Report：Some Recent Developments on Exact Inferences Using Binary Data in Two or Multi-stage Designs

Time：4:00pm  June 16,2017

Place：Room 104,Building of School of Statistics

Reporter： Weizhen Wang, received his B.S. and M.S. at Peking University in 1987 and 1990, respectively, and completed his Ph.D. in Statistics at Cornell University in 1995. After one-year visit at Purdue University, he joined Wright State University, and has been a Professor of Statistics since 2007. His research includes bioequivalence, exact parametric and nonparametric inference, saturated and adaptive designs, categorical data analysis, foundation of statistics, statistical computation, dose-response study and causal inference. His current primary interest is exact statistical inference and its implementation in R 

Abstract：When establish an effective treatment using binary data from a two-stage design, one-sided tests for a proportion p are employed. Researchers typically use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region. However, it is unclear whether the resultant test is of level, especially in adaptive designs. In this talk, we prove that this is true for a large family of tests in both nonadaptive and adaptive two-stage designs by showing that the power function of any test in the family is a nondecreasing function in p, then establish similar results for nonadaptive multi-stage designs with m(> 2) stages. In addition, we derive optimal lower one-sided 1-ａconfidence intervals for p. If time permits, we discuss exact tests for the bivariate case where both the response and the toxicity are considered.