R-Estimation with Right-Censored Data

TL;DR

This paper extends R-estimators to right-censored data in linear models, providing new theoretical representations, asymptotic results, and variance estimation methods for various score functions.

Contribution

It introduces a natural generalization of R-estimators for right-censored data, including new representations and asymptotic properties for bounded nonlinear-in-ranks score functions.

Findings

Exact representation of R-estimators as classes of estimating equations

Asymptotic properties and variance estimation methods established

Generalization of residual distribution function estimation techniques

Abstract

This paper considers the problem of directly generalizing the R-estimator under a linear model formulation with right-censored outcomes. We propose a natural generalization of the rank and corresponding estimating equation for the R-estimator in the case of the Wilcoxon (i.e., linear-in-ranks) score function, and show how it can respectively be exactly represented as members of the classes of estimating equations proposed in Ritov (1990) and Tsiatis (1990). We then establish analogous results for a large class of bounded nonlinear-in-ranks score functions. Asymptotics and variance estimation are obtained as straightforward consequences of these representation results. The self-consistent estimator of the residual distribution function, and the mid-cumulative distribution function (and, where needed, a generalization of it), play critical roles in these developments.