Ranked Set Sampling in Survival Analysis

TL;DR

This paper develops a comprehensive survival analysis framework for ranked set sampling (RSS), including estimators, tests, and variance measures, addressing imperfect ranking and censoring, with theoretical validation and practical implementation.

Contribution

It introduces a unified survival analysis methodology for balanced RSS designs, extending classical tools to handle imperfect ranking and censoring with theoretical and simulation validation.

Findings

Efficiency gains over simple random sampling demonstrated

New variance estimators for censored RSS data proposed

Framework applicable to various survival tests and functionals

Abstract

Ranked set sampling (RSS) is a cost-efficient study design that uses inexpensive baseline ranking to select a more informative subset of individuals for full measurement. While RSS is well known to improve precision over simple random sampling (SRS) for uncensored outcomes, survival analysis under RSS has largely been limited to estimation of the Kaplan-Meier survival curve under random censoring. Consequently, many standard tools routinely used with SRS data, including log-rank and weighted log-rank tests, restricted mean survival time summaries, and window-based mean life measures, are not yet fully developed for RSS settings, particularly when ranking is imperfect and censoring is present. This work develops a unified survival analysis framework for balanced RSS designs that preserves efficiency gains while providing the inferential tools expected in applied practice. We formalize Kaplan-Meier and Nelson-Aalen estimators for right-censored data under both perfect and concomitant-based imperfect ranking and establish their large-sample properties using martingale and empirical process methods adapted to the rank-wise RSS structure. Rank-aware Greenwood-type variance estimators are proposed, and efficiency relative to SRS is evaluated through simulation studies varying set size, number of cycles, censoring proportion, and ranking quality. The framework is further extended to log-rank and Fleming-Harrington weighted tests, as well as restricted and window mean life functionals with asymptotic variance formulas and two-sample comparisons. An implementation plan with real-data illustrations is provided to facilitate practical use.