Abstract
BackgroundA two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Selection of the non-inferiority margin and establishment of assay sensitivity are two major issues in the design, analysis and interpretation for two-arm non-inferiority trials. Alternatively, a three-arm non-inferiority clinical trial including a placebo is usually conducted to assess the assay sensitivity and internal validity of a trial. Recently, some large-sample approaches have been developed to assess the non-inferiority of a new treatment based on the three-arm trial design. However, these methods behave badly with small sample sizes in the three arms. This manuscript aims to develop some reliable small-sample methods to test three-arm non-inferiority.MethodsSaddlepoint approximation, exact and approximate unconditional, and bootstrap-resampling methods are developed to calculate p-values of the Wald-type, score and likelihood ratio tests. Simulation studies are conducted to evaluate their performance in terms of type I error rate and power.ResultsOur empirical results show that the saddlepoint approximation method generally behaves better than the asymptotic method based on the Wald-type test statistic. For small sample sizes, approximate unconditional and bootstrap-resampling methods based on the score test statistic perform better in the sense that their corresponding type I error rates are generally closer to the prespecified nominal level than those of other test procedures.ConclusionsBoth approximate unconditional and bootstrap-resampling test procedures based on the score test statistic are generally recommended for three-arm non-inferiority trials with binary outcomes.
Highlights
A two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns
Simulation study To compare the performance of Asymptotic method (AM), Saddlepoint approximation method (SAM), Exact unconditional method (EUM), Approximate unconditional method (AUM) and Bootstrap-resampling method (BTM) together with test statistics TW, TR and TL under the balanced and unbalanced designs, Figure 1 presents boxplots of their corresponding type I error rates for n = 30 and 60, and λP:λR:λT =1:1:1, 1:2:2 and
The medians of the type I error rates based on AUM and BTM are closer to the prespecified nominal level α = 0.05 than those based on the other three p-value calculation methods for all three test statistics under consideration
Summary
A two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Some large-sample approaches have been developed to assess the non-inferiority of a new treatment based on the three-arm trial design. These methods behave badly with small sample sizes in the three arms. The first issue is the whether the new treatment works at all and how it measures up to accepted therapy In this case, a three-arm non-inferiority clinical trail including the experimental treatment, an active reference treatment and a placebo is usually conducted to assess assay sensitivity and internal validation of a trail [6]. Three-arm trials are recommended in the guidelines of the ICH (The International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use) and EMEA/CPMP (European Medicines Agency/Committee for Proprietary Medical Products) as a useful approach to the assessment of assay sensitivity and internal validation (e.g., see [7])
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