title: Exact p-values for Simon's two-stage designs in clinical trials.
abstract: In a one-sided hypothesis testing problem in clinical trials, the monotonic condition of a tail probability function is fundamentally important to guarantee that the actual type I and II error rates occur at the boundary of their associated parameter spaces. Otherwise, one has to search for the actual rates over the complete parameter space, which could be very computationally intensive. This important property has been extensively studied in traditional one-stage study settings (e.g., non-inferiority or superiority between two binomial proportions), but there is very limited research for this property in a two-stage design setting, e.g., Simon's two-stage design. In this note, we theoretically prove that the tail probability is an increasing function of the parameter in Simon's two-stage design. This proof not only provides theoretical justification that p-value occurs at the boundary of the parameter space, but also helps to reduce the computational intensity for study design search.
authors.affiliation: Department of Environmental and Occupational Health, Epidemiology and Biostatistics Program, School of Community Health Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154.
authors.forename: Guogen
authors.initials: G
authors.lastname: Shan
authors.affiliation: Zhejiang Gongshang University, Hangzhou, Zhejiang, China, 310018.
authors.forename: Hua
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Zhejiang Gongshang University, Hangzhou, Zhejiang, China, 310018.
authors.forename: Tao
authors.initials: T
authors.lastname: Jiang
authors.affiliation: Department of Environmental and Occupational Health, Epidemiology and Biostatistics Program, School of Community Health Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154.
authors.forename: Hanna
authors.initials: H
authors.lastname: Peterson
authors.affiliation: Department of Environmental and Occupational Health, Epidemiology and Biostatistics Program, School of Community Health Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154.
authors.forename: Daniel
authors.initials: D
authors.lastname: Young
authors.affiliation: Department of Biostatistics, University at Buffalo, Buffalo, NY 14214.
authors.forename: Changxing
authors.initials: C
authors.lastname: Ma
keywords: Boundary; Mathematical induction; Monotonic condition; Simon’s two-stage design