In clinical trials, outcomes of count data sometimes have excess zeros. When a test drug is compared to a control, zero-inflated data may be ignored or interest is taken only in the proportion of zero counts. By applying the two-part model, Lachenbruch (2001a) suggested a test statistic called the two-part statistic that combines the test statistics of the zero part and the non-zero part. The test for the zero part is the chi-square test. The test for the non-zero part may be a Wilcoxon test, a t-test, etc. This article proposes methods for calculating the sample size and power for the two-part statistic with zero-inflated Poisson data. We developed the methods of sample size and power for the two-part statistic using the Wilcoxon test adjusted for ties. The relationship between the non-zero part and zero-truncated Poisson distribution is also described. Furthermore, we examine the power of the two-part statistic, conventional methods, and the zero-inflated Poisson model.

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Multiple comparisons are attracting increasing attention in the evaluation of statistical evidence in clinical trials including at least one or any combination of (i) multiple hypotheses, (ii) repeated hypotheses testing at interim analyses, and (iii) mid-course design adaptations. In this paper, we discuss an efficient and sensible multiple testing procedure for two-stage adaptive treatment selection designs including structured hypotheses. Specifically, we extend the Holm procedure for serial gatekeeping structured hypotheses in adaptive clinical trials. The proposed approach is based on the idea of combining partition testing with the inverse normal combination test. A clinical trial example is used to illustrate the implementation of the proposed procedure.

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We discuss toxicity-based dose-finding methods for two-agent combinations in phase I oncology trials. We focus on the four dose-finding methods recently developed, the methods based on 1) a copula-type model, 2) a hierarchical Bayesian model, 3) continual reassessment method with partial ordering (POCRM), and 4) a shrinkage logistic model. We summarize the characteristic of each method and compare the performance among them through simulation studies. In the simulation studies, we examined recommendation rates (RDs) for both true maximum tolerated dose combinations (MTDCs) and unacceptable toxicity dose combinations (UTDCs) under 12 scenarios with 3 × 3, 4 × 4, 2 × 4, and 3 × 5 dose combination matrices. Simulation studies demonstrated that the POCRM and method using the shrinkage logistic model outperformed the other two methods in terms of recommending true MTDCs. The RDs for the UTDCs in the method using the shrinkage logistic model were lower than the other three methods.

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