Uniform Design For Combinations Of Drugs

Contemporary medical research indicates that complex diseases are often the results of mu-tations of multiple genes and proteins which can also be viewed as changes of multiple pathways and targets in the biological network.As the requirements of patients on health increasing,espe-cially for complex diseases,drug treatment by single target is typically unsatisfied for therapies.In contemporary clinical trials,combinations of drugs becomes more and more important and it has broad prospects for development and application in the treatment of disease process.Drugs administrated individually on the human body,will produce their own pharmacological effects.While multiple drug combinations may produce increased efficacy with reduced side effects.As a result,the studies of drug combinations have important medical value.This paper mainly fo-cuses on uniform experimental designs for two and three drug combination experiments.For a two drug combination experiment,the design region can be an arbitrary tetragon.In order to construct uniform designs over an arbitrary tetragon,we propose a novel method here,namely structure mapping between an arbitrary tetragon and the unit square[0,1]2.The transform is used to provide the random representation of a random vector on the design region,then gives an algorithm to gen-erate the uniform distribution on an arbitrary tetragon.For a three drug combination experiment,the design region can be an arbitrary triangular prism.Similar to the case of two drugs,a one-to-one transformation between an arbitrary triangular prism and the unit triangular prism can be constructed.Also,an algorithm which generates the uniform distribution on an arbitrary triangular prism is given.Finally,the proposed method is applied to the study of drug combination,which can be used to test the uniform distribution in the test area,and make the efficiency of the single drug additive model to achieve the best results.