Abstract
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.
Highlights
Survival analysis can be used to evaluate the effects of covariates on the time until a subject experiences the event of the study
The second aim in this paper, is to show, theoretically and by simulation, that using the modified Double Extreme Ranked Set Sampling (DERSS) improves the performance of Accelerated failure time (AFT) survival models and provides more efficient estimators of the hazard ratios compares with their counter parts, simple random sample (SRS), Ranked Set Sampling (RSS) and Extreme Ranked Set Sampling (ERSS)
AFT Model Using DERSSmin we derive the AFT models properties under DERSSmin and show how using DERSSmin improves the performance of the AFT Models
Summary
Survival analysis can be used to evaluate the effects of covariates on the time until a subject experiences the event of the study. Rochani et al (2018) demonstrated that the efficiency of multivariate regression estimator can be improved by using RSS The literature on this topic is extensive in the last 50 years, for example see (Al-Saleh and Samawi, 2000; Al-Saleh and Zheng, 2003; Samawi and Al-Saleh, 2002, Samawi et al, 2009, Samawi et al, 2018.) In addition, Samawi et al (2018) improved the performance of AFT survival model by using a modified ERSS, namely ERSSmin or ERSSmax. The second aim in this paper, is to show, theoretically and by simulation, that using the modified DERSS improves the performance of AFT survival models and provides more efficient estimators of the hazard ratios compares with their counter parts, simple random sample (SRS), RSS and ERSS. I =1 where β is the vector of parameters to be estimated in the presence of right censoring
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