Statistical methods and designs for use in clinical studies based on small sample sizes
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Features common to early phase clinical trials include limited knowledge of the experimental treatment being evaluated, design components reflecting ethical considerations, and small to moderate sample sizes as a result of resource constraints. It is for these reasons that there exist many two-stage designs proposed in the literature for use in this context. The majority of these designs are for binary endpoints and are based on exact probability calculations, or are for continuous endpoints and rooted in asymptotic approximations to a null distribution. We present two-stage designs for continuous outcomes based on the Mann-Whitney test for distributional differences and the Jonckheere-Terpstra test for trend alternatives using Simon's minimax and optimal design criteria. In addition to describing the designs, we present tables of decision rules under a variety of assumed realities for use in trial planning. When testing for trends in 2 by K contingency tables, use of the asymptotic null distribution in conjunction with test statistics, such as that due to Cochran and Armitage, often result in an inflated Type I error rate, and exact approaches based on conditioning on the observed marginal totals prove to be frequently conservative. We explored the use of unconditional approaches to nuisance parameter elimination with the Cochran-Armitage test statistic, a modified nonparametric Baumgartner-Weiß-Schindler statistics due to Neuh ä user (2006), in addition to a newly developed statistic. The proposed procedures are seen to be preferable compared to the original tests due to their less conservative size and superior power properties. Future work will be reviewed.