Fast approximations of pseudo-observations in the context of right-censoring and interval-censoring

TL;DR

This paper introduces fast asymptotic formulas for computing pseudo-observations in right- and interval-censored data, improving efficiency and accuracy for survival analysis without relying on jackknife estimators.

Contribution

It develops novel asymptotic formulas for pseudo-observations that bypass jackknife computations, applicable to both right- and interval-censored data, with theoretical justification and practical validation.

Findings

Formulas are highly accurate even with small samples

Significant reduction in computation time compared to jackknife methods

Validated through simulations and real data applications

Abstract

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.