Sequential Bootstrap for More Powerful Similarity Test

Similarity test is commonly used to study the equivalence between an innovative biological product and a reference product that share similar pharmacokinetic or pharmacodynamic profiles. The goal of the similarity test aims to examine whether their absolute clinical difference is less than a pre-specified equivalence margin. Traditional test is based on the standardized mean comparison and needs to test the two null hypotheses, which correspond to either left- or right-margin, due to lack of prior knowledge which product is better. However, when there is sufficient evidence in the data to favor one product, a more powerful test can be constructed to test only one null hypothesis. In this work, we propose a sequential bootstrap procedure to construct a test statistic adaptively based on the null hypothesis supported in the sequentially resampled data. The final test statistic from our method is tailored to the true null hypothesis, so it leads to a higher power compared to the traditional test. We further derive the asymptotic behavior of the proposed test statistic and show that the asymptotic distribution refers to bandit distribution with a spike density at zero under the null and is a binormal distribution under the alternative. Our numerical study further confirms these theoretical results and demonstrates a large power gain over the traditional test.