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

  • Authors:

  • Guo-Liang Tian;Hong-Bin Fang;Ming Tan;Hong Qin;Man-Lai Tang

  • Affiliations:

  • Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China;Division of Biostatistics, University of Maryland Greenebaum Cancer Center, MSTF Suite 261, 10 South Pine Street, Baltimore, MD 21201, USA;Division of Biostatistics, University of Maryland Greenebaum Cancer Center, MSTF Suite 261, 10 South Pine Street, Baltimore, MD 21201, USA;School of Mathematics and Statistics, Huazhong Normal University, 152 Luoyu Road, Wuhan City, Hubei 430079, PR China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PR China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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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 R^2. 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 R^3. In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space R^n. 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.