Uniform distributions in a class of convex polyhedrons with applications to drug combination studies

Guo-Liang Tian, Hong-Bin Fang, Ming Tan, Hong Qin and Man-Lai Tang

Journal of Multivariate Analysis, 2009, vol. 100, issue 8, 1854-1865

Abstract: Motivated by experimental designs for drug combination studies, in this paper, we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two-dimensional Euclidean space . The key idea is to construct a one-to-one transformation between an arbitrary tetragon and the unit square [0,1]2. This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon. An algorithm is proposed for generating a uniform distribution in an arbitrary triangular prism in . In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space . In particular, SRs for uniform distributions in regions with order restrictions are presented. We apply the proposed method to the experimental design for a drug combination study.

Keywords: Uniform; design; Uniform; distribution; Tetragon; Stochastic; representation; Convex; polyhedron; Drug; combination; study (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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