，本方法在大数据集上的计算效率提升尤为显著。