Sample size recalculation in three-arm non-inferiority trials

Date
2020
DOI
Authors
Lei, Lanyu
Version
OA Version
Citation
Abstract
The three-arm non-inferiority trials include an experimental treatment arm, an active comparator arm and a placebo arm. Such a design allows evaluating the assay sensitivity by testing the superiority of active comparator over placebo, and is a preferred choice when the constancy of the treatment effect is questionable under the current medical setting, or when there is no consensus on the magnitude of a clinically relevant treatment effect. This dissertation, investigating sample size recalculation in active- and placebo-controlled trials at the interim, is composed of three chapters. The first chapter summarizes for the three-arm non-inferiority design, including hypotheses formulations, testing procedures and a few important features. We also compare statistical power between the two forms of the non-inferiority test: fixed margin test and effect preservation test. In the second chapter, the commonly used group sequential designs and sample size recalculation methods are reviewed, and two methods (Method I and Method II) are applied to the three-arm non-inferiority trials with normally distributed endpoint. Method I which was proposed in previous publications, does not require unblinding the experimental treatment effect. However, it has a limitation that the sample sizes of the three arms must meet specific ratios in order to control Type I error. This thesis extends this method to a broader range of sample size allocations. Method II is based on the concept of promising zone of the conditional power. It is a modified group sequential design and recalculate the sample size only when the interim result is promising. The overall type I error control, power and efficiency of the two methods (I vs. II) are compared under various scenarios through simulations. It is found that the method I provide a substantial power gain when the initial active comparator effect is over-estimated at the design stage. However, it cannot handle the uncertainties in the experimental treatment effect. In contrast, the Method II controls type I error at all investigated sample size allocations. It provides moderate power gain if the preserved effect is over-estimated. Once the interim result is promising the recalculated sample size can increase the final rejection probability considerably. When the experimental treatment effect is under-estimated at the design stage, the average sample size can reduce dramatically compared to fixed sample design due to the high probability of rejection at the interim stage. The third chapter investigates how the two methods perform for the binary endpoint. The formula of conditional power for binary outcome is derived. The statistical properties including the variance estimation, the type I error control and actual power are investigated through simulations.
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