Multi-Dimensional Testing to deal with Multiplicity in Clinical Trials

Ophthalmic clinical trials often involve multiple comparisons of different treatment regimes. For example, drug combinations are often compared to their components alone, as well as to the vehicle. Such studies require performing multiple tests of significance, and are prone to Type I error, defined as concluding the treatment is effective when in fact the treatment has no effect. Unless accounted for, the greater the number of statistical tests performed, the greater the Type I error. There are many ways to account for multiplicity. However, if the method is too conservative, the probability to detect the benefit of the treatment, power, will be decreased, and if the method is too liberal the probability to detect false positives will increase. Any method to address this potential problem should fit within the study design, maximize power and minimize false positives. The aim of this work is to compare the power of two methods, fixed sequence testing and multi-dimensional testing. In fixed sequence testing, hypotheses are prospectively ordered and each tested with full α-level, thus efficacy of subsequent hypotheses cannot be claimed if prior hypotheses were not found to be significant. To overcome this drawback, a multi-dimensional testing framework has been developed, where the decision-making process no longer exhibits a simple sequential structure, but is guided by a decision tree with multiple branches that correspond to individual treatment doses.