Sample size adaptation designs and efficiency comparison with group sequential designs

This study is to give a systematic account of sample size adaptation designs (SSADs) and to provide direct proof of the efficiency advantage of general SSADs over group sequential designs (GSDs) from a different perspective. For this purpose, a class of sample size mapping functions to define SSADs is introduced. Under the two-stage adaptive clinical trial setting, theorems are developed to describe the properties of SSADs. Sufficient conditions are derived and used to prove analytically that SSADs based on the weighted combination test can be uniformly more efficient than GSDs in a range of likely values of the true treatment difference $\delta$ . As shown in various scenarios, given a GSD, a fully adaptive SSAD can be obtained that has sufficient statistical power similar to that of the GSD but has a smaller average sample size for all $\delta$ in the range. The associated sample size savings can be substantial. A practical design example and suggestions on the steps to find efficient SSADs are also provided.