Abstract
The mean residual lifetime (MRL) of a unit in a population at a given time t, is the average remaining lifetime among those population units still alive at the time t. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained “free of charge”, at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show that the introduced technique can provide more accurate estimates for the average remaining lifetime of patients with breast cancer.
Award Identifier / Grant number: 1402620049
Acknowledgments
The authors thank an anonymous reviewer for helpful suggestions that have improved the paper. Ehsan Zamanzade's research was carried out in IPM Isfahan branch and was in part supported by a grant from IPM, Iran (No. 1402620049).
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Research ethics: Not applicable.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The authors state no conflict of interest.
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Research funding: Ehsan Zamanzade's research was carried out in IPM Isfahan branch and was in part supported by a grant from IPM, Iran (No. 1402620049).
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Data availability: The data that support the findings of this study are obtained from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) (https://seer.cancer.gov/) with permission reference number 12395-Nov2017.
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Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/ijb-2023-0051).
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