Large sample properties of two tests for independent joint action of two drugs
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.
scientific article; zbMATH DE number 4215234