Informative simultaneous confidence intervals for the fallback procedure

Abstract

The fallback procedure is an extension of the hierarchical test procedure relaxing the predefined hierarchical order. It can be applied for example in dose-finding studies. If interest is in extending the fallback procedure to simultaneous confidence intervals, one finds proposals in the literature, which have, however, the drawback that noninformative rejections may arise. A noninformative rejection means that the confidence interval of a rejected null hypothesis contains all parameters of the alternative and thus gives no useful information about the true value of the effect parameter. We present a modification of the fallback procedure with corresponding simultaneous confidence intervals that is informative in every case where a hypothesis is rejected. The main idea consists of splitting the level between the null hypotheses and a nested family of informative hypotheses constituting the alternative. The splitting weights depend continuously on the parameter. The new method is represented by a simple graph and can be easily implemented by an explicit algorithm. We give an example and compare our approach with an existing extension of the fallback procedure to simultaneous confidence intervals by simulations in the context of a dose-finding clinical trial. As a result, we see that the problem of noninformative rejections can be completely removed by the informative fallback procedure, while the involved power loss can be controlled by careful planning.

Simultaneous confidence intervals for comparisons of several multinomial samples

“…In situations where primary interest is in hypothesis tests alone, various approaches for stepwise corrections of p-values for multiple comparisons may have higher power than the single step approaches in this paper. However, this entails that corresponding simultaneous confidence intervals are difficult to interpret or to construct (e.g., Strassburger and Bretz, 2008;Schmidt and Brannath, 2015). Further methods for p-value adjustment ensuring FWER control have been explicitly customized for application to sparse discrete data: for applications to multivariate binary, two-sample multinomial, dichotomized multivariate data and permutation approaches without distributional assumptions, Westfall and Wolfinger (1997), Westfall and Troendle (2008) and Westfall (2011) show that these methods can lead to substantially increasing power for sparse discrete multivariate data.…”

Contribution to the discussion of “A critical evaluation of the current ‘p‐value controversy’”

“…It can also serve as basis for the construction of more informative (simultaneous) confidence intervals (for new developments see e.g. Brannath and Schmidt, ; Schmidt and Brannath, ). Hence, expulsing p ‐values from science would result in a scientific regress.…”