Large sample properties of two tests for independent joint action of two drugs
type: Item
instance of: scholarly article
title: Large sample properties of two tests for independent joint action of two drugs
zbMATH Open document ID: 0734.62102
author: Wherly P. Hoffman
author: Sue E. Leurgans
published in: The Annals of Statistics
publication date: 1990-01-01T00:00:00Z
review text: In the study of the joint action of drugs, various methods of modeling the action have been proposed. The joint action of two drugs is considered biologically independent if the joint action is dissimilar and noninteractive. The biological independence of two drugs cannot be identified from the probability of response as a function of the dose combination. The testing of independent action in this paper is not testing the equivalent mathematical formulations of independent joint action, but a set of inequalities implied by the independent joint action. If \(p_ 1\) and \(p_ 2\) are the probabilities of response to dose \(z_ 1\) and \(z_ 2\) of drugs A and B, respectively, if \(p_ 3\) is the probability of response to the joint application of both and if there are no spontaneous responses, then independent action implies the following inequalities: \[ Max(p_ 1,p_ 2)\leq p_ 3\leq \min (p_ 1+p_ 2,1). \] The hypothesis that the probabilities do satisfy these inequalities can be tested using the likelihood ratio test or using the bootstrap test. The asymptotic distribution of the bootstrap test is derived and the asymptotic distribution of the likelihood ratio test is also obtained.
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 4215234
zbMATH Keywords: drug interaction
zbMATH Keywords: independent joint action
zbMATH Keywords: joint action of drugs
zbMATH Keywords: biological independence of two drugs
zbMATH Keywords: dose combination
zbMATH Keywords: inequalities
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: bootstrap test
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176347870
OpenAlex ID: W1977099476
DOI: 10.1214/AOS/1176347870
description: scientific article; zbMATH DE number 4215234