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Multiplicity issues arise prevalently in a variety of situations in clinical trials and statistical methods for multiple testing have gradually gained importance with the increasing number of complex clinical trial designs. In general, two types of multiple testing can be performed (Dmitrienko et al., 2009): union-intersection testing (UIT) and intersection-union testing (IUT). The UIT is of the interest in this dissertation. Thus, the familywise error rate (FWER) is required to be controlled in the strong sense. A number of methods have been developed for controlling the FWER, including single-step and stepwise procedures. In single-step approaches, such as the simple Bonferroni method, the rejection decision of a hypothesis does not depend on the decision of any other hypotheses. Single-step approaches can be improved in terms of power through stepwise approaches, while also controlling for the desired error rate. Besides, it is also possible to improve those procedures by a parametric approach. In the first project, we developed a new and powerful single-step progressive parametric multiple (SPPM) testing procedure for correlated normal test statistics. Through simulation studies, we demonstrate that SPPM improves power substantially when the correlation is moderate and/or the magnitude of eect sizes are similar. Group sequential designs (GSD) are clinical trials allowing interim looks with the possibility of early terminations due to ecacy, harm or futility, which can reduce the overall costs and timelines for the development of a new drug. However, repeated looks of data also have multiplicity issues and could inflate the type I error rate. The proper treatments to the error inflation have been discussed widely (Pocock, 1977), (O'Brien and Fleming, 1979), (Wang and Tsiatis, 1987), (Lan and DeMets, 1983). Most literature about GSD focuses on a single endpoint. GSD with multiple endpoints however, has also received considerable attention. The main focus of our second project is a GSD with multiple primary endpoints, in which the trial is to evaluate whether at least one of the endpoints is statistically signicant. In this study design, multiplicity issues arise from repeated interims and multiple endpoints. Therefore, the appropriate adjustments must be made to control the Type I error rate. Our second purpose here is to show that the combination of multiple endpoint and repeated interim analyses can lead to a more powerful design. Via the multivariate normal distribution, a method that allows for simultaneously consideration of interim analyses and all clinical endpoints was proposed. The new approach is derived from the closure principle, thus it can control type I error rate strongly. We evaluate the power under dierent scenarios and show that it compares favorably to other methods when correlation among endpoints is non-zero. In the group sequential design framework, another interesting topic is multiple arm multiple stage design (MAMS), where multiple arms are involved in the trial at the beginning with the flexibility about treatment selection or stopping decisions during the interim analyses. One of major hurdles of MAMS is the computational cost with the increasing number of arms and interim looks. Various designs were implemented to overcome this diculty (Thall et al., 1988; Schaid et al., 1990; Follmann et al., 1994; Stallard and Todd, 2003; Stallard and Friede, 2008; Magirr et al., 2012; Wason et al., 2017), but also control the FWER with the potential inflation from the multiple arm comparisons and multiple interim tests. Here, we consider a more flexible drop-the-loser design allowing the safety information in the treatment selection without a pre-specied dropping-arms mechanism and it still retains reasonable high power. The two dierent types of stopping boundaries are proposed for such a design. A sample size is also adjustable if the winner arm is dropped due to the safety considerations. |
