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We consider a non-inferiority test conducted in the three-arm trials with coefficient of variations (CV) in sample means. A procedure for this non-inferiority test is proposed based on the generalized p-value (GPV) based method under normality assumption and heteroskedasticity. We demonstrated that first, the GPV-based method outperforms the comparable alternative, the Delta method in terms of empirical sizes and powers. Second, under GPV-based method, when the population mean of groups in the trial is estimated by the sample mean with CV, the empirical sizes control the significance level better than when CV is not included, especially when the ratio of the variance of the reference group to that of the experimental group and the ratio of the variance of the placebo group to that of the experimental group are not too small and that the sample size is small. Third, when the CV is included in the sample mean, the empirical powers are always higher, regardless of the sample size and methods. Additionally, when the data violates the normality assumption, it is found that the proposed GPV-based method in conjunction with CV appear to be highly acceptable through simulation results. Finally, the proposed method is illustrated with two data examples. [ABSTRACT FROM AUTHOR]

For the sign testing problem about the normal variances, we develop the heuristic testing procedure based on the concept of generalized test variable and generalized p-value. A detailed simulation study is conducted to empirically investigate the performance of the proposed method. Through the simulation study, especially in small sample sizes, the proposed test not only adequately controls empirical size at the nominal level, but also uniformly more powerful than likelihood ratio test, Gutmann's test, Li and Sinha's test and Liu and Chan's test, showing that the proposed method can be recommended in practice. The proposed method is illustrated with the published data. [ABSTRACT FROM AUTHOR]

Non-inferiority tests are often measured for the diagnostic accuracy in medical research. The area under the receiver operating characteristic (ROC) curve is a familiar diagnostic measure for the overall diagnostic accuracy. Nevertheless, since it may not differentiate the diverse shapes of the ROC curves with different diagnostic significance, the partial area under the ROC (PAUROC) curve, another summary measure emerges for such diagnostic processes that require the false-positive rate to be in the clinically interested range. Traditionally, to estimate the PAUROC, the golden standard (GS) test on the true disease status is required. Nevertheless, the GS test may sometimes be infeasible. Besides, in a lot of research fields such as the epidemiology field, the true disease status of the patients may not be known or available. Under the normality assumption on diagnostic test results, based on the expectation-maximization algorithm in combination with the bootstrap method, we propose the heuristic method to construct a non-inferiority test for the difference in the paired PAUROCs without the GS test. Through the simulation study, although the proposed method might provide a liberal test, as a whole, the empirical size of the proposed method sufficiently controls the size at the significance level, and the empirical power of the proposed method in the absence of the GS is as good as that of the non-inferiority in the presence of the GS. The proposed method is illustrated with the published data. [ABSTRACT FROM PUBLISHER]