On the Kaplan–Meier estimator based on ranked set samples

Abstract

When quantification of all sampling units is expensive but a set of units can be ranked, without formal measurement, ranked set sampling (RSS) is a cost-efficient alternate to simple random sampling (SRS). In this paper, we study the Kaplan–Meier estimator of survival probability based on RSS under random censoring time setup, and propose nonparametric estimators of the population mean. We present a simulation study to compare the performance of the suggested estimators. It turns out that RSS design can yield a substantial improvement in efficiency over the SRS design. Additionally, we apply the proposed methods to a real data set from an environmental study.

Keywords:

• ranked set sampling
• censored data
• Kaplan–Meier

Acknowledgements

The authors would like to thank the referee for comments and suggestions which significantly improved the paper. This research has been supported by grants from the Spanish Ministerio de Economía y Competitividad. E. Strzalkowska-Kominiak acknowledges support from Juan de la Cierva scholarship and MTM2011-22392.