Informative Simultaneous Confidence Intervals in Hierarchical Testing

2015

Biometrical J

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.

Informative simultaneous confidence intervals for the fallback procedure

2015

Biometrical J

Simultaneous confidence intervals for ratios with application to the gold standard design with more than one experimental treatment

2019

Statistics in Medicine

Considering a study design with two experimental treatments, a reference treatment and a placebo, we extend a previous approach considering the ratios of effects to a procedure for analyzing multiple ratios. The technical framework for constructing tests and compatible simultaneous confidence intervals is set in a general manner. Besides a single step procedure and its extension to a stepdown procedure, also, an informative stepwise procedure in the spirit of our previous work is developed. The latter is especially interesting, because noninferiority studies require informative confidence intervals to infer more information than just noninferiority at the prespecified margin. Results from a simulation study for the three methods are shown. We also argue that an extension to more than two experimental treatments is straightforward.

Single‐stage, three‐arm, adaptive test strategies for non‐inferiority trials with an unstable reference

Scharpenberg

2022

Statistics in Medicine

For indications where only unstable reference treatments are available and use of placebo is ethically justified, three-arm "gold standard" designs with an experimental, reference and placebo arm are recommended for non-inferiority trials.In such designs, the demonstration of efficacy of the reference or experimental treatment is a requirement. They have the disadvantage that only little can be concluded from the trial if the reference fails to be efficacious. To overcome this, we investigate novel single-stage, adaptive test strategies where non-inferiority is tested only if the reference shows sufficient efficacy and otherwise 𝛿-superiority of the experimental treatment over placebo is tested. With a properly chosen superiority margin, 𝛿-superiority indirectly shows non-inferiority. We optimize the sample size for several decision rules and find that the natural, data driven test strategy, which tests non-inferiority if the reference's efficacy test is significant, leads to the smallest overall and placebo sample sizes. We proof that under specific constraints on the sample sizes, this procedure controls the family-wise error rate. All optimal sample sizes are found to meet this constraint. We finally show how to account for a relevant placebo drop-out rate in an efficient way and apply the new test strategy to a real life data set.