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Double Extreme Ranked Set Sampling (DERSS) was first introduced by Samawi (2002) as a modification to the well-known Ranked Set Sampling (RSS) and Extreme Ranked Set Sampling (ERSS). In this article, we provide a modification to DERSS scheme with ranking based on an easy-to-rank baseline auxiliary variable known to be associated with survival time. We show that using the modified DERSS improves the performance of the Accelerated failure time (AFT) survival model and provides a more efficient estimator of the hazard ratio than that based on their counter parts simple random sample (SRS), RSS and ERSS, which results in reducing the sample size required and hence the total cost of the study. Our theoretical and simulation studies show the superiority of using the modified DERSS for AFT survival models compared with using SRS, RSS and ERSS. A numerical example based on Worcester Heart Attack Study is presented to illustrate the implementation of the DERSS.
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