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Clinical studies sometimes provide clustered data with censored failure times. A crucial factor of the randomized design that lessens selection bias is the random allocation rule. Given this, the weighted rank tests' p-values for stratified survival clustered sampling based on the random allocation rule are approximated using the double saddle-point approximation technique. For tests of significance and confidence intervals for the treatment effect, this approximation can be utilized. Through simulation experiments, the accuracy of the saddle-point approximation is examined by comparing saddle-point and normal approximations to the exact underlying permutation distribution. [ABSTRACT FROM AUTHOR]

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the effcacy of the proposed methods. [ABSTRACT FROM AUTHOR]

In clinical trials, Clustered data with censored failure times often arise from a litter-matched tumorigenesis experiment. Based on such data, the mutual and widely used class of two-sample tests is the weighted log-rank tests. A double saddle-point approximation is used to calculate the p-values of the null permutation distribution of these tests. This approximation is superior to the asymptotic normal approximation. This precision allows us to determine exact confidence intervals for the treatment impact. The findings reveal the efficiency of saddle-point approximation using two real clustered data sets. Extensive simulation studies are carried out to assess the performance of the saddle-point approximation. [ABSTRACT FROM AUTHOR]

Clustered data frequently occur in biomedical research fields and clinical trials. The log-rank tests are widely used for two-independent samples of clustered data tests. The randomized block design and truncated binomial design are used for forcing balance in clinical trials and reducing selection bias. In this paper, survival clustered data are randomized by generalized randomized block, and subsequently clustered data in each block are randomized by truncated binomial design. Consequently, the p-values of the null permutation distribution of log-rank tests for clustered data are approximated via the double saddlepoint approximation method. Comprehensive numerical studies are carried out to assess the accuracy of the saddlepoint approximation. This approximation has a great accuracy over the asymptotic normal approximation. [ABSTRACT FROM AUTHOR]

In this paper, order statistics from independent and non identically distributed random variables is used to obtain ordered ranked set sampling (ORSS). Bayesian inference of unknown parameters under a squared error loss function of the Pareto distribution is determined. We compute the minimum posterior expected loss (the posterior risk) of the derived estimates and compare them with those based on the corresponding simple random sample (SRS) to assess the efficiency of the obtained estimates. Two-sample Bayesian prediction for future observations is introduced by using SRS and ORSS for one- andm-cycle. A simulation study and real data are applied to show the proposed results. [ABSTRACT FROM AUTHOR]

In this article, maximum likelihood estimation and Bayes estimators are derived for linear exponential distribution based on one- and m-cycle extreme ranked set sampling and simple random sample. These estimators are compared via their biases and mean squared error. This is done with respect to both symmetric and asymmetric loss functions. A reallife data set and simulation study are used to illustrate our procedures. This unequivocally shows that, in all circumstances taken into consideration for this study, ranked set sampling is more effective than both extreme ranked set sampling and simple random sample. Over a high number of cycles, a significant improvement is shown. [ABSTRACT FROM AUTHOR]