Background
The goal of a non-inferiority test is to determine whether the experimental treatment is statistically not inferior to the active control in a clinical trial. The three-arm clinical trial for non-inferiority test is validated by the recommendation from U.S. Food and Drug Administration (FDA). The three-arm trial, consisting of a placebo, reference, and an experimental treatment, shows the substantial superiority of the comparator over the placebo which is assessed prior to the comparison of reference and new experiment treatment [In the above literatures, the test statistic of a non-inferiority test in the three-arm trial is the sample mean difference between the experimental and placebo groups denominated by that between the reference and placebo groups in the three-arm trial. It’s well perceived that the sample mean is an unbiased estimator for population mean. Casting aside the unbiasedness, Searls [Typically, in the three-arm non-inferiority tests, variances of the effects of trials are assumed to be homogeneous. But if the variances are heterogeneous, the impacts of heteroskedasticity on the test results are evaluated less times. The heteroskedasticity is an issue frequently encountered in the field of econometrics, which results in the problem of biased variance estimates and hence distorts the results of hypothesis tests such as CHOW’s coefficient stability test, Student’s Tsui and Weerahandi [The article is organized as follows. The statistical problem of the non-inferiority hypothesis test with unknown CV in three-arm trial is formulated and the test procedures implemented in bootstrap method and Delta method are derived in the second part of the article. In addition, we propose the GPV-based test for the ratio of mean differences which explicitly incorporating the unknown CV to assess the non-inferiority in a three-arm trial in the second part of the article. Furthermore, the empirical size and power of the proposed testing procedures are examined in simulation studies under a variety of scenarios. The proposed method is applied to a numerical example in the literature. Conclusion and some remarks are drawn in finally.