Abstract
The paper investigates the class of two-parameter log-logistic dose-response bioassay models in the binomial set-up. The dose is defined by the potency adjusted mixing proportions of two similar compounds. The aim is to investigate the D- and Ds- optimal mixture designs for estimating the full set of parameters or only the potency for a best guess of the parameter values. An indication has been given for finding the optimal design for the estimation of the mixture at which the probability of success attains a given value.
Highlights
Non-linear models find wide application in many areas of research, like agriculture, pharmaceutical, chemical, biomedical, pharmacokinetics, toxicology and clinical research etc., as they are found to be more reasonable and accurate than linear models for defining the processes
In the existing literature on designs for parameter estimation in dose response models with two similar compounds or drugs, the amounts of the compounds have been taken as the covariates
The response function is assumed to be two-parameter log-logistic, where the mixing proportions of the compounds are taken as the covariates
Summary
Non-linear models find wide application in many areas of research, like agriculture, pharmaceutical, chemical, biomedical, pharmacokinetics, toxicology and clinical research etc., as they are found to be more reasonable and accurate than linear models for defining the processes. The non-linear dose-response models are in particular very useful in agricultural and medical research to approximate the relationship between the response and the concentration of a compound/drug. In the existing literature on designs for parameter estimation in dose response models with two similar compounds or drugs, the amounts of the compounds have been taken as the covariates. We consider modeling the response as a function of the potency adjusted mixing proportions of two similar compounds. As sigmoidal models are extensively used in practice, we use the two parameter log-logistic (LL2) dose response function for binary data. We indicate how to find the locally optimal design for the estimation of the mixing proportions at which the probability of success attains a given value in the absence of interaction effect
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