Abstract
Various approaches including hypothesis test and confidence interval (CI) construction have been proposed to assess non-inferiority and assay sensitivity via a known fraction or pre-specified margin in three-arm trials with continuous or discrete endpoints. However, there is little work done on the construction of the non-inferiority margin from historical data and simultaneous generalized CIs (SGCIs) in a three-arm trial with the normally distributed endpoints. Based on the generalized fiducial method and the square-and-add method, we propose two simultaneous CIs for assessing non-inferiority and assay sensitivity in a three-arm trial. For comparison, we also consider the Wald-type Bonferroni simultaneous CI and parametric bootstrap simultaneous CI. An algorithm for evaluating the optimal sample size for attaining the pre-specified power is given. Simulation studies are conducted to investigate the performance of the proposed CIs in terms of their empirical coverage probabilities. An example taken from the mildly asthmatic study is illustrated using the proposed simultaneous CIs. Empirical results show that the proposed generalized fiducial method and the square-and-add method behave better than other two compared CIs.
Highlights
In modern clinical trials, it is extremely interesting to demonstrate whether a new treatment that is less toxic, less expensive or easier to administer is not inferior to an expensive and technical pathological reference treatment by more than a pre-specified margin
Empirical results demonstrated that the GF-SCI and HG-SCI perform better than the WB-SCI and PB-SCI
WB-SCI methods are liberal regardless of the balanced and unbalanced designs in that their empirical coverage probability (ECP) are less than the pre-specified confidence level 95%, but the PB-SCI method behaves better than the WB-SCI method in that the ECPs for the former are closer to the pre-specified confidence level than those for the latter; (iii) when the sample size is large (e.g., n = 150 and 300), the PB-SCI method has the same performance as the GF-SCI and HG-SCI methods, but the WB-SCI method is liberal
Summary
It is extremely interesting to demonstrate whether a new treatment that is less toxic, less expensive or easier to administer is not inferior to an expensive and technical pathological reference treatment by more than a pre-specified margin. This is usually called a two-arm non-inferiority trial that does not include a placebo. If ethically acceptable and practically feasible, it is generally recognized that three-arm non-inferiority trials including a placebo can surmount the difficulties mentioned above [4] Two-arm non-inferiority trials have some shortcomings, such as the selection of the non-inferiority margin and the assessment of assay sensitivity (i.e., the ability to differentiate between an effective treatment and a less effective or ineffective treatment).
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