Responder analyses are often recommended by regulatory guidance or clinical communities to support a primary analysis of a continuous endpoint of interest. When there is uncertainty about the optimal cutoff value for response, multiple responder cutoffs may be proposed, resulting in multiple tests and potential inflation of type I error. In those cases, the minimum p-value (minP) approach has been proposed in the literature allowing adequate control of type I error. However, the proposed approach is primarily based on bootstrap or permutation, which can be computationally intensive especially when studying the operating characteristics.
We develop the asymptotic minP approach for responder analysis. In particular, we derive the asymptotic distribution of the minP test statistic and give analytical form of the critical values of minP under null distribution and the power function under the alternative. In addition, we derive closed-form power functions of minP that takes into account missing data. We conduct numerical studies to compare its operating characteristic with the permutation approach.