The Study Of Three-arm Non-inferiority Clinical Trial With Placebo Arm And Its Two-stage Sample Size Adjustment

The non-inferiority clinical trials with active control have attracted researchers'interests since many diseases have already had effective treatments following the development in medicine. Without comparing with placebo, the efficacy of the active control can't be determined contemporarily, so the two-arm non-inferiority trial gives rise to problems, known as assay sensitivity and constancy of active control. Thus, non-inferiority studies need to fulfill high quality requirements due to external validation. If ethically justifiable, it may be advisable to use an additional placebo arm for internal validation instead. A three-arm non-inferiority trial including placebo can not only test whether the experimental treatment is superior to placebo but also test whether experimental treatment is non-inferior to active control. However, traditionally this kind of three-arm trial would include pairwise testing of the arms and the design is more complicated than normal non-inferiority design, thus, it needs a proper evaluate method. Sample size estimation is one of the most important issues at the clinical trial design stage. Nevertheless, researchers are not sure of all parameters in the initial design and hope to modify unreasonable sample size before the end of trial to avoid a failure trial caused by lack of sample size or an unnecessary expenditure of resources caused by recruiting more subjects than need. Currently, the issue of sample size adjustment (SSA) is hotly discussed in two sample design but few in three-arm design.This article discussed and compared two design methods of three-arm non-inferiority clinical trials and discussed a two stage sample size recalculation procedure using Monte Carlo simulation when active control's effect size or variance was not the same as initial estimation in three-arm non-inferiority trials.The main tasks and results of the study are listed as following.1. We made comparison of two kinds of design method for three-arm non-inferiority trials, which were traditional test method based on fixed non-inferiority margin and Pigeot's integrated method in which non-inferiority margin is a fraction of active control's effect size. A true sample was used to demonstrate how to estimate sample size and determine margin. Then the powers of Pigeot's test method and traditional test method were compared by Monte Carlo simulation when the sample sizes are the same. The results indicated that Pigeot's method had higher power because it utilized information of all samples, thus, saved trial cost.2. A comparison of the typeâ… error and power achieved when recalculating sample size based on active control's effect size with no recalculation was made by Monte Carlo simulation in this essay. Besides, we investigated the feasibility of performing assay sensitivity test after the first stage and its impact on the power. The results showed that compared to not performing sample size recalculation, the recalculation procedure achieved power much closer to the nominal and also can preserve the typeâ… error under optimal sample size allocation. Meanwhile, performing assay sensitivity test after the first stage is feasible and meaningful.3. The power of sample size recalculation procedure was investigated using variance both under blinded and under unblinded internal pilot study (IPS). And the results indicated that it was convenient to adjust sample size in blinded IPS, but it would overestimate sample size needed thus leading to waste of resources. Unblinded SSA is recommended accordingly4. The typeâ… error and power of SSA procedure based on variance and active control's effect size was studied. And the results indicated that it was necessary to have a conservative attitude when we estimated active control's effect size at the initial because we could adjust bias when active control's effect size was underestimated while it couldn't maintain typeâ… error or achieve the desired power when active control's effect size was overestimated at the initial.The achievements of this study consist in the following three points: Firstly, we proposed a two stage SSA procedure of three-arm non-inferiority trials based on active control's effect size and/or variance. Secondly, through simulations, we conformed the feasibility and necessity of performing assay sensitivity test after the first stage. Finally, we compared the power of sample size recalculation procedure using variance under blinded IPS with unblinded IPS and gave a suggestion about which SSA method should be taken.