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Simon's optimal two-stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints. With this approach, the second-stage sample size is fixed when the trial passes the first stage with sufficient activity. Adaptive designs, such as those due to Banerjee and Tsiatis (2006) and Englert and Kieser (2013), are flexible in the sense that the second-stage sample size depends on the response from the first stage, and these designs are often seen to reduce the expected sample size under the null hypothesis as compared with Simon's approach. An unappealing trait of the existing designs is that they are not associated with a second-stage sample size, which is a non-increasing function of the first-stage response rate. In this paper, an efficient intelligent process, the branch-and-bound algorithm, is used in extensively searching for the optimal adaptive design with the smallest expected sample size under the null, while the type I and II error rates are maintained and the aforementioned monotonicity characteristic is respected. The proposed optimal design is observed to have smaller expected sample sizes compared to Simon's optimal design, and the maximum total sample size of the proposed adaptive design is very close to that from Simon's method. The proposed optimal adaptive two-stage design is recommended for use in practice to improve the flexibility and efficiency of early phase therapeutic development. [ABSTRACT FROM AUTHOR]

Lloyd ( Aust. Nz. J. Stat., 50, 329-345, 2008) developed an exact testing approach to control for nuisance parameters, which was shown to be advantageous in testing for differences between two population proportions. We utilized this approach to obtain unconditional tests for trends in 2 × K contingency tables. We compare the unconditional procedure with other unconditional and conditional approaches based on the well-known Cochran-Armitage test statistic. We give an example to illustrate the approach, and provide a comparison between the methods with regards to type I error and power. The proposed procedure is preferable because it is less conservative and has superior power properties. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Testing involving the intra-class kappa coefficient is commonly performed in order to assess agreement involving categorical ratings. A number of procedures have been proposed, which make use of the limiting null distribution as the sample size goes to infinity in order to compute the observed significance. As with many tests based on asymptotic null distributions, these tests are associated with problematic type I error control for selected sample sizes and points in the parameter space. We propose and study a collection of exact testing approaches for both the one-sample and K-sample scenarios. For the one-sample case, p-values are obtained using the exact distribution of the test statistic conditional on a sufficient statistic. In addition, unconditional approaches are considered on the basis of maximization across the nuisance parameter space. Numerical evaluation reveals advantages with the exact unconditional procedures. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]